Properties

Label 143.2.h.c.27.2
Level $143$
Weight $2$
Character 143.27
Analytic conductor $1.142$
Analytic rank $0$
Dimension $28$
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] = [143,2,Mod(14,143)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(143, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([8, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("143.14");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 143 = 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 143.h (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.14186074890\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 27.2
Character \(\chi\) \(=\) 143.27
Dual form 143.2.h.c.53.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.545888 - 1.68007i) q^{2} +(-2.73308 - 1.98570i) q^{3} +(-0.906607 + 0.658689i) q^{4} +(0.676170 - 2.08104i) q^{5} +(-1.84416 + 5.67573i) q^{6} +(-0.0983727 + 0.0714719i) q^{7} +(-1.25676 - 0.913087i) q^{8} +(2.59967 + 8.00096i) q^{9} +O(q^{10})\) \(q+(-0.545888 - 1.68007i) q^{2} +(-2.73308 - 1.98570i) q^{3} +(-0.906607 + 0.658689i) q^{4} +(0.676170 - 2.08104i) q^{5} +(-1.84416 + 5.67573i) q^{6} +(-0.0983727 + 0.0714719i) q^{7} +(-1.25676 - 0.913087i) q^{8} +(2.59967 + 8.00096i) q^{9} -3.86540 q^{10} +(3.23459 - 0.733108i) q^{11} +3.78579 q^{12} +(0.309017 + 0.951057i) q^{13} +(0.173778 + 0.126257i) q^{14} +(-5.98034 + 4.34497i) q^{15} +(-1.54059 + 4.74144i) q^{16} +(0.715201 - 2.20116i) q^{17} +(12.0230 - 8.73526i) q^{18} +(-4.64768 - 3.37674i) q^{19} +(0.757736 + 2.33207i) q^{20} +0.410782 q^{21} +(-2.99739 - 5.03414i) q^{22} -4.16613 q^{23} +(1.62170 + 4.99108i) q^{24} +(0.171570 + 0.124653i) q^{25} +(1.42915 - 1.03834i) q^{26} +(5.65056 - 17.3906i) q^{27} +(0.0421076 - 0.129594i) q^{28} +(4.88799 - 3.55134i) q^{29} +(10.5644 + 7.67552i) q^{30} +(-0.411140 - 1.26536i) q^{31} +5.70007 q^{32} +(-10.2961 - 4.41927i) q^{33} -4.08853 q^{34} +(0.0822192 + 0.253045i) q^{35} +(-7.62702 - 5.54136i) q^{36} +(0.408587 - 0.296856i) q^{37} +(-3.13604 + 9.65175i) q^{38} +(1.04394 - 3.21293i) q^{39} +(-2.74995 + 1.99796i) q^{40} +(-3.50036 - 2.54316i) q^{41} +(-0.224241 - 0.690142i) q^{42} -6.11640 q^{43} +(-2.44961 + 2.79523i) q^{44} +18.4081 q^{45} +(2.27424 + 6.99938i) q^{46} +(4.75718 + 3.45630i) q^{47} +(13.6256 - 9.89959i) q^{48} +(-2.15855 + 6.64333i) q^{49} +(0.115768 - 0.356296i) q^{50} +(-6.32555 + 4.59578i) q^{51} +(-0.906607 - 0.658689i) q^{52} +(0.460825 + 1.41828i) q^{53} -32.3021 q^{54} +(0.661507 - 7.22701i) q^{55} +0.188891 q^{56} +(5.99729 + 18.4578i) q^{57} +(-8.63479 - 6.27354i) q^{58} +(5.35440 - 3.89020i) q^{59} +(2.55984 - 7.87837i) q^{60} +(-0.107334 + 0.330340i) q^{61} +(-1.90145 + 1.38149i) q^{62} +(-0.827581 - 0.601273i) q^{63} +(-0.0304230 - 0.0936323i) q^{64} +2.18813 q^{65} +(-1.80416 + 19.7106i) q^{66} +13.8719 q^{67} +(0.801475 + 2.46669i) q^{68} +(11.3863 + 8.27267i) q^{69} +(0.380250 - 0.276268i) q^{70} +(1.67708 - 5.16151i) q^{71} +(4.03842 - 12.4290i) q^{72} +(3.85926 - 2.80392i) q^{73} +(-0.721782 - 0.524405i) q^{74} +(-0.221391 - 0.681372i) q^{75} +6.43784 q^{76} +(-0.265798 + 0.303300i) q^{77} -5.96782 q^{78} +(-2.80132 - 8.62158i) q^{79} +(8.82543 + 6.41205i) q^{80} +(-29.5579 + 21.4751i) q^{81} +(-2.36188 + 7.26913i) q^{82} +(-1.17806 + 3.62568i) q^{83} +(-0.372418 + 0.270577i) q^{84} +(-4.09711 - 2.97672i) q^{85} +(3.33887 + 10.2760i) q^{86} -20.4111 q^{87} +(-4.73448 - 2.03212i) q^{88} +5.23054 q^{89} +(-10.0488 - 30.9269i) q^{90} +(-0.0983727 - 0.0714719i) q^{91} +(3.77704 - 2.74418i) q^{92} +(-1.38894 + 4.27472i) q^{93} +(3.20993 - 9.87915i) q^{94} +(-10.1697 + 7.38875i) q^{95} +(-15.5787 - 11.3186i) q^{96} +(-2.91446 - 8.96978i) q^{97} +12.3396 q^{98} +(14.2744 + 23.9740i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - 3 q^{2} - 7 q^{3} - 5 q^{4} - 7 q^{5} - 4 q^{6} - 7 q^{7} + q^{8} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q - 3 q^{2} - 7 q^{3} - 5 q^{4} - 7 q^{5} - 4 q^{6} - 7 q^{7} + q^{8} - 6 q^{9} - 24 q^{10} - 5 q^{11} + 38 q^{12} - 7 q^{13} - 7 q^{14} + 8 q^{15} - 19 q^{16} + 7 q^{17} + 5 q^{18} + 5 q^{19} + 9 q^{20} - 33 q^{22} + 50 q^{23} - 7 q^{24} - 34 q^{25} + 2 q^{26} - 19 q^{27} + 30 q^{28} + 8 q^{29} - 6 q^{30} + 17 q^{31} + 24 q^{32} - 26 q^{33} + 26 q^{34} - 4 q^{35} - 27 q^{36} + 17 q^{37} - 51 q^{38} - 2 q^{39} + 39 q^{40} - 23 q^{41} + 80 q^{42} - 32 q^{43} + q^{44} + 78 q^{45} - 31 q^{46} - 29 q^{47} + 52 q^{48} - 52 q^{49} + 6 q^{50} + 7 q^{51} - 5 q^{52} - 16 q^{53} - 42 q^{54} - 5 q^{55} + 34 q^{56} - 7 q^{57} - 13 q^{58} - 11 q^{59} - 74 q^{60} + 37 q^{61} + 23 q^{62} - 38 q^{63} + 67 q^{64} + 18 q^{65} - 65 q^{66} + 58 q^{67} - 68 q^{68} - 28 q^{69} + 44 q^{70} - 47 q^{71} + 10 q^{72} + 44 q^{73} - 46 q^{74} + 17 q^{75} + 6 q^{76} + 21 q^{77} + 26 q^{78} + 51 q^{79} + 23 q^{80} - 14 q^{81} - 47 q^{82} - 13 q^{83} - 107 q^{84} - q^{85} + 38 q^{86} - 12 q^{87} + 9 q^{88} + 38 q^{89} - 74 q^{90} - 7 q^{91} - 41 q^{92} - 51 q^{93} - 5 q^{94} + 47 q^{95} - 71 q^{96} - 20 q^{97} + 162 q^{98} + 60 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/143\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.545888 1.68007i −0.386001 1.18799i −0.935752 0.352660i \(-0.885277\pi\)
0.549751 0.835329i \(-0.314723\pi\)
\(3\) −2.73308 1.98570i −1.57794 1.14644i −0.919005 0.394246i \(-0.871006\pi\)
−0.658938 0.752197i \(-0.728994\pi\)
\(4\) −0.906607 + 0.658689i −0.453304 + 0.329344i
\(5\) 0.676170 2.08104i 0.302393 0.930669i −0.678245 0.734836i \(-0.737259\pi\)
0.980637 0.195833i \(-0.0627409\pi\)
\(6\) −1.84416 + 5.67573i −0.752874 + 2.31711i
\(7\) −0.0983727 + 0.0714719i −0.0371814 + 0.0270139i −0.606221 0.795296i \(-0.707315\pi\)
0.569039 + 0.822310i \(0.307315\pi\)
\(8\) −1.25676 0.913087i −0.444331 0.322825i
\(9\) 2.59967 + 8.00096i 0.866557 + 2.66699i
\(10\) −3.86540 −1.22235
\(11\) 3.23459 0.733108i 0.975265 0.221040i
\(12\) 3.78579 1.09286
\(13\) 0.309017 + 0.951057i 0.0857059 + 0.263776i
\(14\) 0.173778 + 0.126257i 0.0464442 + 0.0337437i
\(15\) −5.98034 + 4.34497i −1.54412 + 1.12187i
\(16\) −1.54059 + 4.74144i −0.385147 + 1.18536i
\(17\) 0.715201 2.20116i 0.173462 0.533861i −0.826098 0.563526i \(-0.809444\pi\)
0.999560 + 0.0296658i \(0.00944430\pi\)
\(18\) 12.0230 8.73526i 2.83386 2.05892i
\(19\) −4.64768 3.37674i −1.06625 0.774677i −0.0910164 0.995849i \(-0.529012\pi\)
−0.975235 + 0.221173i \(0.929012\pi\)
\(20\) 0.757736 + 2.33207i 0.169435 + 0.521467i
\(21\) 0.410782 0.0896399
\(22\) −2.99739 5.03414i −0.639047 1.07328i
\(23\) −4.16613 −0.868697 −0.434349 0.900745i \(-0.643021\pi\)
−0.434349 + 0.900745i \(0.643021\pi\)
\(24\) 1.62170 + 4.99108i 0.331028 + 1.01880i
\(25\) 0.171570 + 0.124653i 0.0343140 + 0.0249306i
\(26\) 1.42915 1.03834i 0.280280 0.203635i
\(27\) 5.65056 17.3906i 1.08745 3.34683i
\(28\) 0.0421076 0.129594i 0.00795759 0.0244910i
\(29\) 4.88799 3.55134i 0.907678 0.659466i −0.0327488 0.999464i \(-0.510426\pi\)
0.940426 + 0.339997i \(0.110426\pi\)
\(30\) 10.5644 + 7.67552i 1.92880 + 1.40135i
\(31\) −0.411140 1.26536i −0.0738429 0.227265i 0.907322 0.420436i \(-0.138123\pi\)
−0.981165 + 0.193171i \(0.938123\pi\)
\(32\) 5.70007 1.00764
\(33\) −10.2961 4.41927i −1.79232 0.769296i
\(34\) −4.08853 −0.701177
\(35\) 0.0822192 + 0.253045i 0.0138976 + 0.0427723i
\(36\) −7.62702 5.54136i −1.27117 0.923560i
\(37\) 0.408587 0.296856i 0.0671713 0.0488028i −0.553693 0.832721i \(-0.686782\pi\)
0.620864 + 0.783918i \(0.286782\pi\)
\(38\) −3.13604 + 9.65175i −0.508733 + 1.56572i
\(39\) 1.04394 3.21293i 0.167165 0.514480i
\(40\) −2.74995 + 1.99796i −0.434805 + 0.315905i
\(41\) −3.50036 2.54316i −0.546664 0.397175i 0.279890 0.960032i \(-0.409702\pi\)
−0.826554 + 0.562857i \(0.809702\pi\)
\(42\) −0.224241 0.690142i −0.0346011 0.106491i
