Properties

Label 287.2.e.d.165.13
Level $287$
Weight $2$
Character 287.165
Analytic conductor $2.292$
Analytic rank $0$
Dimension $34$
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] = [287,2,Mod(165,287)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(287, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("287.165");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 287 = 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 287.e (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.29170653801\)
Analytic rank: \(0\)
Dimension: \(34\)
Relative dimension: \(17\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 165.13
Character \(\chi\) \(=\) 287.165
Dual form 287.2.e.d.247.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.834451 + 1.44531i) q^{2} +(0.106774 - 0.184938i) q^{3} +(-0.392616 + 0.680030i) q^{4} +(-0.501668 - 0.868914i) q^{5} +0.356391 q^{6} +(2.44503 - 1.01086i) q^{7} +2.02733 q^{8} +(1.47720 + 2.55858i) q^{9} +O(q^{10})\) \(q+(0.834451 + 1.44531i) q^{2} +(0.106774 - 0.184938i) q^{3} +(-0.392616 + 0.680030i) q^{4} +(-0.501668 - 0.868914i) q^{5} +0.356391 q^{6} +(2.44503 - 1.01086i) q^{7} +2.02733 q^{8} +(1.47720 + 2.55858i) q^{9} +(0.837234 - 1.45013i) q^{10} +(1.75783 - 3.04466i) q^{11} +(0.0838424 + 0.145219i) q^{12} -5.76131 q^{13} +(3.50126 + 2.69032i) q^{14} -0.214261 q^{15} +(2.47694 + 4.29018i) q^{16} +(-2.43292 + 4.21394i) q^{17} +(-2.46530 + 4.27002i) q^{18} +(1.97335 + 3.41794i) q^{19} +0.787850 q^{20} +(0.0741198 - 0.560113i) q^{21} +5.86730 q^{22} +(-1.94368 - 3.36655i) q^{23} +(0.216466 - 0.374931i) q^{24} +(1.99666 - 3.45831i) q^{25} +(-4.80753 - 8.32689i) q^{26} +1.27155 q^{27} +(-0.272543 + 2.05957i) q^{28} -5.00025 q^{29} +(-0.178790 - 0.309673i) q^{30} +(-1.70274 + 2.94923i) q^{31} +(-2.10643 + 3.64845i) q^{32} +(-0.375383 - 0.650182i) q^{33} -8.12060 q^{34} +(-2.10494 - 1.61741i) q^{35} -2.31988 q^{36} +(-3.40066 - 5.89012i) q^{37} +(-3.29332 + 5.70420i) q^{38} +(-0.615159 + 1.06549i) q^{39} +(-1.01705 - 1.76157i) q^{40} +1.00000 q^{41} +(0.871387 - 0.360261i) q^{42} +1.87465 q^{43} +(1.38031 + 2.39076i) q^{44} +(1.48213 - 2.56712i) q^{45} +(3.24381 - 5.61844i) q^{46} +(-2.95678 - 5.12129i) q^{47} +1.05789 q^{48} +(4.95634 - 4.94315i) q^{49} +6.66445 q^{50} +(0.519545 + 0.899879i) q^{51} +(2.26198 - 3.91787i) q^{52} +(-5.26714 + 9.12296i) q^{53} +(1.06105 + 1.83779i) q^{54} -3.52739 q^{55} +(4.95688 - 2.04934i) q^{56} +0.842811 q^{57} +(-4.17246 - 7.22691i) q^{58} +(-1.39180 + 2.41066i) q^{59} +(0.0841221 - 0.145704i) q^{60} +(-1.60434 - 2.77881i) q^{61} -5.68341 q^{62} +(6.19816 + 4.76257i) q^{63} +2.87689 q^{64} +(2.89026 + 5.00608i) q^{65} +(0.626476 - 1.08509i) q^{66} +(-3.67953 + 6.37313i) q^{67} +(-1.91040 - 3.30891i) q^{68} -0.830138 q^{69} +(0.581185 - 4.39194i) q^{70} -12.7360 q^{71} +(2.99477 + 5.18709i) q^{72} +(6.11743 - 10.5957i) q^{73} +(5.67537 - 9.83002i) q^{74} +(-0.426383 - 0.738517i) q^{75} -3.09907 q^{76} +(1.22024 - 9.22120i) q^{77} -2.05328 q^{78} +(4.18907 + 7.25569i) q^{79} +(2.48520 - 4.30449i) q^{80} +(-4.29583 + 7.44059i) q^{81} +(0.834451 + 1.44531i) q^{82} -14.9762 q^{83} +(0.351793 + 0.270313i) q^{84} +4.88206 q^{85} +(1.56430 + 2.70944i) q^{86} +(-0.533897 + 0.924738i) q^{87} +(3.56371 - 6.17252i) q^{88} +(-2.79096 - 4.83409i) q^{89} +4.94704 q^{90} +(-14.0866 + 5.82386i) q^{91} +3.05247 q^{92} +(0.363617 + 0.629803i) q^{93} +(4.93457 - 8.54692i) q^{94} +(1.97993 - 3.42934i) q^{95} +(0.449826 + 0.779121i) q^{96} +18.3180 q^{97} +(11.2802 + 3.03863i) q^{98} +10.3867 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34 q - 3 q^{2} - q^{3} - 25 q^{4} + q^{5} + 4 q^{6} - 2 q^{7} + 18 q^{8} - 26 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 34 q - 3 q^{2} - q^{3} - 25 q^{4} + q^{5} + 4 q^{6} - 2 q^{7} + 18 q^{8} - 26 q^{9} + 2 q^{10} - 15 q^{11} - 4 q^{12} - 10 q^{13} + 21 q^{14} + 48 q^{15} - 33 q^{16} - 4 q^{17} - 10 q^{18} - 5 q^{19} - 52 q^{20} + 12 q^{21} + 32 q^{22} - 12 q^{23} - 16 q^{24} - 24 q^{25} - 31 q^{26} - 22 q^{27} + 60 q^{28} + 28 q^{29} + 33 q^{30} + 3 q^{31} - 16 q^{32} - 4 q^{33} - 48 q^{34} + 45 q^{35} + 114 q^{36} - 24 q^{37} - 45 q^{39} - 36 q^{40} + 34 q^{41} + 65 q^{42} + 28 q^{43} + 9 q^{44} + 21 q^{45} - 44 q^{46} - 19 q^{47} - 120 q^{48} - 10 q^{49} - 8 q^{50} - 2 q^{51} + 25 q^{52} - 4 q^{53} - 68 q^{54} + 18 q^{55} + 25 q^{56} - 24 q^{57} + q^{58} + 27 q^{59} - 66 q^{60} + q^{61} - 46 q^{62} + 37 q^{63} + 150 q^{64} - 22 q^{65} + 16 q^{66} - 49 q^{67} - 45 q^{68} + 24 q^{69} + 73 q^{70} + 80 q^{71} + 23 q^{72} + 14 q^{73} - 33 q^{74} - 27 q^{75} - 18 q^{76} - 20 q^{77} - 24 q^{78} - 61 q^{79} + 82 q^{80} - 53 q^{81} - 3 q^{82} - 36 q^{83} + 188 q^{84} - 26 q^{85} + 4 q^{86} + 17 q^{87} - 74 q^{88} - 18 q^{89} - 40 q^{90} + 7 q^{91} + 56 q^{92} + 36 q^{93} + 5 q^{94} - 20 q^{95} - 148 q^{96} + 52 q^{97} + 142 q^{98} + 76 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/287\mathbb{Z}\right)^\times\).