\(43\) −6.11640 −0.932742 −0.466371 0.884589i \(-0.654439\pi\)
−0.466371 + 0.884589i \(0.654439\pi\)
\(44\) −2.44961 + 2.79523i −0.369293 + 0.421396i
\(45\) 18.4081 2.74412
\(46\) 2.27424 + 6.99938i 0.335318 + 1.03200i
\(47\) 4.75718 + 3.45630i 0.693907 + 0.504153i 0.877942 0.478767i \(-0.158916\pi\)
−0.184035 + 0.982920i \(0.558916\pi\)
\(48\) 13.6256 9.89959i 1.96669 1.42888i
\(49\) −2.15855 + 6.64333i −0.308364 + 0.949048i
\(50\) 0.115768 0.356296i 0.0163720 0.0503879i
\(51\) −6.32555 + 4.59578i −0.885754 + 0.643538i
\(52\) −0.906607 0.658689i −0.125724 0.0913437i
\(53\) 0.460825 + 1.41828i 0.0632992 + 0.194815i 0.977705 0.209984i \(-0.0673413\pi\)
−0.914405 + 0.404799i \(0.867341\pi\)
\(54\) −32.3021 −4.39575
\(55\) 0.661507 7.22701i 0.0891975 0.974489i
\(56\) 0.188891 0.0252416
\(57\) 5.99729 + 18.4578i 0.794361 + 2.44479i
\(58\) −8.63479 6.27354i −1.13380 0.823756i
\(59\) 5.35440 3.89020i 0.697084 0.506461i −0.181897 0.983318i \(-0.558224\pi\)
0.878981 + 0.476856i \(0.158224\pi\)
\(60\) 2.55984 7.87837i 0.330473 1.01709i
\(61\) −0.107334 + 0.330340i −0.0137427 + 0.0422957i −0.957693 0.287793i \(-0.907079\pi\)
0.943950 + 0.330088i \(0.107079\pi\)
\(62\) −1.90145 + 1.38149i −0.241485 + 0.175449i
\(63\) −0.827581 0.601273i −0.104265 0.0757532i
\(64\) −0.0304230 0.0936323i −0.00380287 0.0117040i
\(65\) 2.18813 0.271405
\(66\) −1.80416 + 19.7106i −0.222077 + 2.42621i
\(67\) 13.8719 1.69472 0.847360 0.531018i \(-0.178190\pi\)
0.847360 + 0.531018i \(0.178190\pi\)
\(68\) 0.801475 + 2.46669i 0.0971931 + 0.299130i
\(69\) 11.3863 + 8.27267i 1.37076 + 0.995912i
\(70\) 0.380250 0.276268i 0.0454486 0.0330203i
\(71\) 1.67708 5.16151i 0.199032 0.612559i −0.800873 0.598834i \(-0.795631\pi\)
0.999906 0.0137252i \(-0.00436900\pi\)
\(72\) 4.03842 12.4290i 0.475933 1.46477i
\(73\) 3.85926 2.80392i 0.451693 0.328174i −0.338571 0.940941i \(-0.609944\pi\)
0.790264 + 0.612767i \(0.209944\pi\)
\(74\) −0.721782 0.524405i −0.0839054 0.0609608i
\(75\) −0.221391 0.681372i −0.0255641 0.0786781i
\(76\) 6.43784 0.738471
\(77\) −0.265798 + 0.303300i −0.0302905 + 0.0345642i
\(78\) −5.96782 −0.675722
\(79\) −2.80132 8.62158i −0.315173 0.970003i −0.975683 0.219186i \(-0.929660\pi\)
0.660510 0.750817i \(-0.270340\pi\)
\(80\) 8.82543 + 6.41205i 0.986713 + 0.716889i
\(81\) −29.5579 + 21.4751i −3.28421 + 2.38612i
\(82\) −2.36188 + 7.26913i −0.260826 + 0.802741i
\(83\) −1.17806 + 3.62568i −0.129308 + 0.397971i −0.994661 0.103192i \(-0.967094\pi\)
0.865353 + 0.501163i \(0.167094\pi\)
\(84\) −0.372418 + 0.270577i −0.0406341 + 0.0295224i
\(85\) −4.09711 2.97672i −0.444394 0.322871i
\(86\) 3.33887 + 10.2760i 0.360039 + 1.10809i
\(87\) −20.4111 −2.18830
\(88\) −4.73448 2.03212i −0.504697 0.216625i
\(89\) 5.23054 0.554436 0.277218 0.960807i \(-0.410588\pi\)
0.277218 + 0.960807i \(0.410588\pi\)
\(90\) −10.0488 30.9269i −1.05923 3.25999i
\(91\) −0.0983727 0.0714719i −0.0103123 0.00749229i
\(92\) 3.77704 2.74418i 0.393784 0.286101i
\(93\) −1.38894 + 4.27472i −0.144026 + 0.443268i
\(94\) 3.20993 9.87915i 0.331079 1.01896i
\(95\) −10.1697 + 7.38875i −1.04339 + 0.758070i
\(96\) −15.5787 11.3186i −1.59000 1.15520i
\(97\) −2.91446 8.96978i −0.295918 0.910743i −0.982911 0.184079i \(-0.941070\pi\)
0.686993 0.726664i \(-0.258930\pi\)
\(98\) 12.3396 1.24649
\(99\) 14.2744 + 23.9740i 1.43463 + 2.40947i
\(100\) −0.237654 −0.0237654
\(101\) −4.07225 12.5331i −0.405204 1.24709i −0.920725 0.390213i \(-0.872401\pi\)
0.515521 0.856877i \(-0.327599\pi\)
\(102\) 11.1743 + 8.11858i 1.10642 + 0.803859i
\(103\) 3.96993 2.88432i 0.391169 0.284201i −0.374765 0.927120i \(-0.622277\pi\)
0.765934 + 0.642919i \(0.222277\pi\)
\(104\) 0.480038 1.47741i 0.0470716 0.144872i
\(105\) 0.277759 0.854853i 0.0271065 0.0834251i
\(106\) 2.13124 1.54844i 0.207005 0.150398i
\(107\) −3.67146 2.66747i −0.354934 0.257874i 0.396002 0.918250i \(-0.370397\pi\)
−0.750936 + 0.660375i \(0.770397\pi\)
\(108\) 6.33218 + 19.4884i 0.609314 + 1.87528i
\(109\) 9.44166 0.904347 0.452174 0.891930i \(-0.350649\pi\)
0.452174 + 0.891930i \(0.350649\pi\)
\(110\) −12.5030 + 2.83376i −1.19211 + 0.270188i
\(111\) −1.70617 −0.161942
\(112\) −0.187328 0.576537i −0.0177009 0.0544777i
\(113\) −1.67272 1.21530i −0.157356 0.114326i 0.506321 0.862345i \(-0.331005\pi\)
−0.663677 + 0.748019i \(0.731005\pi\)
\(114\) 27.7365 20.1517i 2.59776 1.88738i
\(115\) −2.81701 + 8.66987i −0.262688 + 0.808469i
\(116\) −2.09227 + 6.43933i −0.194262 + 0.597877i
\(117\) −6.80603 + 4.94487i −0.629217 + 0.457153i
\(118\) −9.45872 6.87216i −0.870745 0.632634i
\(119\) 0.0869651 + 0.267651i 0.00797208 + 0.0245355i
\(120\) 11.4832 1.04826
\(121\) 9.92511 4.74260i 0.902282 0.431146i
\(122\) 0.613587 0.0555516
\(123\) 4.51681 + 13.9013i 0.407267 + 1.25344i
\(124\) 1.20622 + 0.876369i 0.108322 + 0.0787003i
\(125\) 9.22660 6.70352i 0.825253 0.599581i
\(126\) −0.558414 + 1.71862i −0.0497475 + 0.153107i
\(127\) −5.03721 + 15.5029i −0.446980 + 1.37566i 0.433317 + 0.901241i \(0.357343\pi\)
−0.880297 + 0.474422i \(0.842657\pi\)
\(128\) 9.08221 6.59861i 0.802761 0.583240i
\(129\) 16.7166 + 12.1453i 1.47181 + 1.06934i
\(130\) −1.19448 3.67622i −0.104762 0.322426i
\(131\) −0.915990 −0.0800304 −0.0400152 0.999199i \(-0.512741\pi\)
−0.0400152 + 0.999199i \(0.512741\pi\)
\(132\) 12.2455 2.77539i 1.06583 0.241567i
\(133\) 0.698547 0.0605717
\(134\) −7.57249 23.3057i −0.654164 2.01331i
\(135\) −32.3698 23.5181i −2.78595 2.02411i
\(136\) −2.90869 + 2.11329i −0.249418 + 0.181213i
\(137\) 2.49872 7.69027i 0.213480 0.657024i −0.785778 0.618509i \(-0.787737\pi\)
0.999258 0.0385152i \(-0.0122628\pi\)
\(138\) 7.68299 23.6458i 0.654019 2.01286i
\(139\) 2.07025 1.50412i 0.175596 0.127578i −0.496516 0.868028i \(-0.665387\pi\)
0.672112 + 0.740450i \(0.265387\pi\)
\(140\) −0.241218 0.175255i −0.0203867 0.0148118i
\(141\) −6.13860 18.8927i −0.516963 1.59105i
\(142\) −9.58720 −0.804540
\(143\) 1.69677 + 2.84973i 0.141891 + 0.238307i
\(144\) −41.9411 −3.49509
\(145\) −4.08535 12.5734i −0.339270 1.04416i
\(146\) −6.81751 4.95321i −0.564221 0.409930i
\(147\) 19.0911 13.8705i 1.57461 1.14402i
\(148\) −0.174892 + 0.538264i −0.0143761 + 0.0442450i
\(149\) −3.16081 + 9.72798i −0.258944 + 0.796947i 0.734083 + 0.679060i \(0.237612\pi\)
−0.993027 + 0.117887i \(0.962388\pi\)
\(150\) −1.02390 + 0.743906i −0.0836009 + 0.0607396i
\(151\) 3.45691 + 2.51159i 0.281319 + 0.204391i 0.719493 0.694500i \(-0.244374\pi\)
−0.438173 + 0.898891i \(0.644374\pi\)
\(152\) 2.75775 + 8.48747i 0.223683 + 0.688425i
\(153\) 19.4707 1.57411
\(154\) 0.654661 + 0.280992i 0.0527541 + 0.0226430i
\(155\) −2.91126 −0.233838
\(156\) 1.16987 + 3.60050i 0.0936647 + 0.288270i
\(157\) 17.2394 + 12.5252i 1.37585 + 0.999617i 0.997254 + 0.0740566i \(0.0235945\pi\)
0.378600 + 0.925560i \(0.376405\pi\)
\(158\) −12.9556 + 9.41283i −1.03070 + 0.748844i
\(159\) 1.55679 4.79132i 0.123462 0.379976i
\(160\) 3.85422 11.8621i 0.304703 0.937779i
\(161\) 0.409833 0.297761i 0.0322994 0.0234669i
\(162\) 52.2149 + 37.9363i 4.10239 + 2.98056i
\(163\) 5.54688 + 17.0715i 0.434465 + 1.33715i 0.893634 + 0.448797i \(0.148147\pi\)
−0.459169 + 0.888349i \(0.651853\pi\)
\(164\) 4.84860 0.378612
\(165\) −16.1586 + 18.4384i −1.25795 + 1.43543i
\(166\) 6.73449 0.522698
\(167\) 7.50423 + 23.0957i 0.580695 + 1.78720i 0.615911 + 0.787816i \(0.288788\pi\)
−0.0352158 + 0.999380i \(0.511212\pi\)
\(168\) −0.516253 0.375080i −0.0398298 0.0289380i
\(169\) −0.809017 + 0.587785i −0.0622321 + 0.0452143i
\(170\) −2.76454 + 8.50839i −0.212031 + 0.652563i
\(171\) 14.9347 45.9643i 1.14209 3.51498i
\(172\) 5.54517 4.02880i 0.422815 0.307193i
\(173\) −20.8062 15.1166i −1.58187 1.14929i −0.914514 0.404555i \(-0.867426\pi\)
−0.667355 0.744740i \(-0.732574\pi\)