\(n\) \(206\) \(211\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.834451 + 1.44531i 0.590046 + 1.02199i 0.994226 + 0.107310i \(0.0342236\pi\)
−0.404180 + 0.914679i \(0.632443\pi\)
\(3\) 0.106774 0.184938i 0.0616461 0.106774i −0.833555 0.552436i \(-0.813698\pi\)
0.895201 + 0.445662i \(0.147032\pi\)
\(4\) −0.392616 + 0.680030i −0.196308 + 0.340015i
\(5\) −0.501668 0.868914i −0.224353 0.388590i 0.731772 0.681549i \(-0.238693\pi\)
−0.956125 + 0.292959i \(0.905360\pi\)
\(6\) 0.356391 0.145496
\(7\) 2.44503 1.01086i 0.924134 0.382068i
\(8\) 2.02733 0.716769
\(9\) 1.47720 + 2.55858i 0.492400 + 0.852861i
\(10\) 0.837234 1.45013i 0.264757 0.458572i
\(11\) 1.75783 3.04466i 0.530007 0.917999i −0.469380 0.882996i \(-0.655523\pi\)
0.999387 0.0350028i \(-0.0111440\pi\)
\(12\) 0.0838424 + 0.145219i 0.0242032 + 0.0419212i
\(13\) −5.76131 −1.59790 −0.798950 0.601397i \(-0.794611\pi\)
−0.798950 + 0.601397i \(0.794611\pi\)
\(14\) 3.50126 + 2.69032i 0.935751 + 0.719017i
\(15\) −0.214261 −0.0553219
\(16\) 2.47694 + 4.29018i 0.619234 + 1.07255i
\(17\) −2.43292 + 4.21394i −0.590069 + 1.02203i 0.404154 + 0.914691i \(0.367566\pi\)
−0.994223 + 0.107338i \(0.965767\pi\)
\(18\) −2.46530 + 4.27002i −0.581076 + 1.00645i
\(19\) 1.97335 + 3.41794i 0.452717 + 0.784129i 0.998554 0.0537626i \(-0.0171214\pi\)
−0.545837 + 0.837892i \(0.683788\pi\)
\(20\) 0.787850 0.176169
\(21\) 0.0741198 0.560113i 0.0161743 0.122227i
\(22\) 5.86730 1.25091
\(23\) −1.94368 3.36655i −0.405285 0.701974i 0.589070 0.808082i \(-0.299494\pi\)
−0.994355 + 0.106108i \(0.966161\pi\)
\(24\) 0.216466 0.374931i 0.0441860 0.0765324i
\(25\) 1.99666 3.45831i 0.399332 0.691663i
\(26\) −4.80753 8.32689i −0.942834 1.63304i
\(27\) 1.27155 0.244710
\(28\) −0.272543 + 2.05957i −0.0515058 + 0.389222i
\(29\) −5.00025 −0.928523 −0.464261 0.885698i \(-0.653680\pi\)
−0.464261 + 0.885698i \(0.653680\pi\)
\(30\) −0.178790 0.309673i −0.0326424 0.0565384i
\(31\) −1.70274 + 2.94923i −0.305821 + 0.529697i −0.977444 0.211196i \(-0.932264\pi\)
0.671623 + 0.740893i \(0.265598\pi\)
\(32\) −2.10643 + 3.64845i −0.372368 + 0.644961i
\(33\) −0.375383 0.650182i −0.0653457 0.113182i
\(34\) −8.12060 −1.39267
\(35\) −2.10494 1.61741i −0.355800 0.273392i
\(36\) −2.31988 −0.386647
\(37\) −3.40066 5.89012i −0.559065 0.968329i −0.997575 0.0696026i \(-0.977827\pi\)
0.438510 0.898726i \(-0.355506\pi\)
\(38\) −3.29332 + 5.70420i −0.534248 + 0.925344i
\(39\) −0.615159 + 1.06549i −0.0985043 + 0.170615i
\(40\) −1.01705 1.76157i −0.160809 0.278529i
\(41\) 1.00000 0.156174
\(42\) 0.871387 0.360261i 0.134458 0.0555894i
\(43\) 1.87465 0.285881 0.142940 0.989731i \(-0.454344\pi\)
0.142940 + 0.989731i \(0.454344\pi\)
\(44\) 1.38031 + 2.39076i 0.208089 + 0.360421i
\(45\) 1.48213 2.56712i 0.220942 0.382683i
\(46\) 3.24381 5.61844i 0.478273 0.828393i
\(47\) −2.95678 5.12129i −0.431290 0.747016i 0.565695 0.824615i \(-0.308608\pi\)
−0.996985 + 0.0775985i \(0.975275\pi\)
\(48\) 1.05789 0.152694
\(49\) 4.95634 4.94315i 0.708048 0.706164i
\(50\) 6.66445 0.942496
\(51\) 0.519545 + 0.899879i 0.0727509 + 0.126008i
\(52\) 2.26198 3.91787i 0.313680 0.543310i
\(53\) −5.26714 + 9.12296i −0.723498 + 1.25314i 0.236091 + 0.971731i \(0.424134\pi\)
−0.959589 + 0.281404i \(0.909200\pi\)
\(54\) 1.06105 + 1.83779i 0.144390 + 0.250091i
\(55\) −3.52739 −0.475634
\(56\) 4.95688 2.04934i 0.662391 0.273855i
\(57\) 0.842811 0.111633
\(58\) −4.17246 7.22691i −0.547871 0.948940i
\(59\) −1.39180 + 2.41066i −0.181196 + 0.313841i −0.942288 0.334803i \(-0.891330\pi\)
0.761092 + 0.648644i \(0.224664\pi\)
\(60\) 0.0841221 0.145704i 0.0108601 0.0188103i
\(61\) −1.60434 2.77881i −0.205415 0.355790i 0.744850 0.667232i \(-0.232521\pi\)
−0.950265 + 0.311443i \(0.899188\pi\)
\(62\) −5.68341 −0.721793
\(63\) 6.19816 + 4.76257i 0.780894 + 0.600028i
\(64\) 2.87689 0.359611
\(65\) 2.89026 + 5.00608i 0.358493 + 0.620928i
\(66\) 0.626476 1.08509i 0.0771139 0.133565i
\(67\) −3.67953 + 6.37313i −0.449526 + 0.778602i −0.998355 0.0573327i \(-0.981740\pi\)
0.548829 + 0.835935i \(0.315074\pi\)
\(68\) −1.91040 3.30891i −0.231670 0.401265i
\(69\) −0.830138 −0.0999369
\(70\) 0.581185 4.39194i 0.0694649 0.524937i
\(71\) −12.7360 −1.51149 −0.755745 0.654866i \(-0.772725\pi\)
−0.755745 + 0.654866i \(0.772725\pi\)
\(72\) 2.99477 + 5.18709i 0.352937 + 0.611304i
\(73\) 6.11743 10.5957i 0.715992 1.24013i −0.246584 0.969121i \(-0.579308\pi\)
0.962576 0.271012i \(-0.0873585\pi\)
\(74\) 5.67537 9.83002i 0.659748 1.14272i
\(75\) −0.426383 0.738517i −0.0492345 0.0852767i
\(76\) −3.09907 −0.355488
\(77\) 1.22024 9.22120i 0.139059 1.05085i
\(78\) −2.05328 −0.232488
\(79\) 4.18907 + 7.25569i 0.471308 + 0.816329i 0.999461 0.0328201i \(-0.0104488\pi\)
−0.528154 + 0.849149i \(0.677116\pi\)
\(80\) 2.48520 4.30449i 0.277854 0.481257i
\(81\) −4.29583 + 7.44059i −0.477314 + 0.826732i
\(82\) 0.834451 + 1.44531i 0.0921497 + 0.159608i
\(83\) −14.9762 −1.64385 −0.821923 0.569599i \(-0.807099\pi\)
−0.821923 + 0.569599i \(0.807099\pi\)
\(84\) 0.351793 + 0.270313i 0.0383838 + 0.0294935i
\(85\) 4.88206 0.529534
\(86\) 1.56430 + 2.70944i 0.168683 + 0.292167i
\(87\) −0.533897 + 0.924738i −0.0572398 + 0.0991423i
\(88\) 3.56371 6.17252i 0.379893 0.657993i
\(89\) −2.79096 4.83409i −0.295842 0.512413i 0.679339 0.733825i \(-0.262267\pi\)
−0.975180 + 0.221412i \(0.928933\pi\)
\(90\) 4.94704 0.521464
\(91\) −14.0866 + 5.82386i −1.47667 + 0.610507i
\(92\) 3.05247 0.318242
\(93\) 0.363617 + 0.629803i 0.0377053 + 0.0653076i
\(94\) 4.93457 8.54692i 0.508962 0.881548i
\(95\) 1.97993 3.42934i 0.203137 0.351843i
\(96\) 0.449826 + 0.779121i 0.0459101 + 0.0795187i
\(97\) 18.3180 1.85991 0.929957 0.367668i \(-0.119844\pi\)
0.929957 + 0.367668i \(0.119844\pi\)
\(98\) 11.2802 + 3.03863i 1.13947 + 0.306948i
\(99\) 10.3867 1.04390
\(100\) 1.56784 + 2.71558i 0.156784 + 0.271558i
\(101\) 1.99815 3.46090i 0.198824 0.344373i −0.749324 0.662204i \(-0.769621\pi\)
0.948147 + 0.317831i \(0.102955\pi\)
\(102\) −0.867070 + 1.50181i −0.0858527 + 0.148701i
\(103\) 1.48485 + 2.57183i 0.146306 + 0.253410i 0.929860 0.367915i \(-0.119928\pi\)
−0.783553 + 0.621325i \(0.786595\pi\)
\(104\) −11.6801 −1.14533
\(105\) −0.523874 + 0.216587i −0.0511248 + 0.0211367i
\(106\) −17.5807 −1.70759
\(107\) −5.85331 10.1382i −0.565861 0.980100i −0.996969 0.0777998i \(-0.975211\pi\)
0.431108 0.902300i \(-0.358123\pi\)
\(108\) −0.499231 + 0.864694i −0.0480385 + 0.0832052i
\(109\) −7.27889 + 12.6074i −0.697191 + 1.20757i 0.272246 + 0.962228i \(0.412234\pi\)
−0.969437 + 0.245342i \(0.921100\pi\)
\(110\) −2.94344 5.09818i −0.280646 0.486093i
\(111\) −1.45241 −0.137857
\(112\) 10.3929 + 7.98579i 0.982041 + 0.754586i
\(113\) 10.1579 0.955576 0.477788 0.878475i \(-0.341439\pi\)
0.477788 + 0.878475i \(0.341439\pi\)
\(114\) 0.703284 + 1.21812i 0.0658686 + 0.114088i
\(115\) −1.95016 + 3.37778i −0.181853 + 0.314979i
\(116\) 1.96318 3.40032i 0.182276 0.315712i
\(117\) −8.51060 14.7408i −0.786805 1.36279i
\(118\) −4.64554 −0.427657
\(119\) −1.68887 + 12.7625i −0.154818 + 1.16994i
\(120\) −0.434377 −0.0396530
\(121\) −0.679961 1.17773i −0.0618146 0.107066i
\(122\) 2.67749 4.63755i 0.242409 0.419864i
\(123\) 0.106774 0.184938i 0.00962750 0.0166753i
\(124\) −1.33704 2.31583i −0.120070 0.207967i
\(125\) −9.02332 −0.807070
\(126\) −1.71134 + 12.9324i −0.152459 + 1.15211i
\(127\) 12.0850 1.07237 0.536186 0.844100i \(-0.319865\pi\)
0.536186 + 0.844100i \(0.319865\pi\)
\(128\) 6.61349 + 11.4549i 0.584555 + 1.01248i
\(129\) 0.200164 0.346694i 0.0176234 0.0305247i
\(130\) −4.82357 + 8.35466i −0.423055 + 0.732752i
\(131\) 4.30481 + 7.45614i 0.376113 + 0.651446i 0.990493 0.137564i \(-0.0439272\pi\)
−0.614380 + 0.789010i \(0.710594\pi\)
\(132\) 0.589524 0.0513115
\(133\) 8.27994 + 6.36219i 0.717962 + 0.551672i
\(134\) −12.2815 −1.06096
\(135\) −0.637897 1.10487i −0.0549014 0.0950920i
\(136\) −4.93232 + 8.54303i −0.422943 + 0.732559i
\(137\) 0.0862307 0.149356i 0.00736718 0.0127603i −0.862318 0.506367i \(-0.830988\pi\)
0.869685 + 0.493606i \(0.164322\pi\)
\(138\) −0.692709 1.19981i −0.0589673 0.102134i
\(139\) 8.79715 0.746164 0.373082 0.927798i \(-0.378301\pi\)
0.373082 + 0.927798i \(0.378301\pi\)
\(140\) 1.92632 0.796404i 0.162804 0.0673084i
\(141\) −1.26283 −0.106349
\(142\) −10.6276 18.4075i −0.891848 1.54473i
\(143\) −10.1274 + 17.5412i −0.846898 + 1.46687i
\(144\) −7.31786 + 12.6749i −0.609821 + 1.05624i
\(145\) 2.50846 + 4.34479i 0.208317 + 0.360815i
\(146\) 20.4188 1.68987
\(147\) −0.384969 1.44442i −0.0317517 0.119134i
\(148\) 5.34061 0.438995
\(149\) −0.343506 0.594969i −0.0281411 0.0487418i 0.851612 0.524173i \(-0.175625\pi\)
−0.879753 + 0.475431i \(0.842292\pi\)
\(150\) 0.711592 1.23251i 0.0581012 0.100634i
\(151\) −4.45320 + 7.71317i −0.362396 + 0.627689i −0.988355 0.152168i \(-0.951375\pi\)
0.625958 + 0.779856i \(0.284708\pi\)
\(152\) 4.00063 + 6.92929i 0.324494 + 0.562039i
\(153\) −14.3756 −1.16220
\(154\) 14.3457 5.93100i 1.15601 0.477934i
\(155\) 3.41684 0.274447
\(156\) −0.483042 0.836654i −0.0386743 0.0669859i
\(157\) 7.95246 13.7741i 0.634676 1.09929i −0.351908 0.936035i \(-0.614467\pi\)
0.986584 0.163256i \(-0.0521997\pi\)
\(158\) −6.99115 + 12.1090i −0.556186 + 0.963342i
\(159\) 1.12479 + 1.94819i 0.0892017 + 0.154502i
\(160\) 4.22692 0.334167
\(161\) −8.15545 6.26653i −0.642739 0.493872i
\(162\) −14.3386 −1.12655
\(163\) −10.1276 17.5415i −0.793254 1.37396i −0.923942 0.382533i \(-0.875052\pi\)
0.130687 0.991424i \(-0.458282\pi\)
\(164\) −0.392616 + 0.680030i −0.0306581 + 0.0531014i
\(165\) −0.376635 + 0.652351i −0.0293210 + 0.0507854i
\(166\) −12.4969 21.6452i −0.969944 1.67999i
\(167\) 16.9622 1.31258 0.656288 0.754511i \(-0.272126\pi\)
0.656288 + 0.754511i \(0.272126\pi\)
\(168\) 0.150265 1.13553i 0.0115932 0.0876083i
\(169\) 20.1927 1.55329
\(170\) 4.07384 + 7.05610i 0.312449 + 0.541178i
\(171\) −5.83005 + 10.0980i −0.445835 + 0.772210i
\(172\) −0.736015 + 1.27482i −0.0561206 + 0.0972037i
\(173\) 6.93416 + 12.0103i 0.527195 + 0.913128i 0.999498 + 0.0316916i \(0.0100895\pi\)
−0.472303 + 0.881436i \(0.656577\pi\)
\(174\) −1.78204 −0.135096
\(175\) 1.38603 10.4740i 0.104774 0.791761i
\(176\) 17.4162 1.31279
\(177\) 0.297216 + 0.514793i 0.0223401 + 0.0386942i
\(178\) 4.65784 8.06762i 0.349120 0.604694i
\(179\) −6.15100 + 10.6538i −0.459747 + 0.796306i −0.998947 0.0458720i \(-0.985393\pi\)
0.539200 + 0.842178i \(0.318727\pi\)
\(180\) 1.16381 + 2.01578i 0.0867454 + 0.150247i
\(181\) −1.79830 −0.133666 −0.0668332 0.997764i \(-0.521290\pi\)
−0.0668332 + 0.997764i \(0.521290\pi\)
\(182\) −20.1718 15.4998i −1.49524 1.14892i
\(183\) −0.685210 −0.0506522
\(184\) −3.94047 6.82510i −0.290496 0.503153i
\(185\) −3.41200 + 5.90976i −0.250855 + 0.434494i
\(186\) −0.606841 + 1.05108i −0.0444958 + 0.0770689i
\(187\) 8.55333 + 14.8148i 0.625481 + 1.08337i
\(188\) 4.64351 0.338662
\(189\) 3.10898 1.28536i 0.226145 0.0934960i
\(190\) 6.60862 0.479439