\(174\) 11.1422 + 34.2921i 0.844688 + 2.59968i
\(175\) −0.0257870 −0.00194931
\(176\) −1.50718 + 16.4660i −0.113608 + 1.24117i
\(177\) −22.3588 −1.68059
\(178\) −2.85529 8.78768i −0.214013 0.658664i
\(179\) −7.33045 5.32588i −0.547904 0.398075i 0.279108 0.960260i \(-0.409961\pi\)
−0.827012 + 0.562184i \(0.809961\pi\)
\(180\) −16.6889 + 12.1252i −1.24392 + 0.903761i
\(181\) −4.84834 + 14.9217i −0.360374 + 1.10912i 0.592453 + 0.805605i \(0.298160\pi\)
−0.952827 + 0.303513i \(0.901840\pi\)
\(182\) −0.0663774 + 0.204289i −0.00492022 + 0.0151429i
\(183\) 0.949308 0.689713i 0.0701749 0.0509851i
\(184\) 5.23581 + 3.80404i 0.385989 + 0.280437i
\(185\) −0.341494 1.05101i −0.0251072 0.0772719i
\(186\) 7.94003 0.582192
\(187\) 0.699691 7.64418i 0.0511665 0.558997i
\(188\) −6.58952 −0.480590
\(189\) 0.687082 + 2.11462i 0.0499778 + 0.153816i
\(190\) 17.9652 + 13.0525i 1.30333 + 0.946924i
\(191\) −14.3758 + 10.4447i −1.04020 + 0.755749i −0.970324 0.241807i \(-0.922260\pi\)
−0.0698749 + 0.997556i \(0.522260\pi\)
\(192\) −0.102777 + 0.316315i −0.00741729 + 0.0228281i
\(193\) −1.46006 + 4.49359i −0.105097 + 0.323456i −0.989753 0.142788i \(-0.954393\pi\)
0.884656 + 0.466244i \(0.154393\pi\)
\(194\) −13.4789 + 9.79298i −0.967727 + 0.703095i
\(195\) −5.98034 4.34497i −0.428261 0.311150i
\(196\) −2.41893 7.44471i −0.172781 0.531765i
\(197\) 10.3412 0.736779 0.368389 0.929672i \(-0.379909\pi\)
0.368389 + 0.929672i \(0.379909\pi\)
\(198\) 32.4857 37.0691i 2.30866 2.63439i
\(199\) 23.1675 1.64230 0.821151 0.570710i \(-0.193332\pi\)
0.821151 + 0.570710i \(0.193332\pi\)
\(200\) −0.101803 0.313317i −0.00719854 0.0221548i
\(201\) −37.9129 27.5454i −2.67417 1.94290i
\(202\) −18.8335 + 13.6833i −1.32512 + 0.962756i
\(203\) −0.227024 + 0.698709i −0.0159340 + 0.0490397i
\(204\) 2.70760 8.33313i 0.189570 0.583436i
\(205\) −7.65925 + 5.56477i −0.534945 + 0.388661i
\(206\) −7.01300 5.09524i −0.488619 0.355003i
\(207\) −10.8306 33.3330i −0.752776 2.31680i
\(208\) −4.98545 −0.345679
\(209\) −17.5088 7.51510i −1.21111 0.519830i
\(210\) −1.58784 −0.109571
\(211\) 5.41870 + 16.6770i 0.373038 + 1.14809i 0.944792 + 0.327669i \(0.106263\pi\)
−0.571754 + 0.820425i \(0.693737\pi\)
\(212\) −1.35199 0.982278i −0.0928550 0.0674631i
\(213\) −14.8328 + 10.7767i −1.01633 + 0.738404i
\(214\) −2.47734 + 7.62445i −0.169347 + 0.521197i
\(215\) −4.13573 + 12.7285i −0.282054 + 0.868074i
\(216\) −22.9805 + 16.6963i −1.56363 + 1.13604i
\(217\) 0.130882 + 0.0950917i 0.00888488 + 0.00645524i
\(218\) −5.15409 15.8627i −0.349079 1.07435i
\(219\) −16.1154 −1.08898
\(220\) 4.16062 + 6.98778i 0.280509 + 0.471116i
\(221\) 2.31444 0.155686
\(222\) 0.931376 + 2.86648i 0.0625098 + 0.192386i
\(223\) 1.14269 + 0.830215i 0.0765203 + 0.0555953i 0.625388 0.780314i \(-0.284941\pi\)
−0.548867 + 0.835909i \(0.684941\pi\)
\(224\) −0.560731 + 0.407395i −0.0374654 + 0.0272202i
\(225\) −0.551318 + 1.69678i −0.0367545 + 0.113119i
\(226\) −1.12867 + 3.47370i −0.0750782 + 0.231067i
\(227\) 10.9641 7.96591i 0.727715 0.528716i −0.161125 0.986934i \(-0.551512\pi\)
0.888840 + 0.458218i \(0.151512\pi\)
\(228\) −17.5951 12.7836i −1.16527 0.846615i
\(229\) −3.19015 9.81828i −0.210811 0.648810i −0.999425 0.0339206i \(-0.989201\pi\)
0.788613 0.614889i \(-0.210799\pi\)
\(230\) 16.1038 1.06185
\(231\) 1.32871 0.301147i 0.0874227 0.0198140i
\(232\) −9.38570 −0.616201
\(233\) −0.0616963 0.189882i −0.00404186 0.0124396i 0.949015 0.315230i \(-0.102082\pi\)
−0.953057 + 0.302791i \(0.902082\pi\)
\(234\) 12.0230 + 8.73526i 0.785971 + 0.571042i
\(235\) 10.4094 7.56284i 0.679031 0.493345i
\(236\) −2.29191 + 7.05377i −0.149191 + 0.459161i
\(237\) −9.46362 + 29.1260i −0.614728 + 1.89194i
\(238\) 0.402200 0.292215i 0.0260707 0.0189415i
\(239\) −6.13610 4.45814i −0.396911 0.288373i 0.371370 0.928485i \(-0.378888\pi\)
−0.768282 + 0.640112i \(0.778888\pi\)
\(240\) −11.3882 35.0493i −0.735105 2.26242i
\(241\) 4.38526 0.282479 0.141240 0.989975i \(-0.454891\pi\)
0.141240 + 0.989975i \(0.454891\pi\)
\(242\) −13.3859 14.0859i −0.860478 0.905479i
\(243\) 68.5702 4.39878
\(244\) −0.120282 0.370189i −0.00770024 0.0236989i
\(245\) 12.3655 + 8.98405i 0.790002 + 0.573970i
\(246\) 20.8895 15.1771i 1.33187 0.967657i
\(247\) 1.77526 5.46368i 0.112957 0.347645i
\(248\) −0.638679 + 1.96565i −0.0405562 + 0.124819i
\(249\) 10.4192 7.57002i 0.660292 0.479730i
\(250\) −16.2991 11.8420i −1.03084 0.748952i
\(251\) −0.0523971 0.161262i −0.00330728 0.0101787i 0.949389 0.314102i \(-0.101703\pi\)
−0.952697 + 0.303923i \(0.901703\pi\)
\(252\) 1.14634 0.0722128
\(253\) −13.4757 + 3.05422i −0.847210 + 0.192017i
\(254\) 28.7958 1.80681
\(255\) 5.28685 + 16.2712i 0.331075 + 1.01894i
\(256\) −16.2033 11.7724i −1.01271 0.735774i
\(257\) −13.6904 + 9.94665i −0.853983 + 0.620455i −0.926241 0.376931i \(-0.876979\pi\)
0.0722585 + 0.997386i \(0.476979\pi\)
\(258\) 11.2796 34.7150i 0.702237 2.16126i
\(259\) −0.0189769 + 0.0584050i −0.00117917 + 0.00362911i
\(260\) −1.98378 + 1.44130i −0.123029 + 0.0893856i
\(261\) 41.1213 + 29.8764i 2.54534 + 1.84930i
\(262\) 0.500028 + 1.53893i 0.0308918 + 0.0950752i
\(263\) 9.22898 0.569083 0.284542 0.958664i \(-0.408159\pi\)
0.284542 + 0.958664i \(0.408159\pi\)
\(264\) 8.90452 + 14.9552i 0.548036 + 0.920428i
\(265\) 3.26308 0.200450
\(266\) −0.381328 1.17361i −0.0233807 0.0719585i
\(267\) −14.2955 10.3863i −0.874869 0.635630i
\(268\) −12.5764 + 9.13726i −0.768223 + 0.558147i
\(269\) 3.74251 11.5183i 0.228185 0.702281i −0.769768 0.638324i \(-0.779628\pi\)
0.997953 0.0639568i \(-0.0203720\pi\)
\(270\) −21.8417 + 67.2218i −1.32924 + 4.09099i
\(271\) −2.64787 + 1.92379i −0.160846 + 0.116862i −0.665297 0.746579i \(-0.731695\pi\)
0.504451 + 0.863441i \(0.331695\pi\)
\(272\) 9.33486 + 6.78217i 0.566009 + 0.411230i
\(273\) 0.126939 + 0.390677i 0.00768267 + 0.0236448i
\(274\) −14.2842 −0.862940
\(275\) 0.646342 + 0.277421i 0.0389759 + 0.0167291i
\(276\) −15.7721 −0.949366
\(277\) −4.03204 12.4093i −0.242262 0.745604i −0.996075 0.0885156i \(-0.971788\pi\)
0.753813 0.657089i \(-0.228212\pi\)
\(278\) −3.65715 2.65708i −0.219342 0.159361i
\(279\) 9.05525 6.57903i 0.542124 0.393876i
\(280\) 0.127722 0.393089i 0.00763286 0.0234915i
\(281\) 6.73500 20.7282i 0.401776 1.23654i −0.521781 0.853080i \(-0.674732\pi\)
0.923557 0.383461i \(-0.125268\pi\)
\(282\) −28.3900 + 20.6265i −1.69060 + 1.22829i
\(283\) 18.4086 + 13.3747i 1.09428 + 0.795041i 0.980117 0.198421i \(-0.0635814\pi\)
0.114163 + 0.993462i \(0.463581\pi\)
\(284\) 1.87938 + 5.78414i 0.111521 + 0.343225i
\(285\) 42.4665 2.51550
\(286\) 3.86150 4.40632i 0.228336 0.260551i
\(287\) 0.526104 0.0310550
\(288\) 14.8183 + 45.6061i 0.873177 + 2.68736i
\(289\) 9.41968 + 6.84380i 0.554099 + 0.402576i
\(290\) −18.8941 + 13.7273i −1.10950 + 0.806097i
\(291\) −9.84582 + 30.3023i −0.577172 + 1.77635i
\(292\) −1.65193 + 5.08411i −0.0966717 + 0.297525i
\(293\) −15.5499 + 11.2977i −0.908434 + 0.660016i −0.940618 0.339466i \(-0.889754\pi\)
0.0321844 + 0.999482i \(0.489754\pi\)
\(294\) −33.7251 24.5027i −1.96689 1.42903i
\(295\) −4.47517 13.7732i −0.260555 0.801904i
\(296\) −0.784550 −0.0456010
\(297\) 5.52802 60.3940i 0.320768 3.50442i
\(298\) 18.0691 1.04672
\(299\) −1.28740 3.96222i −0.0744525 0.229141i
\(300\) 0.649527 + 0.471909i 0.0375005 + 0.0272457i
\(301\) 0.601687 0.437151i 0.0346806 0.0251970i
\(302\) 2.33257 7.17890i 0.134224 0.413099i
\(303\) −13.7572 + 42.3402i −0.790328 + 2.43238i
\(304\) 23.1708 16.8346i 1.32893 0.965528i
\(305\) 0.614875 + 0.446733i 0.0352076 + 0.0255798i
\(306\) −10.6288 32.7122i −0.607610 1.87003i
\(307\) −15.5200 −0.885775 −0.442888 0.896577i \(-0.646046\pi\)
−0.442888 + 0.896577i \(0.646046\pi\)
\(308\) 0.0411945 0.450052i 0.00234727 0.0256441i
\(309\) −16.5775 −0.943063