\(191\) 1.08278 + 1.87543i 0.0783472 + 0.135701i 0.902537 0.430612i \(-0.141702\pi\)
−0.824190 + 0.566314i \(0.808369\pi\)
\(192\) 0.307177 0.532047i 0.0221686 0.0383972i
\(193\) −3.51757 + 6.09260i −0.253200 + 0.438555i −0.964405 0.264429i \(-0.914816\pi\)
0.711205 + 0.702985i \(0.248150\pi\)
\(194\) 15.2855 + 26.4753i 1.09743 + 1.90081i
\(195\) 1.23442 0.0883988
\(196\) 1.41556 + 5.31122i 0.101111 + 0.379373i
\(197\) −9.47409 −0.675001 −0.337500 0.941325i \(-0.609581\pi\)
−0.337500 + 0.941325i \(0.609581\pi\)
\(198\) 8.66717 + 15.0120i 0.615949 + 1.06685i
\(199\) −1.77877 + 3.08091i −0.126093 + 0.218400i −0.922160 0.386809i \(-0.873577\pi\)
0.796066 + 0.605209i \(0.206911\pi\)
\(200\) 4.04788 7.01114i 0.286229 0.495763i
\(201\) 0.785757 + 1.36097i 0.0554231 + 0.0959955i
\(202\) 6.66944 0.469260
\(203\) −12.2258 + 5.05454i −0.858080 + 0.354759i
\(204\) −0.815927 −0.0571263
\(205\) −0.501668 0.868914i −0.0350380 0.0606876i
\(206\) −2.47806 + 4.29213i −0.172655 + 0.299047i
\(207\) 5.74239 9.94612i 0.399124 0.691303i
\(208\) −14.2704 24.7171i −0.989475 1.71382i
\(209\) 13.8753 0.959773
\(210\) −0.750182 0.576429i −0.0517675 0.0397774i
\(211\) 21.6699 1.49182 0.745908 0.666049i \(-0.232016\pi\)
0.745908 + 0.666049i \(0.232016\pi\)
\(212\) −4.13593 7.16363i −0.284057 0.492000i
\(213\) −1.35988 + 2.35538i −0.0931775 + 0.161388i
\(214\) 9.76860 16.9197i 0.667768 1.15661i
\(215\) −0.940449 1.62891i −0.0641381 0.111090i
\(216\) 2.57785 0.175401
\(217\) −1.18200 + 8.93218i −0.0802391 + 0.606356i
\(218\) −24.2955 −1.64550
\(219\) −1.30637 2.26270i −0.0882762 0.152899i
\(220\) 1.38491 2.39873i 0.0933706 0.161723i
\(221\) 14.0168 24.2778i 0.942871 1.63310i
\(222\) −1.21197 2.09919i −0.0813418 0.140888i
\(223\) 8.57235 0.574047 0.287023 0.957924i \(-0.407334\pi\)
0.287023 + 0.957924i \(0.407334\pi\)
\(224\) −1.46223 + 11.0499i −0.0976994 + 0.738301i
\(225\) 11.7978 0.786523
\(226\) 8.47628 + 14.6813i 0.563834 + 0.976589i
\(227\) 6.28343 10.8832i 0.417046 0.722345i −0.578595 0.815615i \(-0.696399\pi\)
0.995641 + 0.0932701i \(0.0297320\pi\)
\(228\) −0.330901 + 0.573137i −0.0219144 + 0.0379569i
\(229\) −9.90998 17.1646i −0.654870 1.13427i −0.981926 0.189263i \(-0.939390\pi\)
0.327057 0.945005i \(-0.393943\pi\)
\(230\) −6.50925 −0.429207
\(231\) −1.57506 1.21026i −0.103631 0.0796289i
\(232\) −10.1371 −0.665536
\(233\) −12.3302 21.3565i −0.807776 1.39911i −0.914401 0.404809i \(-0.867338\pi\)
0.106625 0.994299i \(-0.465995\pi\)
\(234\) 14.2034 24.6009i 0.928502 1.60821i
\(235\) −2.96664 + 5.13837i −0.193522 + 0.335190i
\(236\) −1.09288 1.89293i −0.0711405 0.123219i
\(237\) 1.78914 0.116217
\(238\) −19.8551 + 8.20876i −1.28701 + 0.532095i
\(239\) 22.9924 1.48726 0.743629 0.668593i \(-0.233103\pi\)
0.743629 + 0.668593i \(0.233103\pi\)
\(240\) −0.530710 0.919217i −0.0342572 0.0593352i
\(241\) 8.59097 14.8800i 0.553393 0.958504i −0.444634 0.895712i \(-0.646666\pi\)
0.998027 0.0627919i \(-0.0200004\pi\)
\(242\) 1.13479 1.96551i 0.0729469 0.126348i
\(243\) 2.82469 + 4.89251i 0.181204 + 0.313855i
\(244\) 2.51956 0.161298
\(245\) −6.78161 1.82681i −0.433261 0.116711i
\(246\) 0.356391 0.0227227
\(247\) −11.3691 19.6918i −0.723397 1.25296i
\(248\) −3.45201 + 5.97906i −0.219203 + 0.379671i
\(249\) −1.59907 + 2.76966i −0.101337 + 0.175520i
\(250\) −7.52951 13.0415i −0.476208 0.824817i
\(251\) 23.4755 1.48176 0.740879 0.671638i \(-0.234409\pi\)
0.740879 + 0.671638i \(0.234409\pi\)
\(252\) −5.67219 + 2.34507i −0.357314 + 0.147726i
\(253\) −13.6666 −0.859215
\(254\) 10.0843 + 17.4666i 0.632748 + 1.09595i
\(255\) 0.521278 0.902881i 0.0326437 0.0565406i
\(256\) −8.16037 + 14.1342i −0.510023 + 0.883386i
\(257\) 6.95657 + 12.0491i 0.433939 + 0.751604i 0.997208 0.0746689i \(-0.0237900\pi\)
−0.563269 + 0.826273i \(0.690457\pi\)
\(258\) 0.668107 0.0415945
\(259\) −14.2688 10.9639i −0.886619 0.681265i
\(260\) −4.53905 −0.281500
\(261\) −7.38636 12.7935i −0.457204 0.791901i
\(262\) −7.18430 + 12.4436i −0.443847 + 0.768766i
\(263\) −10.6662 + 18.4745i −0.657709 + 1.13918i 0.323499 + 0.946229i \(0.395141\pi\)
−0.981207 + 0.192956i \(0.938192\pi\)
\(264\) −0.761024 1.31813i −0.0468378 0.0811254i
\(265\) 10.5694 0.649275
\(266\) −2.28614 + 17.2760i −0.140172 + 1.05926i
\(267\) −1.19201 −0.0729499
\(268\) −2.88928 5.00438i −0.176491 0.305691i
\(269\) 13.6361 23.6184i 0.831406 1.44004i −0.0655176 0.997851i \(-0.520870\pi\)
0.896923 0.442186i \(-0.145797\pi\)
\(270\) 1.06459 1.84392i 0.0647887 0.112217i
\(271\) 12.1631 + 21.0671i 0.738854 + 1.27973i 0.953012 + 0.302933i \(0.0979660\pi\)
−0.214158 + 0.976799i \(0.568701\pi\)
\(272\) −24.1047 −1.46156
\(273\) −0.427027 + 3.22699i −0.0258449 + 0.195306i
\(274\) 0.287821 0.0173879
\(275\) −7.01959 12.1583i −0.423297 0.733172i
\(276\) 0.325925 0.564519i 0.0196184 0.0339801i
\(277\) 0.610732 1.05782i 0.0366953 0.0635581i −0.847094 0.531442i \(-0.821650\pi\)
0.883790 + 0.467884i \(0.154984\pi\)
\(278\) 7.34078 + 12.7146i 0.440271 + 0.762572i
\(279\) −10.0611 −0.602344
\(280\) −4.26741 3.27901i −0.255026 0.195959i
\(281\) −16.7952 −1.00192 −0.500960 0.865470i \(-0.667020\pi\)
−0.500960 + 0.865470i \(0.667020\pi\)
\(282\) −1.05377 1.82518i −0.0627510 0.108688i
\(283\) −1.36928 + 2.37166i −0.0813953 + 0.140981i −0.903850 0.427851i \(-0.859271\pi\)
0.822454 + 0.568831i \(0.192604\pi\)
\(284\) 5.00037 8.66089i 0.296717 0.513929i
\(285\) −0.422811 0.732330i −0.0250452 0.0433795i
\(286\) −33.8034 −1.99883
\(287\) 2.44503 1.01086i 0.144326 0.0596690i
\(288\) −12.4465 −0.733416
\(289\) −3.33817 5.78188i −0.196363 0.340111i
\(290\) −4.18638 + 7.25102i −0.245833 + 0.425795i
\(291\) 1.95589 3.38771i 0.114657 0.198591i
\(292\) 4.80360 + 8.32008i 0.281109 + 0.486896i
\(293\) 7.34300 0.428983 0.214491 0.976726i \(-0.431191\pi\)
0.214491 + 0.976726i \(0.431191\pi\)
\(294\) 1.76639 1.76170i 0.103018 0.102744i
\(295\) 2.79288 0.162608
\(296\) −6.89426 11.9412i −0.400721 0.694068i
\(297\) 2.23518 3.87144i 0.129698 0.224644i
\(298\) 0.573277 0.992945i 0.0332090 0.0575198i
\(299\) 11.1981 + 19.3957i 0.647605 + 1.12168i
\(300\) 0.669619 0.0386605
\(301\) 4.58356 1.89500i 0.264192 0.109226i
\(302\) −14.8639 −0.855321
\(303\) −0.426702 0.739070i −0.0245134 0.0424585i
\(304\) −9.77572 + 16.9320i −0.560676 + 0.971119i
\(305\) −1.60970 + 2.78808i −0.0921709 + 0.159645i
\(306\) −11.9957 20.7772i −0.685750 1.18775i
\(307\) −30.3452 −1.73189 −0.865945 0.500139i \(-0.833282\pi\)
−0.865945 + 0.500139i \(0.833282\pi\)
\(308\) 5.79161 + 4.45019i 0.330007 + 0.253573i
\(309\) 0.634173 0.0360768
\(310\) 2.85118 + 4.93839i 0.161936 + 0.280482i
\(311\) −3.46143 + 5.99537i −0.196280 + 0.339967i −0.947319 0.320291i \(-0.896219\pi\)
0.751040 + 0.660257i \(0.229553\pi\)
\(312\) −1.24713 + 2.16009i −0.0706049 + 0.122291i
\(313\) −15.3777 26.6350i −0.869201 1.50550i −0.862814 0.505521i \(-0.831300\pi\)
−0.00638714 0.999980i \(-0.502033\pi\)
\(314\) 26.5438 1.49795
\(315\) 1.02885 7.77489i 0.0579693 0.438066i
\(316\) −6.57878 −0.370085
\(317\) −1.45302 2.51670i −0.0816096 0.141352i 0.822332 0.569008i \(-0.192673\pi\)
−0.903941 + 0.427656i \(0.859339\pi\)
\(318\) −1.87716 + 3.25134i −0.105266 + 0.182326i
\(319\) −8.78961 + 15.2240i −0.492123 + 0.852383i
\(320\) −1.44324 2.49977i −0.0806797 0.139741i
\(321\) −2.49993 −0.139533
\(322\) 2.25176 17.0163i 0.125486 0.948279i
\(323\) −19.2040 −1.06854
\(324\) −3.37322 5.84258i −0.187401 0.324588i
\(325\) −11.5034 + 19.9244i −0.638092 + 1.10521i
\(326\) 16.9020 29.2750i 0.936113 1.62139i
\(327\) 1.55439 + 2.69229i 0.0859582 + 0.148884i
\(328\) 2.02733 0.111941
\(329\) −12.4063 9.53282i −0.683981 0.525561i
\(330\) −1.25713 −0.0692029
\(331\) −2.32737 4.03113i −0.127924 0.221571i 0.794948 0.606677i \(-0.207498\pi\)
−0.922872 + 0.385106i \(0.874165\pi\)
\(332\) 5.87987 10.1842i 0.322700 0.558932i
\(333\) 10.0469 17.4017i 0.550567 0.953609i
\(334\) 14.1541 + 24.5157i 0.774479 + 1.34144i
\(335\) 7.38360 0.403409
\(336\) 2.58658 1.06938i 0.141109 0.0583393i
\(337\) 23.8266 1.29792 0.648960 0.760823i \(-0.275204\pi\)
0.648960 + 0.760823i \(0.275204\pi\)
\(338\) 16.8498 + 29.1847i 0.916509 + 1.58744i
\(339\) 1.08460 1.87859i 0.0589076 0.102031i
\(340\) −1.91677 + 3.31995i −0.103952 + 0.180050i
\(341\) 5.98627 + 10.3685i 0.324174 + 0.561487i
\(342\) −19.4596 −1.05225
\(343\) 7.12157 17.0963i 0.384528 0.923113i
\(344\) 3.80052 0.204910
\(345\) 0.416454 + 0.721319i 0.0224211 + 0.0388345i
\(346\) −11.5724 + 20.0440i −0.622138 + 1.07757i
\(347\) 8.58994 14.8782i 0.461132 0.798704i −0.537885 0.843018i \(-0.680777\pi\)
0.999018 + 0.0443135i \(0.0141100\pi\)
\(348\) −0.419233 0.726133i −0.0224732 0.0389248i
\(349\) 10.7991 0.578063 0.289031 0.957320i \(-0.406667\pi\)
0.289031 + 0.957320i \(0.406667\pi\)
\(350\) 16.2948 6.73681i 0.870993 0.360098i
\(351\) −7.32581 −0.391023
\(352\) 7.40552 + 12.8267i 0.394716 + 0.683668i
\(353\) −2.10949 + 3.65374i −0.112277 + 0.194469i −0.916688 0.399604i \(-0.869148\pi\)
0.804411 + 0.594073i \(0.202481\pi\)
\(354\) −0.496024 + 0.859138i −0.0263634 + 0.0456627i
\(355\) 6.38926 + 11.0665i 0.339107 + 0.587350i
\(356\) 4.38310 0.232304
\(357\) 2.17995 + 1.67504i 0.115375 + 0.0886528i
\(358\) −20.5308 −1.08509
\(359\) −0.977388 1.69289i −0.0515846 0.0893471i 0.839080 0.544008i \(-0.183094\pi\)
−0.890665 + 0.454661i \(0.849761\pi\)
\(360\) 3.00476 5.20439i 0.158365 0.274296i
\(361\) 1.71179 2.96491i 0.0900944 0.156048i
\(362\) −1.50059 2.59910i −0.0788693 0.136606i
\(363\) −0.290409 −0.0152425
\(364\) 1.57021 11.8658i 0.0823012 0.621939i
\(365\) −12.2757 −0.642538
\(366\) −0.571774 0.990342i −0.0298871 0.0517660i
\(367\) −1.07134 + 1.85561i −0.0559233 + 0.0968619i −0.892632 0.450787i \(-0.851144\pi\)
0.836709 + 0.547648i \(0.184477\pi\)
\(368\) 9.62873 16.6775i 0.501932 0.869372i
\(369\) 1.47720 + 2.55858i 0.0768999 + 0.133195i
\(370\) −11.3886 −0.592065
\(371\) −3.65631 + 27.6302i −0.189826 + 1.43449i
\(372\) −0.571047 −0.0296074
\(373\) 4.49415 + 7.78410i 0.232698 + 0.403046i 0.958601 0.284752i \(-0.0919112\pi\)
−0.725903 + 0.687797i \(0.758578\pi\)
\(374\) −14.2747 + 24.7244i −0.738125 + 1.27847i
\(375\) −0.963457 + 1.66876i −0.0497527 + 0.0861742i
\(376\) −5.99436 10.3825i −0.309135 0.535438i
\(377\) 28.8080 1.48369
\(378\) 4.45203 + 3.42088i 0.228988 + 0.175951i
\(379\) 25.3654 1.30293 0.651467 0.758677i \(-0.274154\pi\)
0.651467 + 0.758677i \(0.274154\pi\)
\(380\) 1.55470 + 2.69283i 0.0797546 + 0.138139i
\(381\) 1.29037 2.23498i 0.0661075 0.114502i
\(382\) −1.80705 + 3.12991i −0.0924569 + 0.160140i
\(383\) −12.2791 21.2680i −0.627432 1.08674i −0.988065 0.154036i \(-0.950773\pi\)
0.360633 0.932708i \(-0.382561\pi\)
\(384\) 2.82460 0.144142
\(385\) −8.62458 + 3.56569i −0.439549 + 0.181725i
\(386\) −11.7409 −0.597598
\(387\) 2.76922 + 4.79644i 0.140768 + 0.243816i
\(388\) −7.19195 + 12.4568i −0.365116 + 0.632399i
\(389\) 11.6636 20.2019i 0.591368 1.02428i −0.402681 0.915341i \(-0.631921\pi\)