\(310\) 1.58922 + 4.89112i 0.0902617 + 0.277797i
\(311\) 17.3975 + 12.6400i 0.986521 + 0.716750i 0.959157 0.282876i \(-0.0912885\pi\)
0.0273647 + 0.999626i \(0.491288\pi\)
\(312\) −4.24566 + 3.08465i −0.240363 + 0.174634i
\(313\) −4.97733 + 15.3187i −0.281336 + 0.865862i 0.706138 + 0.708075i \(0.250436\pi\)
−0.987473 + 0.157787i \(0.949564\pi\)
\(314\) 11.6324 35.8007i 0.656452 2.02035i
\(315\) −1.81086 + 1.31566i −0.102030 + 0.0741293i
\(316\) 8.21864 + 5.97119i 0.462334 + 0.335906i
\(317\) −1.37241 4.22384i −0.0770821 0.237234i 0.905089 0.425221i \(-0.139804\pi\)
−0.982172 + 0.187987i \(0.939804\pi\)
\(318\) −8.89958 −0.499064
\(319\) 13.2071 15.0705i 0.739457 0.843788i
\(320\) −0.215423 −0.0120425
\(321\) 4.73760 + 14.5808i 0.264427 + 0.813822i
\(322\) −0.723982 0.526004i −0.0403460 0.0293131i
\(323\) −10.7568 + 7.81526i −0.598523 + 0.434853i
\(324\) 12.6520 38.9389i 0.702890 2.16327i
\(325\) −0.0655339 + 0.201693i −0.00363517 + 0.0111879i
\(326\) 25.6534 18.6383i 1.42081 1.03228i
\(327\) −25.8048 18.7483i −1.42701 1.03678i
\(328\) 2.07697 + 6.39227i 0.114682 + 0.352954i
\(329\) −0.715005 −0.0394195
\(330\) 39.7986 + 17.0823i 2.19084 + 0.940348i
\(331\) 1.65739 0.0910986 0.0455493 0.998962i \(-0.485496\pi\)
0.0455493 + 0.998962i \(0.485496\pi\)
\(332\) −1.32016 4.06305i −0.0724534 0.222989i
\(333\) 3.43733 + 2.49736i 0.188364 + 0.136855i
\(334\) 34.7058 25.2153i 1.89902 1.37972i
\(335\) 9.37976 28.8679i 0.512471 1.57722i
\(336\) −0.632846 + 1.94770i −0.0345246 + 0.106256i
\(337\) 19.5807 14.2262i 1.06663 0.774952i 0.0913260 0.995821i \(-0.470889\pi\)
0.975303 + 0.220869i \(0.0708895\pi\)
\(338\) 1.42915 + 1.03834i 0.0777357 + 0.0564783i
\(339\) 2.15845 + 6.64301i 0.117231 + 0.360799i
\(340\) 5.67520 0.307781
\(341\) −2.25751 3.79150i −0.122251 0.205321i
\(342\) −85.3760 −4.61660
\(343\) −0.525495 1.61731i −0.0283740 0.0873263i
\(344\) 7.68682 + 5.58481i 0.414446 + 0.301113i
\(345\) 24.9148 18.1017i 1.34137 0.974563i
\(346\) −14.0391 + 43.2079i −0.754747 + 2.32287i
\(347\) 1.00283 3.08641i 0.0538350 0.165687i −0.920524 0.390686i \(-0.872238\pi\)
0.974359 + 0.224999i \(0.0722378\pi\)
\(348\) 18.5049 13.4446i 0.991966 0.720706i
\(349\) −1.17578 0.854257i −0.0629383 0.0457273i 0.555871 0.831268i \(-0.312385\pi\)
−0.618810 + 0.785541i \(0.712385\pi\)
\(350\) 0.0140768 + 0.0433239i 0.000752437 + 0.00231576i
\(351\) 18.2856 0.976013
\(352\) 18.4374 4.17877i 0.982716 0.222729i
\(353\) −29.1171 −1.54975 −0.774874 0.632115i \(-0.782187\pi\)
−0.774874 + 0.632115i \(0.782187\pi\)
\(354\) 12.2054 + 37.5643i 0.648709 + 1.99652i
\(355\) −9.60732 6.98013i −0.509904 0.370467i
\(356\) −4.74205 + 3.44530i −0.251328 + 0.182601i
\(357\) 0.293792 0.904198i 0.0155491 0.0478552i
\(358\) −4.94625 + 15.2230i −0.261418 + 0.804561i
\(359\) 2.54992 1.85263i 0.134580 0.0977778i −0.518459 0.855103i \(-0.673494\pi\)
0.653038 + 0.757325i \(0.273494\pi\)
\(360\) −23.1345 16.8082i −1.21930 0.885871i
\(361\) 4.32725 + 13.3179i 0.227750 + 0.700943i
\(362\) 27.7161 1.45672
\(363\) −36.5435 6.74636i −1.91803 0.354092i
\(364\) 0.136263 0.00714213
\(365\) −3.22554 9.92721i −0.168833 0.519614i
\(366\) −1.67698 1.21840i −0.0876572 0.0636867i
\(367\) −9.77416 + 7.10134i −0.510207 + 0.370687i −0.812902 0.582400i \(-0.802114\pi\)
0.302695 + 0.953087i \(0.402114\pi\)
\(368\) 6.41829 19.7535i 0.334576 1.02972i
\(369\) 11.2479 34.6176i 0.585545 1.80212i
\(370\) −1.57935 + 1.14747i −0.0821067 + 0.0596540i
\(371\) −0.146699 0.106583i −0.00761626 0.00553354i
\(372\) −1.55649 4.79037i −0.0807001 0.248369i
\(373\) −12.9240 −0.669180 −0.334590 0.942364i \(-0.608598\pi\)
−0.334590 + 0.942364i \(0.608598\pi\)
\(374\) −13.2247 + 2.99733i −0.683833 + 0.154988i
\(375\) −38.5282 −1.98959
\(376\) −2.82272 8.68745i −0.145571 0.448021i
\(377\) 4.88799 + 3.55134i 0.251744 + 0.182903i
\(378\) 3.17764 2.30869i 0.163440 0.118746i
\(379\) −4.40813 + 13.5668i −0.226430 + 0.696881i 0.771713 + 0.635971i \(0.219400\pi\)
−0.998143 + 0.0609097i \(0.980600\pi\)
\(380\) 4.35308 13.3974i 0.223308 0.687272i
\(381\) 44.5512 32.3684i 2.28243 1.65828i
\(382\) 25.3954 + 18.4508i 1.29934 + 0.944025i
\(383\) −2.00840 6.18121i −0.102624 0.315845i 0.886541 0.462650i \(-0.153101\pi\)
−0.989166 + 0.146805i \(0.953101\pi\)
\(384\) −37.9252 −1.93536
\(385\) 0.451454 + 0.758219i 0.0230082 + 0.0386424i
\(386\) 8.34658 0.424830
\(387\) −15.9006 48.9371i −0.808274 2.48761i
\(388\) 8.55056 + 6.21234i 0.434089 + 0.315384i
\(389\) 2.22563 1.61701i 0.112844 0.0819858i −0.529932 0.848040i \(-0.677783\pi\)
0.642776 + 0.766054i \(0.277783\pi\)
\(390\) −4.03526 + 12.4193i −0.204333 + 0.628873i
\(391\) −2.97962 + 9.17033i −0.150686 + 0.463763i
\(392\) 8.77871 6.37811i 0.443392 0.322143i
\(393\) 2.50347 + 1.81888i 0.126283 + 0.0917503i
\(394\) −5.64513 17.3739i −0.284397 0.875285i
\(395\) −19.8360 −0.998058
\(396\) −28.7327 12.3326i −1.44387 0.619735i
\(397\) −3.98758 −0.200131 −0.100065 0.994981i \(-0.531905\pi\)
−0.100065 + 0.994981i \(0.531905\pi\)
\(398\) −12.6469 38.9231i −0.633931 1.95104i
\(399\) −1.90918 1.38710i −0.0955787 0.0694420i
\(400\) −0.855354 + 0.621451i −0.0427677 + 0.0310725i
\(401\) 1.11143 3.42063i 0.0555022 0.170818i −0.919463 0.393177i \(-0.871376\pi\)
0.974965 + 0.222359i \(0.0713758\pi\)
\(402\) −25.5819 + 78.7331i −1.27591 + 3.92685i
\(403\) 1.07638 0.782034i 0.0536182 0.0389559i
\(404\) 11.9473 + 8.68025i 0.594403 + 0.431859i
\(405\) 24.7043 + 76.0319i 1.22756 + 3.77806i
\(406\) 1.29781 0.0644092
\(407\) 1.10398 1.25974i 0.0547224 0.0624432i
\(408\) 12.1460 0.601317
\(409\) −8.14240 25.0597i −0.402616 1.23912i −0.922870 0.385112i \(-0.874163\pi\)
0.520254 0.854012i \(-0.325837\pi\)
\(410\) 13.5303 + 9.83034i 0.668214 + 0.485486i
\(411\) −22.0997 + 16.0564i −1.09010 + 0.792004i
\(412\) −1.69930 + 5.22990i −0.0837184 + 0.257659i
\(413\) −0.248687 + 0.765379i −0.0122371 + 0.0376618i
\(414\) −50.0895 + 36.3922i −2.46177 + 1.78858i
\(415\) 6.74862 + 4.90316i 0.331277 + 0.240687i
\(416\) 1.76142 + 5.42109i 0.0863607 + 0.265791i
\(417\) −8.64488 −0.423342
\(418\) −3.06803 + 33.5185i −0.150062 + 1.63944i
\(419\) −18.9753 −0.927002 −0.463501 0.886096i \(-0.653407\pi\)
−0.463501 + 0.886096i \(0.653407\pi\)
\(420\) 0.311264 + 0.957972i 0.0151881 + 0.0467443i
\(421\) 5.65138 + 4.10597i 0.275431 + 0.200113i 0.716922 0.697153i \(-0.245550\pi\)
−0.441491 + 0.897266i \(0.645550\pi\)
\(422\) 25.0606 18.2076i 1.21993 0.886331i
\(423\) −15.2866 + 47.0473i −0.743259 + 2.28752i
\(424\) 0.715863 2.20320i 0.0347654 0.106997i
\(425\) 0.397089 0.288502i 0.0192616 0.0139944i
\(426\) 26.2026 + 19.0373i 1.26952 + 0.922359i
\(427\) −0.0130513 0.0401678i −0.000631598 0.00194386i
\(428\) 5.08561 0.245822
\(429\) 1.02130 11.1578i 0.0493090 0.538704i
\(430\) 23.6424 1.14014
\(431\) 8.01090 + 24.6550i 0.385872 + 1.18759i 0.935846 + 0.352409i \(0.114637\pi\)
−0.549974 + 0.835181i \(0.685363\pi\)
\(432\) 73.7515 + 53.5836i 3.54837 + 2.57804i
\(433\) 8.39649 6.10041i 0.403510 0.293167i −0.367459 0.930040i \(-0.619772\pi\)
0.770969 + 0.636873i \(0.219772\pi\)
\(434\) 0.0883135 0.271801i 0.00423918 0.0130469i
\(435\) −13.8014 + 42.4764i −0.661727 + 2.03659i
\(436\) −8.55988 + 6.21912i −0.409944 + 0.297842i
\(437\) 19.3628 + 14.0679i 0.926249 + 0.672960i
\(438\) 8.79720 + 27.0750i 0.420347 + 1.29369i
\(439\) 1.50138 0.0716568 0.0358284 0.999358i \(-0.488593\pi\)
0.0358284 + 0.999358i \(0.488593\pi\)
\(440\) −7.43024 + 8.47857i −0.354223 + 0.404200i
\(441\) −58.7646 −2.79831
\(442\) −1.26342 3.88842i −0.0600950 0.184953i
\(443\) −6.16836 4.48158i −0.293068 0.212926i 0.431529 0.902099i \(-0.357974\pi\)
−0.724597 + 0.689173i \(0.757974\pi\)
\(444\) 1.54682 1.12383i 0.0734090 0.0533348i
\(445\) 3.53674 10.8850i 0.167657 0.515997i