0.994048 0.108939i \(-0.0347452\pi\)
\(390\) 1.03006 + 1.78412i 0.0521594 + 0.0903427i
\(391\) 18.9152 0.956584
\(392\) 10.0481 10.0214i 0.507507 0.506157i
\(393\) 1.83857 0.0927435
\(394\) −7.90566 13.6930i −0.398281 0.689843i
\(395\) 4.20305 7.27989i 0.211478 0.366291i
\(396\) −4.07797 + 7.06325i −0.204926 + 0.354942i
\(397\) 8.94086 + 15.4860i 0.448729 + 0.777221i 0.998304 0.0582232i \(-0.0185435\pi\)
−0.549575 + 0.835445i \(0.685210\pi\)
\(398\) −5.93717 −0.297604
\(399\) 2.06070 0.851961i 0.103164 0.0426514i
\(400\) 19.7824 0.989120
\(401\) 10.9423 + 18.9526i 0.546433 + 0.946449i 0.998515 + 0.0544730i \(0.0173479\pi\)
−0.452083 + 0.891976i \(0.649319\pi\)
\(402\) −1.31135 + 2.27133i −0.0654043 + 0.113284i
\(403\) 9.81001 16.9914i 0.488671 0.846404i
\(404\) 1.56901 + 2.71761i 0.0780612 + 0.135206i
\(405\) 8.62031 0.428347
\(406\) −17.5072 13.4523i −0.868866 0.667624i
\(407\) −23.9112 −1.18523
\(408\) 1.05329 + 1.82435i 0.0521456 + 0.0903188i
\(409\) −8.75032 + 15.1560i −0.432675 + 0.749416i −0.997103 0.0760671i \(-0.975764\pi\)
0.564427 + 0.825483i \(0.309097\pi\)
\(410\) 0.837234 1.45013i 0.0413480 0.0716169i
\(411\) −0.0184144 0.0318947i −0.000908316 0.00157325i
\(412\) −2.33190 −0.114884
\(413\) −0.966147 + 7.30104i −0.0475410 + 0.359261i
\(414\) 19.1670 0.942006
\(415\) 7.51305 + 13.0130i 0.368801 + 0.638782i
\(416\) 12.1358 21.0199i 0.595008 1.03058i
\(417\) 0.939308 1.62693i 0.0459981 0.0796711i
\(418\) 11.5782 + 20.0541i 0.566310 + 0.980877i
\(419\) 7.23185 0.353299 0.176649 0.984274i \(-0.443474\pi\)
0.176649 + 0.984274i \(0.443474\pi\)
\(420\) 0.0583953 0.441285i 0.00284940 0.0215325i
\(421\) 3.50247 0.170700 0.0853500 0.996351i \(-0.472799\pi\)
0.0853500 + 0.996351i \(0.472799\pi\)
\(422\) 18.0824 + 31.3197i 0.880240 + 1.52462i
\(423\) 8.73549 15.1303i 0.424734 0.735661i
\(424\) −10.6782 + 18.4952i −0.518581 + 0.898209i
\(425\) 9.71541 + 16.8276i 0.471267 + 0.816258i
\(426\) −4.53901 −0.219916
\(427\) −6.73164 5.17250i −0.325767 0.250315i
\(428\) 9.19241 0.444332
\(429\) 2.16270 + 3.74590i 0.104416 + 0.180854i
\(430\) 1.56952 2.71848i 0.0756888 0.131097i
\(431\) −5.52640 + 9.57201i −0.266197 + 0.461067i −0.967877 0.251426i \(-0.919101\pi\)
0.701679 + 0.712493i \(0.252434\pi\)
\(432\) 3.14955 + 5.45519i 0.151533 + 0.262463i
\(433\) −32.5407 −1.56381 −0.781904 0.623399i \(-0.785751\pi\)
−0.781904 + 0.623399i \(0.785751\pi\)
\(434\) −13.8961 + 5.74511i −0.667034 + 0.275774i
\(435\) 1.07136 0.0513676
\(436\) −5.71561 9.89972i −0.273728 0.474111i
\(437\) 7.67110 13.2867i 0.366959 0.635591i
\(438\) 2.18020 3.77622i 0.104174 0.180435i
\(439\) −8.79827 15.2390i −0.419918 0.727320i 0.576012 0.817441i \(-0.304608\pi\)
−0.995931 + 0.0901209i \(0.971275\pi\)
\(440\) −7.15119 −0.340920
\(441\) 19.9690 + 5.37918i 0.950902 + 0.256151i
\(442\) 46.7853 2.22535
\(443\) 11.7785 + 20.4010i 0.559615 + 0.969281i 0.997528 + 0.0702643i \(0.0223843\pi\)
−0.437914 + 0.899017i \(0.644282\pi\)
\(444\) 0.570239 0.987683i 0.0270624 0.0468734i
\(445\) −2.80027 + 4.85022i −0.132746 + 0.229922i
\(446\) 7.15320 + 12.3897i 0.338714 + 0.586670i
\(447\) −0.146710 −0.00693915
\(448\) 7.03407 2.90812i 0.332329 0.137396i
\(449\) −8.18594 −0.386318 −0.193159 0.981167i \(-0.561873\pi\)
−0.193159 + 0.981167i \(0.561873\pi\)
\(450\) 9.84472 + 17.0516i 0.464085 + 0.803818i
\(451\) 1.75783 3.04466i 0.0827732 0.143367i
\(452\) −3.98816 + 6.90769i −0.187587 + 0.324910i
\(453\) 0.950974 + 1.64713i 0.0446806 + 0.0773891i
\(454\) 20.9729 0.984305
\(455\) 12.1272 + 9.31838i 0.568533 + 0.436852i
\(456\) 1.70865 0.0800151
\(457\) 4.93519 + 8.54800i 0.230859 + 0.399859i 0.958061 0.286564i \(-0.0925132\pi\)
−0.727202 + 0.686423i \(0.759180\pi\)
\(458\) 16.5388 28.6460i 0.772806 1.33854i
\(459\) −3.09358 + 5.35824i −0.144396 + 0.250101i
\(460\) −1.53133 2.65234i −0.0713985 0.123666i
\(461\) −6.23960 −0.290607 −0.145304 0.989387i \(-0.546416\pi\)
−0.145304 + 0.989387i \(0.546416\pi\)
\(462\) 0.434883 3.28635i 0.0202326 0.152895i
\(463\) −31.4838 −1.46317 −0.731587 0.681748i \(-0.761220\pi\)
−0.731587 + 0.681748i \(0.761220\pi\)
\(464\) −12.3853 21.4520i −0.574973 0.995883i
\(465\) 0.364830 0.631904i 0.0169186 0.0293039i
\(466\) 20.5778 35.6418i 0.953249 1.65108i
\(467\) −0.210282 0.364220i −0.00973070 0.0168541i 0.861119 0.508403i \(-0.169764\pi\)
−0.870850 + 0.491549i \(0.836431\pi\)
\(468\) 13.3656 0.617824
\(469\) −2.55423 + 19.3020i −0.117943 + 0.891282i
\(470\) −9.90205 −0.456748
\(471\) −1.69824 2.94143i −0.0782506 0.135534i
\(472\) −2.82163 + 4.88720i −0.129876 + 0.224952i
\(473\) 3.29531 5.70765i 0.151519 0.262438i
\(474\) 1.49295 + 2.58586i 0.0685734 + 0.118773i
\(475\) 15.7604 0.723137
\(476\) −8.01583 6.15925i −0.367405 0.282309i
\(477\) −31.1225 −1.42500
\(478\) 19.1861 + 33.2312i 0.877550 + 1.51996i
\(479\) −13.9628 + 24.1842i −0.637975 + 1.10500i 0.347902 + 0.937531i \(0.386894\pi\)
−0.985877 + 0.167473i \(0.946439\pi\)
\(480\) 0.451326 0.781720i 0.0206001 0.0356805i
\(481\) 19.5923 + 33.9348i 0.893330 + 1.54729i
\(482\) 28.6749 1.30611
\(483\) −2.02971 + 0.839151i −0.0923551 + 0.0381827i
\(484\) 1.06785 0.0485388
\(485\) −9.18957 15.9168i −0.417277 0.722745i
\(486\) −4.71414 + 8.16512i −0.213838 + 0.370378i
\(487\) −9.16440 + 15.8732i −0.415279 + 0.719284i −0.995458 0.0952051i \(-0.969649\pi\)
0.580179 + 0.814489i \(0.302983\pi\)
\(488\) −3.25253 5.63355i −0.147235 0.255019i
\(489\) −4.32546 −0.195604
\(490\) −3.01861 11.3259i −0.136367 0.511653i