\(446\) 0.771037 2.37301i 0.0365096 0.112365i
\(447\) 27.9556 20.3109i 1.32225 0.960673i
\(448\) 0.00968487 + 0.00703647i 0.000457567 + 0.000332442i
\(449\) 7.68968 + 23.6664i 0.362898 + 1.11689i 0.951287 + 0.308308i \(0.0997627\pi\)
−0.588388 + 0.808579i \(0.700237\pi\)
\(450\) 3.15167 0.148571
\(451\) −13.1866 5.65993i −0.620934 0.266516i
\(452\) 2.31700 0.108983
\(453\) −4.46074 13.7288i −0.209584 0.645033i
\(454\) −19.3685 14.0720i −0.909007 0.660432i
\(455\) −0.215253 + 0.156390i −0.0100912 + 0.00733168i
\(456\) 9.31642 28.6730i 0.436281 1.34274i
\(457\) −6.63267 + 20.4133i −0.310263 + 0.954892i 0.667397 + 0.744702i \(0.267408\pi\)
−0.977660 + 0.210190i \(0.932592\pi\)
\(458\) −14.7539 + 10.7194i −0.689406 + 0.500883i
\(459\) −34.2384 24.8756i −1.59811 1.16109i
\(460\) −3.15682 9.71570i −0.147188 0.452997i
\(461\) 31.3859 1.46179 0.730894 0.682491i \(-0.239103\pi\)
0.730894 + 0.682491i \(0.239103\pi\)
\(462\) −1.23127 2.06793i −0.0572841 0.0962089i
\(463\) 2.92907 0.136126 0.0680628 0.997681i \(-0.478318\pi\)
0.0680628 + 0.997681i \(0.478318\pi\)
\(464\) 9.30807 + 28.6473i 0.432116 + 1.32992i
\(465\) 7.95670 + 5.78088i 0.368983 + 0.268082i
\(466\) −0.285335 + 0.207308i −0.0132179 + 0.00960336i
\(467\) 1.23997 3.81623i 0.0573788 0.176594i −0.918259 0.395979i \(-0.870405\pi\)
0.975638 + 0.219385i \(0.0704052\pi\)
\(468\) 2.91326 8.96611i 0.134666 0.414458i
\(469\) −1.36461 + 0.991451i −0.0630120 + 0.0457809i
\(470\) −18.3884 13.3600i −0.848195 0.616250i
\(471\) −22.2455 68.4645i −1.02502 3.15468i
\(472\) −10.2813 −0.473234
\(473\) −19.7840 + 4.48398i −0.909670 + 0.206174i
\(474\) 54.0998 2.48489
\(475\) −0.376482 1.15869i −0.0172742 0.0531645i
\(476\) −0.255142 0.185372i −0.0116944 0.00849649i
\(477\) −10.1496 + 7.37410i −0.464717 + 0.337637i
\(478\) −4.14036 + 12.7427i −0.189376 + 0.582839i
\(479\) −5.79237 + 17.8271i −0.264660 + 0.814541i 0.727111 + 0.686520i \(0.240862\pi\)
−0.991771 + 0.128021i \(0.959138\pi\)
\(480\) −34.0884 + 24.7666i −1.55591 + 1.13044i
\(481\) 0.408587 + 0.296856i 0.0186300 + 0.0135355i
\(482\) −2.39386 7.36754i −0.109037 0.335582i
\(483\) −1.71137 −0.0778700
\(484\) −5.87428 + 10.8372i −0.267013 + 0.492602i
\(485\) −20.6371 −0.937083
\(486\) −37.4316 115.203i −1.69793 5.22570i
\(487\) 24.0753 + 17.4918i 1.09096 + 0.792627i 0.979561 0.201149i \(-0.0644674\pi\)
0.111397 + 0.993776i \(0.464467\pi\)
\(488\) 0.436522 0.317152i 0.0197604 0.0143568i
\(489\) 18.7388 57.6722i 0.847400 2.60803i
\(490\) 8.34367 25.6792i 0.376928 1.16007i
\(491\) 18.8792 13.7166i 0.852008 0.619020i −0.0736912 0.997281i \(-0.523478\pi\)
0.925699 + 0.378261i \(0.123478\pi\)
\(492\) −13.2516 9.62786i −0.597429 0.434057i
\(493\) −4.32117 13.2992i −0.194616 0.598966i
\(494\) −10.1484 −0.456600
\(495\) 59.5427 13.4951i 2.67625 0.606562i
\(496\) 6.63302 0.297831
\(497\) 0.203925 + 0.627616i 0.00914728 + 0.0281524i
\(498\) −18.4059 13.3727i −0.824788 0.599243i
\(499\) 0.710048 0.515880i 0.0317861 0.0230940i −0.571779 0.820408i \(-0.693746\pi\)
0.603565 + 0.797314i \(0.293746\pi\)
\(500\) −3.94937 + 12.1549i −0.176621 + 0.543585i
\(501\) 25.3513 78.0234i 1.13261 3.48583i
\(502\) −0.242328 + 0.176062i −0.0108156 + 0.00785801i
\(503\) 33.8502 + 24.5936i 1.50930 + 1.09657i 0.966485 + 0.256723i \(0.0826430\pi\)
0.542819 + 0.839850i \(0.317357\pi\)
\(504\) 0.491053 + 1.51131i 0.0218733 + 0.0673189i
\(505\) −28.8354 −1.28316
\(506\) 12.4875 + 20.9729i 0.555138 + 0.932357i
\(507\) 3.37827 0.150034
\(508\) −5.64484 17.3730i −0.250449 0.770804i
\(509\) 9.53170 + 6.92518i 0.422485 + 0.306953i 0.778637 0.627475i \(-0.215911\pi\)
−0.356152 + 0.934428i \(0.615911\pi\)
\(510\) 24.4508 17.7645i 1.08270 0.786627i
\(511\) −0.179245 + 0.551658i −0.00792931 + 0.0244039i
\(512\) −3.99505 + 12.2955i −0.176558 + 0.543390i
\(513\) −84.9856 + 61.7457i −3.75221 + 2.72614i
\(514\) 24.1845 + 17.5711i 1.06673 + 0.775026i
\(515\) −3.31804 10.2119i −0.146210 0.449989i
\(516\) −23.1554 −1.01936
\(517\) 17.9214 + 7.69216i 0.788181 + 0.338301i
\(518\) 0.108484 0.00476651
\(519\) 26.8480 + 82.6298i 1.17850 + 3.62704i
\(520\) −2.74995 1.99796i −0.120593 0.0876162i
\(521\) −26.7232 + 19.4156i −1.17077 + 0.850611i −0.991100 0.133117i \(-0.957501\pi\)
−0.179665 + 0.983728i \(0.557501\pi\)
\(522\) 27.7468 85.3957i 1.21444 3.73767i
\(523\) 6.10323 18.7838i 0.266875 0.821358i −0.724380 0.689401i \(-0.757874\pi\)
0.991255 0.131957i \(-0.0421262\pi\)
\(524\) 0.830443 0.603352i 0.0362781 0.0263576i
\(525\) 0.0704778 + 0.0512052i 0.00307591 + 0.00223478i
\(526\) −5.03799 15.5053i −0.219667 0.676064i
\(527\) −3.07931 −0.134137
\(528\) 36.8158 42.0101i 1.60220 1.82826i
\(529\) −5.64340 −0.245365
\(530\) −1.78128 5.48220i −0.0773737 0.238132i
\(531\) 45.0450 + 32.7271i 1.95479 + 1.42024i
\(532\) −0.633308 + 0.460125i −0.0274574 + 0.0199489i
\(533\) 1.33702 4.11492i 0.0579127 0.178237i
\(534\) −9.64594 + 29.6872i −0.417421 + 1.28469i
\(535\) −8.03365 + 5.83679i −0.347325 + 0.252346i
\(536\) −17.4336 12.6662i −0.753016 0.547098i
\(537\) 9.45910 + 29.1121i 0.408190 + 1.25628i
\(538\) −21.3945 −0.922381
\(539\) −2.11174 + 23.0709i −0.0909590 + 0.993734i
\(540\) 44.8378 1.92951
\(541\) 7.13656 + 21.9641i 0.306824 + 0.944309i 0.978990 + 0.203908i \(0.0653643\pi\)
−0.672166 + 0.740401i \(0.734636\pi\)
\(542\) 4.67753 + 3.39843i 0.200917 + 0.145975i
\(543\) 42.8808 31.1547i 1.84019 1.33698i
\(544\) 4.07670 12.5468i 0.174787 0.537939i
\(545\) 6.38417 19.6485i 0.273468 0.841648i
\(546\) 0.587070 0.426531i 0.0251243 0.0182539i
\(547\) −36.2355 26.3267i −1.54932 1.12565i −0.944133 0.329563i \(-0.893098\pi\)
−0.605187 0.796084i \(-0.706902\pi\)
\(548\) 2.80013 + 8.61793i 0.119616 + 0.368140i
\(549\) −2.92207 −0.124711
\(550\) 0.113257 1.23734i 0.00482930 0.0527604i
\(551\) −34.7098 −1.47869
\(552\) −6.75620 20.7935i −0.287563 0.885028i
\(553\) 0.891774 + 0.647912i 0.0379221 + 0.0275520i
\(554\) −18.6475 + 13.5482i −0.792256 + 0.575608i
\(555\) −1.15366 + 3.55060i −0.0489701 + 0.150715i
\(556\) −0.886153 + 2.72730i −0.0375812 + 0.115663i
\(557\) 10.0308 7.28777i 0.425017 0.308793i −0.354636 0.935004i \(-0.615395\pi\)
0.779653 + 0.626211i \(0.215395\pi\)
\(558\) −15.9964 11.6220i −0.677181 0.492000i
\(559\) −1.89007 5.81704i −0.0799415 0.246035i
\(560\) −1.32646 −0.0560533
\(561\) −17.0913 + 19.5028i −0.721597 + 0.823407i
\(562\) −38.5014 −1.62408
\(563\) 7.03840 + 21.6620i 0.296633 + 0.912943i 0.982668 + 0.185374i \(0.0593497\pi\)
−0.686035 + 0.727569i \(0.740650\pi\)
\(564\) 18.0097 + 13.0848i 0.758344 + 0.550969i
\(565\) −3.66012 + 2.65924i −0.153983 + 0.111875i
\(566\) 12.4213 38.2289i 0.522107 1.60688i
\(567\) 1.37282 4.22512i 0.0576532 0.177438i
\(568\) −6.82059 + 4.95545i −0.286186 + 0.207926i
\(569\) 26.6904 + 19.3917i 1.11892 + 0.812942i 0.984045 0.177921i \(-0.0569370\pi\)
0.134874 + 0.990863i \(0.456937\pi\)
\(570\) −23.1820 71.3467i −0.970986 2.98839i
\(571\) 21.4209 0.896436 0.448218 0.893924i \(-0.352059\pi\)
0.448218 + 0.893924i \(0.352059\pi\)
\(572\) −3.41539 1.46595i −0.142805 0.0612943i
\(573\) 60.0302 2.50780
\(574\) −0.287194 0.883892i −0.0119872 0.0368929i
\(575\) −0.714782 0.519320i −0.0298085 0.0216571i
\(576\) 0.670059 0.486826i 0.0279191 0.0202844i
\(577\) 9.16579 28.2094i 0.381577 1.17437i −0.557356 0.830273i \(-0.688184\pi\)
0.938933 0.344100i \(-0.111816\pi\)
\(578\) 6.35597 19.5617i 0.264374 0.813658i
\(579\) 12.9134 9.38211i 0.536661 0.389907i
\(580\) 11.9858 + 8.70817i 0.497682 + 0.361587i
\(581\) −0.143246 0.440866i −0.00594285 0.0182902i
\(582\) 56.2847 2.33308
\(583\) 2.53033 + 4.24970i 0.104795 + 0.176005i
\(584\) −7.41038 −0.306644
\(585\) 5.68843 + 17.5072i 0.235187 + 0.723833i
\(586\) 27.4693 + 19.9576i 1.13475 + 0.824443i
\(587\) −15.9836 + 11.6128i −0.659715 + 0.479311i −0.866567 0.499061i \(-0.833678\pi\)