\(491\) −8.43902 −0.380848 −0.190424 0.981702i \(-0.560986\pi\)
−0.190424 + 0.981702i \(0.560986\pi\)
\(492\) 0.0838424 + 0.145219i 0.00377991 + 0.00654699i
\(493\) 12.1652 21.0707i 0.547893 0.948978i
\(494\) 18.9739 32.8637i 0.853674 1.47861i
\(495\) −5.21066 9.02513i −0.234202 0.405650i
\(496\) −16.8703 −0.757499
\(497\) −31.1400 + 12.8743i −1.39682 + 0.577492i
\(498\) −5.33737 −0.239173
\(499\) −3.16013 5.47351i −0.141467 0.245028i 0.786582 0.617485i \(-0.211849\pi\)
−0.928049 + 0.372458i \(0.878515\pi\)
\(500\) 3.54269 6.13613i 0.158434 0.274416i
\(501\) 1.81113 3.13696i 0.0809152 0.140149i
\(502\) 19.5891 + 33.9293i 0.874305 + 1.51434i
\(503\) −25.8395 −1.15213 −0.576063 0.817405i \(-0.695412\pi\)
−0.576063 + 0.817405i \(0.695412\pi\)
\(504\) 12.5657 + 9.65530i 0.559721 + 0.430081i
\(505\) −4.00963 −0.178426
\(506\) −11.4041 19.7526i −0.506976 0.878108i
\(507\) 2.15606 3.73441i 0.0957540 0.165851i
\(508\) −4.74477 + 8.21818i −0.210515 + 0.364623i
\(509\) −3.53071 6.11537i −0.156496 0.271059i 0.777107 0.629369i \(-0.216686\pi\)
−0.933603 + 0.358310i \(0.883353\pi\)
\(510\) 1.73992 0.0770452
\(511\) 4.24656 32.0907i 0.187857 1.41961i
\(512\) −0.783754 −0.0346373
\(513\) 2.50921 + 4.34609i 0.110785 + 0.191884i
\(514\) −11.6098 + 20.1088i −0.512088 + 0.886962i
\(515\) 1.48980 2.58041i 0.0656484 0.113706i
\(516\) 0.157175 + 0.272235i 0.00691923 + 0.0119845i
\(517\) −20.7901 −0.914347
\(518\) 3.93969 29.7717i 0.173100 1.30809i
\(519\) 2.96156 0.129998
\(520\) 5.85952 + 10.1490i 0.256957 + 0.445062i
\(521\) −9.76573 + 16.9147i −0.427845 + 0.741048i −0.996681 0.0814019i \(-0.974060\pi\)
0.568837 + 0.822450i \(0.307394\pi\)
\(522\) 12.3271 21.3512i 0.539543 0.934515i
\(523\) −2.87417 4.97820i −0.125679 0.217682i 0.796319 0.604876i \(-0.206777\pi\)
−0.921998 + 0.387195i \(0.873444\pi\)
\(524\) −6.76054 −0.295335
\(525\) −1.78906 1.37468i −0.0780808 0.0599961i
\(526\) −35.6018 −1.55231
\(527\) −8.28525 14.3505i −0.360911 0.625116i
\(528\) 1.85960 3.22092i 0.0809286 0.140172i
\(529\) 3.94424 6.83162i 0.171489 0.297027i
\(530\) 8.81966 + 15.2761i 0.383102 + 0.663552i
\(531\) −8.22383 −0.356884
\(532\) −7.57731 + 3.13272i −0.328518 + 0.135820i
\(533\) −5.76131 −0.249550
\(534\) −0.994675 1.72283i −0.0430438 0.0745540i
\(535\) −5.87284 + 10.1721i −0.253905 + 0.439776i
\(536\) −7.45962 + 12.9204i −0.322206 + 0.558078i
\(537\) 1.31354 + 2.27511i 0.0566833 + 0.0981783i
\(538\) 45.5145 1.96227
\(539\) −6.33779 23.7796i −0.272988 1.02426i
\(540\) 1.00179 0.0431103
\(541\) 17.8156 + 30.8575i 0.765953 + 1.32667i 0.939741 + 0.341886i \(0.111066\pi\)
−0.173788 + 0.984783i \(0.555601\pi\)
\(542\) −20.2990 + 35.1588i −0.871915 + 1.51020i
\(543\) −0.192012 + 0.332574i −0.00824002 + 0.0142721i
\(544\) −10.2496 17.7528i −0.439446 0.761143i
\(545\) 14.6063 0.625667
\(546\) −5.02033 + 2.07557i −0.214850 + 0.0888263i
\(547\) 3.65967 0.156476 0.0782381 0.996935i \(-0.475071\pi\)
0.0782381 + 0.996935i \(0.475071\pi\)
\(548\) 0.0677110 + 0.117279i 0.00289247 + 0.00500991i
\(549\) 4.73987 8.20970i 0.202293 0.350381i
\(550\) 11.7150 20.2910i 0.499529 0.865210i
\(551\) −9.86723 17.0905i −0.420358 0.728082i
\(552\) −1.68296 −0.0716317
\(553\) 17.5769 + 13.5058i 0.747445 + 0.574326i
\(554\) 2.03850 0.0866076
\(555\) 0.728628 + 1.26202i 0.0309285 + 0.0535698i
\(556\) −3.45390 + 5.98232i −0.146478 + 0.253707i
\(557\) 14.2440 24.6713i 0.603536 1.04535i −0.388745 0.921345i \(-0.627091\pi\)
0.992281 0.124009i \(-0.0395753\pi\)
\(558\) −8.39552 14.5415i −0.355411 0.615589i
\(559\) −10.8004 −0.456809
\(560\) 1.72516 13.0368i 0.0729013 0.550905i
\(561\) 3.65310 0.154234
\(562\) −14.0148 24.2744i −0.591179 1.02395i
\(563\) −1.98279 + 3.43428i −0.0835644 + 0.144738i −0.904779 0.425882i \(-0.859964\pi\)
0.821214 + 0.570620i \(0.193297\pi\)
\(564\) 0.495807 0.858762i 0.0208772 0.0361604i
\(565\) −5.09590 8.82636i −0.214386 0.371328i
\(566\) −4.57039 −0.192108
\(567\) −2.98205 + 22.5349i −0.125234 + 0.946378i
\(568\) −25.8201 −1.08339
\(569\) −4.62984 8.01912i −0.194093 0.336179i 0.752510 0.658581i \(-0.228843\pi\)
−0.946603 + 0.322402i \(0.895510\pi\)
\(570\) 0.705630 1.22219i 0.0295556 0.0511918i
\(571\) −9.73144 + 16.8554i −0.407248 + 0.705375i −0.994580 0.103971i \(-0.966845\pi\)
0.587332 + 0.809346i \(0.300178\pi\)
\(572\) −7.95237 13.7739i −0.332505 0.575916i
\(573\) 0.462452 0.0193192
\(574\) 3.50126 + 2.69032i 0.146140 + 0.112292i
\(575\) −15.5234 −0.647372
\(576\) 4.24973 + 7.36076i 0.177072 + 0.306698i
\(577\) −17.6029 + 30.4892i −0.732820 + 1.26928i 0.222853 + 0.974852i \(0.428463\pi\)
−0.955673 + 0.294430i \(0.904870\pi\)
\(578\) 5.57107 9.64938i 0.231726 0.401361i
\(579\) 0.751170 + 1.30107i 0.0312176 + 0.0540704i
\(580\) −3.93945 −0.163577
\(581\) −36.6171 + 15.1387i −1.51913 + 0.628061i
\(582\) 6.52839 0.270610
\(583\) 18.5175 + 32.0733i 0.766918 + 1.32834i
\(584\) 12.4021 21.4810i 0.513201 0.888890i
\(585\) −8.53899 + 14.7900i −0.353044 + 0.611490i
\(586\) 6.12737 + 10.6129i 0.253119 + 0.438416i
\(587\) −11.7669 −0.485673 −0.242836 0.970067i \(-0.578078\pi\)
−0.242836 + 0.970067i \(0.578078\pi\)
\(588\) 1.13339 + 0.305310i 0.0467403 + 0.0125908i
\(589\) −13.4404 −0.553802
\(590\) 2.33052 + 4.03657i 0.0959459 + 0.166183i
\(591\) −1.01159 + 1.75212i −0.0416112 + 0.0720727i
\(592\) 16.8464 29.1789i 0.692384 1.19925i
\(593\) −19.4741 33.7300i −0.799703 1.38513i −0.919809 0.392366i \(-0.871657\pi\)
0.120106 0.992761i \(-0.461677\pi\)