0.206852 + 0.978372i \(0.433678\pi\)
\(588\) −8.17181 + 25.1502i −0.337000 + 1.03718i
\(589\) −2.36193 + 7.26929i −0.0973218 + 0.299526i
\(590\) −20.6969 + 15.0372i −0.852079 + 0.619072i
\(591\) −28.2633 20.5345i −1.16260 0.844675i
\(592\) 0.778061 + 2.39463i 0.0319781 + 0.0984185i
\(593\) −15.9831 −0.656347 −0.328173 0.944618i \(-0.606433\pi\)
−0.328173 + 0.944618i \(0.606433\pi\)
\(594\) −104.484 + 23.6809i −4.28702 + 0.971639i
\(595\) 0.615796 0.0252452
\(596\) −3.54209 10.9014i −0.145090 0.446541i
\(597\) −63.3187 46.0037i −2.59146 1.88281i
\(598\) −5.95403 + 4.32586i −0.243478 + 0.176897i
\(599\) −14.1449 + 43.5334i −0.577943 + 1.77873i 0.0479869 + 0.998848i \(0.484719\pi\)
−0.625930 + 0.779879i \(0.715281\pi\)
\(600\) −0.343917 + 1.05847i −0.0140404 + 0.0432118i
\(601\) −12.5500 + 9.11812i −0.511926 + 0.371936i −0.813554 0.581490i \(-0.802470\pi\)
0.301628 + 0.953426i \(0.402470\pi\)
\(602\) −1.06290 0.772240i −0.0433205 0.0314742i
\(603\) 36.0623 + 110.988i 1.46857 + 4.51980i
\(604\) −4.78842 −0.194838
\(605\) −3.15847 23.8613i −0.128410 0.970101i
\(606\) 78.6443 3.19471
\(607\) −2.80998 8.64823i −0.114054 0.351021i 0.877695 0.479220i \(-0.159080\pi\)
−0.991748 + 0.128199i \(0.959080\pi\)
\(608\) −26.4921 19.2476i −1.07440 0.780595i
\(609\) 2.00790 1.45882i 0.0813642 0.0591145i
\(610\) 0.414890 1.27690i 0.0167984 0.0517001i
\(611\) −1.81708 + 5.59241i −0.0735113 + 0.226245i
\(612\) −17.6523 + 12.8251i −0.713552 + 0.518426i
\(613\) −21.0223 15.2736i −0.849084 0.616896i 0.0758094 0.997122i \(-0.475846\pi\)
−0.924893 + 0.380227i \(0.875846\pi\)
\(614\) 8.47220 + 26.0748i 0.341910 + 1.05229i
\(615\) 31.9833 1.28969
\(616\) 0.610983 0.138477i 0.0246172 0.00557940i
\(617\) 4.31680 0.173788 0.0868940 0.996218i \(-0.472306\pi\)
0.0868940 + 0.996218i \(0.472306\pi\)
\(618\) 9.04947 + 27.8514i 0.364023 + 1.12035i
\(619\) −5.74165 4.17155i −0.230776 0.167669i 0.466388 0.884580i \(-0.345555\pi\)
−0.697164 + 0.716911i \(0.745555\pi\)
\(620\) 2.63937 1.91761i 0.106000 0.0770132i
\(621\) −23.5409 + 72.4516i −0.944666 + 2.90738i
\(622\) 11.7390 36.1290i 0.470692 1.44864i
\(623\) −0.514543 + 0.373837i −0.0206147 + 0.0149775i
\(624\) 13.6256 + 9.89959i 0.545461 + 0.396301i
\(625\) −7.38386 22.7252i −0.295354 0.909007i
\(626\) 28.4535 1.13723
\(627\) 32.9303 + 55.3066i 1.31511 + 2.20873i
\(628\) −23.8796 −0.952898
\(629\) −0.361206 1.11168i −0.0144022 0.0443256i
\(630\) 3.19893 + 2.32416i 0.127449 + 0.0925968i
\(631\) 32.1347 23.3472i 1.27926 0.929439i 0.279733 0.960078i \(-0.409754\pi\)
0.999531 + 0.0306385i \(0.00975408\pi\)
\(632\) −4.35167 + 13.3931i −0.173100 + 0.532748i
\(633\) 18.3058 56.3395i 0.727591 2.23930i
\(634\) −6.34716 + 4.61148i −0.252078 + 0.183145i
\(635\) 28.8562 + 20.9653i 1.14512 + 0.831981i
\(636\) 1.74459 + 5.36928i 0.0691773 + 0.212906i
\(637\) −6.98521 −0.276764
\(638\) −32.5292 13.9621i −1.28784 0.552764i
\(639\) 45.6569 1.80616
\(640\) −7.59084 23.3622i −0.300054 0.923473i
\(641\) −27.6384 20.0805i −1.09165 0.793131i −0.111974 0.993711i \(-0.535717\pi\)
−0.979677 + 0.200580i \(0.935717\pi\)
\(642\) 21.9106 15.9190i 0.864743 0.628272i
\(643\) 12.3438 37.9904i 0.486793 1.49820i −0.342574 0.939491i \(-0.611299\pi\)
0.829367 0.558704i \(-0.188701\pi\)
\(644\) −0.175426 + 0.539905i −0.00691274 + 0.0212752i
\(645\) 36.5781 26.5756i 1.44026 1.04641i
\(646\) 19.0022 + 13.8059i 0.747631 + 0.543185i
\(647\) 1.81207 + 5.57698i 0.0712398 + 0.219254i 0.980337 0.197330i \(-0.0632272\pi\)
−0.909097 + 0.416584i \(0.863227\pi\)
\(648\) 56.7557 2.22957
\(649\) 14.4673 16.5086i 0.567893 0.648017i
\(650\) 0.374632 0.0146943
\(651\) −0.168889 0.519786i −0.00661927 0.0203720i
\(652\) −16.2737 11.8235i −0.637326 0.463044i
\(653\) 11.9366 8.67247i 0.467116 0.339380i −0.329200 0.944260i \(-0.606779\pi\)
0.796316 + 0.604880i \(0.206779\pi\)
\(654\) −17.4119 + 53.5883i −0.680859 + 2.09547i
\(655\) −0.619365 + 1.90621i −0.0242006 + 0.0744818i
\(656\) 17.4509 12.6788i 0.681342 0.495024i
\(657\) 32.4669 + 23.5886i 1.26665 + 0.920278i
\(658\) 0.390313 + 1.20126i 0.0152160 + 0.0468299i
\(659\) −42.1111 −1.64042 −0.820208 0.572065i \(-0.806143\pi\)
−0.820208 + 0.572065i \(0.806143\pi\)
\(660\) 2.50432 27.3599i 0.0974806 1.06498i
\(661\) −13.2231 −0.514317 −0.257159 0.966369i \(-0.582786\pi\)
−0.257159 + 0.966369i \(0.582786\pi\)
\(662\) −0.904751 2.78454i −0.0351641 0.108224i
\(663\) −6.32555 4.59578i −0.245664 0.178485i
\(664\) 4.79110 3.48094i 0.185931 0.135086i
\(665\) 0.472337 1.45370i 0.0183164 0.0563722i
\(666\) 2.31935 7.13823i 0.0898730 0.276601i
\(667\) −20.3640 + 14.7953i −0.788497 + 0.572877i
\(668\) −22.0162 15.9957i −0.851834 0.618894i
\(669\) −1.47451 4.53808i −0.0570079 0.175452i
\(670\) −53.6204 −2.07154
\(671\) −0.105006 + 1.14720i −0.00405373 + 0.0442872i
\(672\) 2.34149 0.0903248
\(673\) 5.07820 + 15.6291i 0.195750 + 0.602458i 0.999967 + 0.00812135i \(0.00258513\pi\)
−0.804217 + 0.594336i \(0.797415\pi\)
\(674\) −34.5899 25.1310i −1.33235 0.968012i
\(675\) 3.13726 2.27935i 0.120753 0.0877323i
\(676\) 0.346293 1.06578i 0.0133190 0.0409916i
\(677\) −9.46120 + 29.1186i −0.363623 + 1.11912i 0.587215 + 0.809431i \(0.300224\pi\)
−0.950839 + 0.309687i \(0.899776\pi\)
\(678\) 9.98246 7.25268i 0.383374 0.278537i
\(679\) 0.927790 + 0.674079i 0.0356053 + 0.0258688i
\(680\) 2.43106 + 7.48203i 0.0932269 + 0.286923i
\(681\) −45.7837 −1.75444
\(682\) −5.13764 + 5.86251i −0.196730 + 0.224487i
\(683\) −32.4731 −1.24255 −0.621274 0.783593i \(-0.713385\pi\)
−0.621274 + 0.783593i \(0.713385\pi\)
\(684\) 16.7363 + 51.5089i 0.639927 + 1.96949i
\(685\) −14.3142 10.3999i −0.546917 0.397358i
\(686\) −2.43033 + 1.76574i −0.0927903 + 0.0674161i
\(687\) −10.7772 + 33.1688i −0.411176 + 1.26547i
\(688\) 9.42285 29.0006i 0.359243 1.10564i
\(689\) −1.20646 + 0.876542i −0.0459623 + 0.0333936i
\(690\) −44.0128 31.9772i −1.67554 1.21735i
\(691\) −12.6950 39.0712i −0.482940 1.48634i −0.834942 0.550338i \(-0.814499\pi\)
0.352002 0.935999i \(-0.385501\pi\)
\(692\) 28.8202 1.09558
\(693\) −3.11768 1.33816i −0.118431 0.0508326i
\(694\) −5.73282 −0.217615
\(695\) −1.73030 5.32531i −0.0656339 0.202000i
\(696\) 25.6518 + 18.6372i 0.972330 + 0.706439i
\(697\) −8.10137 + 5.88599i −0.306861 + 0.222948i
\(698\) −0.793366 + 2.44173i −0.0300293 + 0.0924208i
\(699\) −0.208427 + 0.641471i −0.00788342 + 0.0242627i
\(700\) 0.0233787 0.0169856i 0.000883631 0.000641995i
\(701\) 18.0479 + 13.1125i 0.681658 + 0.495254i 0.873907 0.486092i \(-0.161578\pi\)
−0.192249 + 0.981346i \(0.561578\pi\)
\(702\) −9.98188 30.7211i −0.376742 1.15949i
\(703\) −2.90139 −0.109428
\(704\) −0.167048 0.280558i −0.00629587 0.0105739i
\(705\) −43.4671 −1.63707
\(706\) 15.8947 + 48.9188i 0.598205 + 1.84108i
\(707\) 1.29636 + 0.941863i 0.0487547 + 0.0354224i
\(708\) 20.2706 14.7275i 0.761817 0.553492i
\(709\) −6.22286 + 19.1520i −0.233705 + 0.719269i 0.763586 + 0.645706i \(0.223437\pi\)
−0.997291 + 0.0735625i \(0.976563\pi\)
\(710\) −6.48258 + 19.9513i −0.243287 + 0.748760i
\(711\) 61.6984 44.8265i 2.31387 1.68113i
\(712\) −6.57352 4.77594i −0.246353 0.178986i
\(713\) 1.71286 + 5.27164i 0.0641471 + 0.197424i
\(714\) −1.67949 −0.0628535
\(715\) 7.07771 1.60414i 0.264691 0.0599913i
\(716\) 10.1539 0.379471
\(717\) 7.91793 + 24.3689i 0.295701 + 0.910073i
\(718\) −4.50451 3.27272i −0.168107 0.122137i
\(719\) −15.7474 + 11.4412i −0.587279 + 0.426683i −0.841341 0.540505i \(-0.818233\pi\)
0.254062 + 0.967188i \(0.418233\pi\)
\(720\) −28.3594 + 87.2811i −1.05689 + 3.25278i
\(721\) −0.184385 + 0.567477i −0.00686684 + 0.0211340i
\(722\) 20.0128 14.5402i 0.744801 0.541129i
\(723\) −11.9853 8.70780i −0.445737 0.323847i
\(724\) −5.43319 16.7216i −0.201923 0.621455i
\(725\) 1.28132 0.0475869
\(726\) 8.61428 + 65.0783i 0.319706 + 2.41528i
\(727\) 2.25186 0.0835170 0.0417585 0.999128i \(-0.486704\pi\)
0.0417585 + 0.999128i \(0.486704\pi\)
\(728\) 0.0583704 + 0.179646i 0.00216335 + 0.00665811i
\(729\) −98.7341 71.7345i −3.65682 2.65683i
\(730\) −14.9176 + 10.8383i −0.552126 + 0.401143i
\(731\) −4.37446 + 13.4632i −0.161795 + 0.497954i
\(732\) −0.406344 + 1.25060i −0.0150189 + 0.0462234i
\(733\) 7.14492 5.19108i 0.263903 0.191737i −0.447963 0.894052i \(-0.647850\pi\)
0.711866 + 0.702315i \(0.247850\pi\)
\(734\) 17.2663 + 12.5447i 0.637312 + 0.463035i
\(735\) −15.9562 49.1082i −0.588554 1.81138i
\(736\) −23.7472 −0.875334
\(737\) 44.8698 10.1696i 1.65280 0.374602i
\(738\) −64.3001 −2.36692
\(739\) −10.0280 30.8630i −0.368885 1.13531i −0.947512 0.319720i \(-0.896411\pi\)
0.578627 0.815592i \(-0.303589\pi\)
\(740\) 1.00189 + 0.727916i 0.0368302 + 0.0267587i
\(741\) −15.7011 + 11.4075i −0.576795 + 0.419066i
\(742\) −0.0989861 + 0.304648i −0.00363390 + 0.0111840i
\(743\) 8.81385 27.1262i 0.323349 0.995166i −0.648832 0.760932i \(-0.724742\pi\)
0.972180 0.234233i \(-0.0752580\pi\)
\(744\) 5.64875 4.10406i 0.207093 0.150462i
\(745\) 18.1070 + 13.1555i 0.663391 + 0.481982i
\(746\) 7.05506 + 21.7132i 0.258304 + 0.794978i
\(747\) −32.0715 −1.17344
\(748\) 4.40079 + 7.39114i 0.160909 + 0.270247i
\(749\) 0.551821 0.0201631
\(750\) 21.0321 + 64.7301i 0.767983 + 2.36361i
\(751\) 20.7057 + 15.0435i 0.755561 + 0.548947i 0.897545 0.440922i \(-0.145348\pi\)
−0.141985 + 0.989869i \(0.545348\pi\)
\(752\) −23.7167 + 17.2312i −0.864859 + 0.628357i
\(753\) −0.177012 + 0.544786i −0.00645066 + 0.0198531i
\(754\) 3.29820 10.1508i 0.120113 0.369670i
\(755\) 7.56418 5.49570i 0.275289 0.200009i
\(756\) −2.01579 1.46456i −0.0733136 0.0532654i
\(757\) 0.897877 + 2.76338i 0.0326339 + 0.100437i 0.966047 0.258368i \(-0.0831845\pi\)
−0.933413 + 0.358804i \(0.883185\pi\)
\(758\) 25.1995 0.915289
\(759\) 42.8949 + 18.4112i 1.55699 + 0.668286i
\(760\) 19.5275 0.708336
\(761\) 1.97879 + 6.09010i 0.0717312 + 0.220766i 0.980495 0.196546i \(-0.0629724\pi\)
−0.908763 + 0.417312i \(0.862972\pi\)
\(762\) −78.7011 57.1797i −2.85104 2.07140i
\(763\) −0.928802 + 0.674814i −0.0336249 + 0.0244299i
\(764\) 6.15346 18.9384i 0.222624 0.685168i
\(765\) 13.1655 40.5193i 0.476000 1.46498i
\(766\) −9.28850 + 6.74849i −0.335607 + 0.243833i
\(767\) 5.35440 + 3.89020i 0.193336 + 0.140467i
\(768\) 20.9085 + 64.3497i 0.754470 + 2.32202i
\(769\) −40.4812 −1.45979 −0.729894 0.683560i \(-0.760431\pi\)
−0.729894 + 0.683560i \(0.760431\pi\)
\(770\) 1.02742 1.17238i 0.0370256 0.0422495i
\(771\) 57.1679 2.05885
\(772\) −1.63618 5.03565i −0.0588874 0.181237i
\(773\) 24.9317 + 18.1140i 0.896732 + 0.651514i 0.937624 0.347650i \(-0.113020\pi\)
−0.0408927 + 0.999164i \(0.513020\pi\)
\(774\) −73.5378 + 53.4283i −2.64326 + 1.92044i
\(775\) 0.0871913 0.268347i 0.00313200 0.00963932i
\(776\) −4.52742 + 13.9340i −0.162525 + 0.500201i
\(777\) 0.167840 0.121943i 0.00602123 0.00437468i
\(778\) −3.93164 2.85650i −0.140956 0.102411i
\(779\) 7.68097 + 23.6396i 0.275199 + 0.846976i
\(780\) 8.28380 0.296608
\(781\) 1.64071 17.9248i 0.0587091 0.641401i
\(782\) 17.0333 0.609110
\(783\) −34.1401 105.072i −1.22007 3.75498i
\(784\) −28.1736 20.4693i −1.00620 0.731046i
\(785\) 37.7221 27.4067i 1.34636 0.978188i
\(786\) 1.68923 5.19891i 0.0602528 0.185439i
\(787\) −7.74863 + 23.8478i −0.276209 + 0.850083i 0.712688 + 0.701481i \(0.247477\pi\)
−0.988897 + 0.148602i \(0.952523\pi\)
\(788\) −9.37539 + 6.81162i −0.333985 + 0.242654i
\(789\) −25.2235 18.3260i −0.897981 0.652421i
\(790\) 10.8282 + 33.3259i 0.385251 + 1.18568i
\(791\) 0.251409 0.00893908
\(792\) 3.95084 43.1632i 0.140387 1.53374i
\(793\) −0.347340 −0.0123344
\(794\) 2.17677 + 6.69941i 0.0772507 + 0.237753i
\(795\) −8.91826 6.47949i −0.316298 0.229804i
\(796\) −21.0039 + 15.2602i −0.744462 + 0.540883i
\(797\) 6.34085 19.5151i 0.224604 0.691262i −0.773727 0.633519i \(-0.781610\pi\)
0.998332 0.0577424i \(-0.0183902\pi\)
\(798\) −1.28823 + 3.96476i −0.0456028 + 0.140351i
\(799\) 11.0102 7.99939i 0.389514 0.282998i
\(800\) 0.977961 + 0.710531i 0.0345762 + 0.0251210i
\(801\) 13.5977 + 41.8494i 0.480451 + 1.47868i
\(802\) −6.35361 −0.224354
\(803\) 10.4276 11.8988i 0.367980 0.419899i
\(804\) 52.5160 1.85210
\(805\) −0.342535 1.05422i −0.0120728 0.0371562i
\(806\) −1.90145 1.38149i −0.0669758 0.0486608i
\(807\) −33.1004 + 24.0488i −1.16519 + 0.846558i
\(808\) −6.32598 + 19.4694i −0.222547 + 0.684930i
\(809\) −3.05328 + 9.39703i −0.107348 + 0.330382i −0.990274 0.139129i \(-0.955570\pi\)
0.882927 + 0.469511i \(0.155570\pi\)
\(810\) 114.253 83.0098i 4.01445 2.91667i
\(811\) −32.3846 23.5288i −1.13718 0.826206i −0.150452 0.988617i \(-0.548073\pi\)
−0.986723 + 0.162411i \(0.948073\pi\)
\(812\) −0.254410 0.782993i −0.00892803 0.0274777i
\(813\) 11.0569 0.387782
\(814\) −2.71911 1.16709i −0.0953048 0.0409065i
\(815\) 39.2771 1.37582
\(816\) −12.0456 37.0724i −0.421679 1.29779i
\(817\) 28.4271 + 20.6535i 0.994537 + 0.722574i
\(818\) −37.6573 + 27.3596i −1.31666 + 0.956606i
\(819\) 0.316108 0.972880i 0.0110457 0.0339952i
\(820\) 3.27848 10.0901i 0.114490 0.352363i
\(821\) 11.8023 8.57490i 0.411904 0.299266i −0.362468 0.931996i \(-0.618066\pi\)
0.774372 + 0.632730i \(0.218066\pi\)
\(822\) 39.0398 + 28.3641i 1.36167 + 0.989312i
\(823\) 9.80940 + 30.1902i 0.341934 + 1.05236i 0.963205 + 0.268769i \(0.0866167\pi\)
−0.621271 + 0.783596i \(0.713383\pi\)
\(824\) −7.62288 −0.265555
\(825\) −1.21563 2.04165i −0.0423228 0.0710813i
\(826\) 1.42165 0.0494654
\(827\) −9.51981 29.2990i −0.331036 1.01882i −0.968642 0.248462i \(-0.920075\pi\)
0.637605 0.770363i \(-0.279925\pi\)
\(828\) 31.7751 + 23.0860i 1.10426 + 0.802294i
\(829\) −28.6139 + 20.7892i −0.993800 + 0.722038i −0.960750 0.277416i \(-0.910522\pi\)
−0.0330502 + 0.999454i \(0.510522\pi\)
\(830\) 4.55366 14.0147i 0.158060 0.486459i
\(831\) −13.6213 + 41.9221i −0.472518 + 1.45426i
\(832\) 0.0796484 0.0578679i 0.00276131 0.00200621i
\(833\) 13.0793 + 9.50264i 0.453170 + 0.329247i
\(834\) 4.71913 + 14.5240i 0.163410 + 0.502925i
\(835\) 53.1371 1.83888
\(836\) 20.8238 4.71963i 0.720205 0.163232i
\(837\) −24.3285 −0.840918
\(838\) 10.3584 + 31.8798i 0.357824 + 1.10127i
\(839\) −29.2734 21.2684i −1.01063 0.734266i −0.0462892 0.998928i \(-0.514740\pi\)
−0.964341 + 0.264662i \(0.914740\pi\)
\(840\) −1.12963 + 0.820724i −0.0389759 + 0.0283177i
\(841\) 2.31901 7.13717i 0.0799657 0.246109i
\(842\) 3.81329 11.7361i 0.131415 0.404453i
\(843\) −59.5672 + 43.2781i −2.05160 + 1.49058i
\(844\) −15.8976 11.5503i −0.547218 0.397577i
\(845\) 0.676170 + 2.08104i 0.0232610 + 0.0715899i
\(846\) 87.3875 3.00444
\(847\) −0.637396 + 1.17591i −0.0219012 + 0.0404047i
\(848\) −7.43461 −0.255306
\(849\) −23.7542 73.1080i −0.815243 2.50906i
\(850\) −0.701469 0.509647i −0.0240602 0.0174807i
\(851\) −1.70223 + 1.23674i −0.0583515 + 0.0423949i
\(852\) 6.34906 19.5404i 0.217515 0.669443i
\(853\) −15.9420 + 49.0645i −0.545845 + 1.67994i 0.173128 + 0.984899i \(0.444613\pi\)
−0.718973 + 0.695038i \(0.755387\pi\)
\(854\) −0.0603602 + 0.0438543i −0.00206548 + 0.00150066i
\(855\) −85.5551 62.1594i −2.92592 2.12581i
\(856\) 2.17850 + 6.70473i 0.0744595 + 0.229163i
\(857\) 45.6165 1.55823 0.779115 0.626881i \(-0.215669\pi\)
0.779115 + 0.626881i \(0.215669\pi\)
\(858\) −19.3034 + 4.37505i −0.659008 + 0.149362i
\(859\) 6.62386 0.226003 0.113002 0.993595i \(-0.463953\pi\)
0.113002 + 0.993595i \(0.463953\pi\)
\(860\) −4.63461 14.2639i −0.158039 0.486394i
\(861\) −1.43788 1.04468i −0.0490030 0.0356027i
\(862\) 37.0491 26.9178i 1.26190 0.916822i
\(863\) 11.8998 36.6238i 0.405074 1.24669i −0.515760 0.856733i \(-0.672490\pi\)
0.920834 0.389956i \(-0.127510\pi\)
\(864\) 32.2086 99.1279i 1.09576 3.37240i
\(865\) −45.5268 + 33.0772i −1.54796 + 1.12466i
\(866\) −14.8327 10.7766i −0.504034 0.366202i
\(867\) −12.1550 37.4093i −0.412806 1.27049i
\(868\) −0.181295 −0.00615355
\(869\) −15.3817 25.8336i −0.521787 0.876344i
\(870\) 78.8973 2.67487
\(871\) 4.28665 + 13.1929i 0.145248 + 0.447026i
\(872\) −11.8659 8.62106i −0.401829 0.291946i
\(873\) 64.1902 46.6369i 2.17251 1.57842i
\(874\) 13.0651 40.2104i 0.441935 1.36014i
\(875\) −0.428532 + 1.31889i −0.0144870 + 0.0445865i
\(876\) 14.6103 10.6150i 0.493638 0.358649i
\(877\) −12.6072 9.15966i −0.425715 0.309300i 0.354218 0.935163i \(-0.384747\pi\)
−0.779933 + 0.625863i \(0.784747\pi\)
\(878\) −0.819583 2.52242i −0.0276596 0.0851275i
\(879\) 64.9328 2.19013
\(880\) 33.2473 + 14.2703i 1.12077 + 0.481053i
\(881\) −6.59737 −0.222271 −0.111136 0.993805i \(-0.535449\pi\)
−0.111136 + 0.993805i \(0.535449\pi\)
\(882\) 32.0789 + 98.7286i 1.08015 + 3.32437i
\(883\) −17.3032 12.5715i −0.582299 0.423065i 0.257254 0.966344i \(-0.417182\pi\)
−0.839552 + 0.543279i \(0.817182\pi\)
\(884\) −2.09829 + 1.52450i −0.0705731 + 0.0512744i
\(885\) −15.1183 + 46.5295i −0.508197 + 1.56407i
\(886\) −4.16213 + 12.8097i −0.139830 + 0.430351i
\(887\) −36.2104 + 26.3084i −1.21583 + 0.883350i −0.995747 0.0921321i \(-0.970632\pi\)
−0.220080 + 0.975482i \(0.570632\pi\)
\(888\) 2.14424 + 1.55788i 0.0719559 + 0.0522790i
\(889\) −0.612501 1.88509i −0.0205426 0.0632237i
\(890\) −20.2182 −0.677714
\(891\) −79.8640 + 91.1321i −2.67555 + 3.05304i
\(892\) −1.58283 −0.0529969
\(893\) −10.4389 32.1275i −0.349323 1.07511i
\(894\) −49.3843 35.8798i −1.65166 1.20000i
\(895\) −16.0400 + 11.6537i −0.536158 + 0.389542i
\(896\) −0.421826 + 1.29825i −0.0140922 + 0.0433714i
\(897\) −4.34920 + 13.3855i −0.145215 + 0.446927i
\(898\) 35.5635 25.8384i 1.18677 0.862239i
\(899\) −6.50336 4.72497i −0.216899 0.157586i
\(900\) −0.617822 1.90146i −0.0205941 0.0633821i
\(901\) 3.45144 0.114984
\(902\) −2.31066 + 25.2441i −0.0769366 + 0.840538i
\(903\) −2.51251 −0.0836110
\(904\) 0.992522 + 3.05467i 0.0330108 + 0.101597i
\(905\) 27.7742 + 20.1792i 0.923247 + 0.670778i
\(906\) −20.6302 + 14.9887i −0.685393 + 0.497967i
\(907\) 8.41973 25.9133i 0.279573 0.860436i −0.708400 0.705811i \(-0.750583\pi\)
0.987973 0.154626i \(-0.0494171\pi\)
\(908\) −4.69311 + 14.4439i −0.155746 + 0.479338i
\(909\) 89.6903 65.1638i 2.97484 2.16135i
\(910\) 0.380250 + 0.276268i 0.0126052 + 0.00915819i
\(911\) 3.55701 + 10.9474i 0.117849 + 0.362702i 0.992531 0.121996i \(-0.0389295\pi\)
−0.874682 + 0.484698i \(0.838930\pi\)
\(912\) −96.7559 −3.20391
\(913\) −1.15251 + 12.5912i −0.0381425 + 0.416709i
\(914\) 37.9164 1.25416
\(915\) −0.793425 2.44191i −0.0262298 0.0807271i
\(916\) 9.35940 + 6.80000i 0.309243 + 0.224678i
\(917\) 0.0901084 0.0654676i 0.00297564 0.00216193i
\(918\) −23.1025 + 71.1021i −0.762495 + 2.34672i
\(919\) −15.4523 + 47.5572i −0.509724 + 1.56877i 0.282958 + 0.959132i \(0.408684\pi\)
−0.792682 + 0.609636i \(0.791316\pi\)
\(920\) 11.4566 8.32374i 0.377714 0.274425i
\(921\) 42.4175 + 30.8181i 1.39770 + 1.01549i
\(922\) −17.1332 52.7306i −0.564252 1.73659i
\(923\) 5.42714 0.178636
\(924\) −1.00626 + 1.14823i −0.0331034 + 0.0377739i
\(925\) 0.107105 0.00352160
\(926\) −1.59894 4.92105i −0.0525446 0.161716i
\(927\) 33.3979 + 24.2650i 1.09693 + 0.796967i
\(928\) 27.8619 20.2429i 0.914612 0.664505i
\(929\) −6.07033 + 18.6826i −0.199161 + 0.612955i 0.800742 + 0.599010i \(0.204439\pi\)
−0.999903 + 0.0139451i \(0.995561\pi\)
\(930\) 5.36882 16.5235i 0.176050 0.541827i
\(931\) 32.4650 23.5872i 1.06400 0.773040i
\(932\) 0.181007 + 0.131509i 0.00592909 + 0.00430773i
\(933\) −22.4495 69.0923i −0.734962 2.26198i
\(934\) −7.08841 −0.231940
\(935\) −15.4347 6.62485i −0.504769 0.216656i
\(936\) 13.0686 0.427161
\(937\) 0.785137 + 2.41640i 0.0256493 + 0.0789405i 0.963062 0.269281i \(-0.0867859\pi\)
−0.937412 + 0.348221i \(0.886786\pi\)
\(938\) 2.41063 + 1.75143i 0.0787099 + 0.0571861i
\(939\) 44.0217 31.9836i 1.43659 1.04375i
\(940\) −4.45564 + 13.7131i −0.145327 + 0.447270i
\(941\) −0.424996 + 1.30800i −0.0138545 + 0.0426396i −0.957745 0.287620i \(-0.907136\pi\)
0.943890 + 0.330259i \(0.107136\pi\)
\(942\) −102.882 + 74.7479i −3.35206 + 2.43542i
\(943\) 14.5829 + 10.5951i 0.474886 + 0.345025i
\(944\) 10.1962 + 31.3808i 0.331859 + 1.02136i
\(945\) 4.86519 0.158265
\(946\) 18.3333 + 30.7908i 0.596066 + 1.00110i
\(947\) 42.8968 1.39396 0.696979 0.717092i \(-0.254527\pi\)
0.696979 + 0.717092i \(0.254527\pi\)
\(948\) −10.6052 32.6394i −0.344441 1.06008i
\(949\) 3.85926 + 2.80392i 0.125277 + 0.0910191i
\(950\) −1.74117 + 1.26503i −0.0564910 + 0.0410431i
\(951\) −4.63637 + 14.2693i −0.150344 + 0.462713i
\(952\) 0.135095 0.415779i 0.00437845 0.0134755i
\(953\) 7.52652 5.46834i 0.243808 0.177137i −0.459170 0.888348i \(-0.651853\pi\)
0.702978 + 0.711212i \(0.251853\pi\)
\(954\) 17.9295 + 13.0266i 0.580490 + 0.421750i
\(955\) 12.0152 + 36.9790i 0.388803 + 1.19661i
\(956\) 8.49956 0.274895
\(957\) −66.0216 + 14.9636i −2.13418 + 0.483703i
\(958\) 33.1127 1.06982
\(959\) 0.303832 + 0.935100i 0.00981126 + 0.0301960i
\(960\) 0.588769 + 0.427766i 0.0190024 + 0.0138061i
\(961\) 23.6474 17.1809i 0.762820 0.554221i
\(962\) 0.275696 0.848505i 0.00888880 0.0273569i
\(963\) 11.7978 36.3098i 0.380178 1.17007i
\(964\) −3.97571 + 2.88852i −0.128049 + 0.0930330i
\(965\) 8.36409 + 6.07687i 0.269250 + 0.195621i
\(966\) 0.934215 + 2.87522i 0.0300579 + 0.0925087i
\(967\) 29.6970 0.954991 0.477496 0.878634i \(-0.341545\pi\)
0.477496 + 0.878634i \(0.341545\pi\)
\(968\) −16.8038 3.10219i −0.540096 0.0997082i
\(969\) 44.9179 1.44297
\(970\) 11.2656 + 34.6718i 0.361715 + 1.11324i
\(971\) −26.6630 19.3718i −0.855657 0.621671i 0.0710427 0.997473i \(-0.477367\pi\)
−0.926700 + 0.375802i \(0.877367\pi\)
\(972\) −62.1663 + 45.1664i −1.99398 + 1.44871i
\(973\) −0.0961532 + 0.295929i −0.00308253 + 0.00948705i
\(974\) 16.2449 49.9968i 0.520522 1.60200i
\(975\) 0.579610 0.421111i 0.0185624 0.0134864i
\(976\) −1.40093 1.01784i −0.0448428 0.0325802i
\(977\) −5.57704 17.1644i −0.178425 0.549137i 0.821348 0.570428i \(-0.193222\pi\)
−0.999773 + 0.0212906i \(0.993222\pi\)
\(978\) −107.123 −3.42541
\(979\) 16.9186 3.83455i 0.540722 0.122553i
\(980\) −17.1283 −0.547145
\(981\) 24.5452 + 75.5424i 0.783668 + 2.41188i
\(982\) −33.3507 24.2307i −1.06426 0.773233i
\(983\) 8.45127 6.14021i 0.269554 0.195842i −0.444795 0.895633i \(-0.646723\pi\)
0.714348 + 0.699790i \(0.246723\pi\)
\(984\) 7.01658 21.5948i 0.223680 0.688417i
\(985\) 6.99240 21.5204i 0.222796 0.685697i
\(986\) −19.9847 + 14.5197i −0.636443 + 0.462403i
\(987\) 1.95417 + 1.41978i 0.0622018 + 0.0451922i
\(988\) 1.98940 + 6.12275i 0.0632913 + 0.194791i
\(989\) 25.4817 0.810271
\(990\) −55.1764 92.6691i −1.75362 2.94522i
\(991\) 34.2296 1.08734 0.543670 0.839299i \(-0.317034\pi\)
0.543670 + 0.839299i \(0.317034\pi\)
\(992\) −2.34353 7.21263i −0.0744070 0.229001i
\(993\) −4.52979 3.29108i −0.143748 0.104439i
\(994\) 0.943119 0.685216i 0.0299139 0.0217337i
\(995\) 15.6652 48.2125i 0.496620 1.52844i
\(996\) −4.45987 + 13.7261i −0.141316 + 0.434927i
\(997\) −44.5495 + 32.3671i −1.41090 + 1.02508i −0.417705 + 0.908583i \(0.637166\pi\)
−0.993191 + 0.116494i \(0.962834\pi\)
\(998\) −1.25432 0.911318i −0.0397049 0.0288473i
\(999\) −2.85377 8.78299i −0.0902892 0.277882i
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 143.2.h.c.27.2 28
11.3 even 5 1573.2.a.s.1.4 14
11.8 odd 10 1573.2.a.r.1.11 14
11.9 even 5 inner 143.2.h.c.53.2 yes 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
143.2.h.c.27.2 28 1.1 even 1 trivial
143.2.h.c.53.2 yes 28 11.9 even 5 inner
1573.2.a.r.1.11 14 11.8 odd 10
1573.2.a.s.1.4 14 11.3 even 5