\(594\) 7.46058 0.306111
\(595\) 11.9368 4.93507i 0.489361 0.202318i
\(596\) 0.539463 0.0220973
\(597\) 0.379853 + 0.657924i 0.0155463 + 0.0269271i
\(598\) −18.6886 + 32.3696i −0.764233 + 1.32369i
\(599\) 21.9575 38.0315i 0.897158 1.55392i 0.0660480 0.997816i \(-0.478961\pi\)
0.831110 0.556107i \(-0.187706\pi\)
\(600\) −0.864419 1.49722i −0.0352898 0.0611237i
\(601\) −28.3881 −1.15798 −0.578988 0.815336i \(-0.696552\pi\)
−0.578988 + 0.815336i \(0.696552\pi\)
\(602\) 6.56362 + 5.04339i 0.267513 + 0.205553i
\(603\) −21.7416 −0.885385
\(604\) −3.49679 6.05662i −0.142282 0.246440i
\(605\) −0.682229 + 1.18165i −0.0277365 + 0.0480411i
\(606\) 0.712124 1.23343i 0.0289281 0.0501049i
\(607\) 3.50085 + 6.06365i 0.142095 + 0.246116i 0.928285 0.371868i \(-0.121283\pi\)
−0.786190 + 0.617985i \(0.787949\pi\)
\(608\) −16.6269 −0.674310
\(609\) −0.370617 + 2.80070i −0.0150182 + 0.113490i
\(610\) −5.37285 −0.217540
\(611\) 17.0349 + 29.5053i 0.689159 + 1.19366i
\(612\) 5.64409 9.77584i 0.228149 0.395165i
\(613\) −5.04436 + 8.73709i −0.203740 + 0.352888i −0.949730 0.313069i \(-0.898643\pi\)
0.745991 + 0.665956i \(0.231976\pi\)
\(614\) −25.3215 43.8582i −1.02189 1.76997i
\(615\) −0.214261 −0.00863983
\(616\) 2.47383 18.6944i 0.0996735 0.753219i
\(617\) −18.3132 −0.737262 −0.368631 0.929576i \(-0.620173\pi\)
−0.368631 + 0.929576i \(0.620173\pi\)
\(618\) 0.529186 + 0.916577i 0.0212870 + 0.0368701i
\(619\) −6.31274 + 10.9340i −0.253730 + 0.439474i −0.964550 0.263901i \(-0.914991\pi\)
0.710820 + 0.703374i \(0.248324\pi\)
\(620\) −1.34150 + 2.32355i −0.0538761 + 0.0933161i
\(621\) −2.47149 4.28074i −0.0991773 0.171780i
\(622\) −11.5536 −0.463256
\(623\) −11.7106 8.99823i −0.469174 0.360506i
\(624\) −6.09484 −0.243989
\(625\) −5.45659 9.45109i −0.218263 0.378043i
\(626\) 25.6639 44.4512i 1.02574 1.77663i
\(627\) 1.48152 2.56607i 0.0591663 0.102479i
\(628\) 6.24452 + 10.8158i 0.249184 + 0.431599i
\(629\) 33.0941 1.31955
\(630\) 12.0957 5.00075i 0.481903 0.199235i
\(631\) 18.6742 0.743409 0.371705 0.928351i \(-0.378773\pi\)
0.371705 + 0.928351i \(0.378773\pi\)
\(632\) 8.49263 + 14.7097i 0.337819 + 0.585119i
\(633\) 2.31378 4.00759i 0.0919647 0.159287i
\(634\) 2.42494 4.20012i 0.0963068 0.166808i
\(635\) −6.06266 10.5008i −0.240589 0.416713i
\(636\) −1.76644 −0.0700439
\(637\) −28.5550 + 28.4790i −1.13139 + 1.12838i
\(638\) −29.3380 −1.16150
\(639\) −18.8137 32.5862i −0.744257 1.28909i
\(640\) 6.63555 11.4931i 0.262293 0.454305i
\(641\) −0.577181 + 0.999707i −0.0227973 + 0.0394860i −0.877199 0.480127i \(-0.840591\pi\)
0.854402 + 0.519613i \(0.173924\pi\)
\(642\) −2.08607 3.61318i −0.0823306 0.142601i
\(643\) −25.1954 −0.993611 −0.496806 0.867862i \(-0.665494\pi\)
−0.496806 + 0.867862i \(0.665494\pi\)
\(644\) 7.46338 3.08561i 0.294098 0.121590i
\(645\) −0.401663 −0.0158155
\(646\) −16.0248 27.7557i −0.630486 1.09203i
\(647\) −21.2669 + 36.8354i −0.836090 + 1.44815i 0.0570506 + 0.998371i \(0.481830\pi\)
−0.893140 + 0.449778i \(0.851503\pi\)
\(648\) −8.70905 + 15.0845i −0.342124 + 0.592576i
\(649\) 4.89309 + 8.47508i 0.192071 + 0.332676i
\(650\) −38.3960 −1.50601
\(651\) 1.52570 + 1.17232i 0.0597967 + 0.0459470i
\(652\) 15.9050 0.622888
\(653\) 0.545599 + 0.945006i 0.0213509 + 0.0369809i 0.876503 0.481396i \(-0.159870\pi\)
−0.855153 + 0.518376i \(0.826537\pi\)
\(654\) −2.59413 + 4.49317i −0.101439 + 0.175697i
\(655\) 4.31917 7.48101i 0.168764 0.292307i
\(656\) 2.47694 + 4.29018i 0.0967081 + 0.167503i
\(657\) 36.1467 1.41022
\(658\) 3.42544 25.8856i 0.133538 1.00913i
\(659\) 23.5037 0.915573 0.457786 0.889062i \(-0.348642\pi\)
0.457786 + 0.889062i \(0.348642\pi\)
\(660\) −0.295745 0.512246i −0.0115119 0.0199391i
\(661\) −8.32643 + 14.4218i −0.323861 + 0.560943i −0.981281 0.192581i \(-0.938314\pi\)
0.657420 + 0.753524i \(0.271648\pi\)
\(662\) 3.88416 6.72756i 0.150962 0.261474i
\(663\) −2.99326 5.18448i −0.116249 0.201349i
\(664\) −30.3616 −1.17826
\(665\) 1.37441 10.3863i 0.0532975 0.402762i
\(666\) 33.5346 1.29944
\(667\) 9.71887 + 16.8336i 0.376316 + 0.651799i
\(668\) −6.65963 + 11.5348i −0.257669 + 0.446295i
\(669\) 0.915305 1.58536i 0.0353878 0.0612934i
\(670\) 6.16125 + 10.6716i 0.238030 + 0.412280i
\(671\) −11.2807 −0.435486
\(672\) 1.88742 + 1.45026i 0.0728087 + 0.0559451i
\(673\) 40.5668 1.56374 0.781868 0.623444i \(-0.214267\pi\)
0.781868 + 0.623444i \(0.214267\pi\)
\(674\) 19.8821 + 34.4369i 0.765832 + 1.32646i
\(675\) 2.53886 4.39743i 0.0977206 0.169257i
\(676\) −7.92797 + 13.7317i −0.304922 + 0.528140i
\(677\) −1.85888 3.21967i −0.0714425 0.123742i 0.828091 0.560593i \(-0.189427\pi\)
−0.899534 + 0.436851i \(0.856094\pi\)
\(678\) 3.62019 0.139033
\(679\) 44.7881 18.5169i 1.71881 0.710614i
\(680\) 9.89755 0.379554
\(681\) −1.34182 2.32410i −0.0514185 0.0890595i
\(682\) −9.99049 + 17.3040i −0.382555 + 0.662605i
\(683\) 0.845641 1.46469i 0.0323576 0.0560449i −0.849393 0.527761i \(-0.823032\pi\)
0.881751 + 0.471716i \(0.156365\pi\)
\(684\) −4.57794 7.92923i −0.175042 0.303182i
\(685\) −0.173037 −0.00661139
\(686\) 30.6521 3.97314i 1.17030 0.151695i
\(687\) −4.23252 −0.161481
\(688\) 4.64338 + 8.04257i 0.177027 + 0.306620i
\(689\) 30.3457 52.5602i 1.15608 2.00238i
\(690\) −0.695020 + 1.20381i −0.0264590 + 0.0458283i
\(691\) 12.0739 + 20.9127i 0.459314 + 0.795555i 0.998925 0.0463595i \(-0.0147620\pi\)
−0.539611 + 0.841915i \(0.681429\pi\)
\(692\) −10.8898 −0.413970
\(693\) 25.3957 10.4994i 0.964704 0.398841i
\(694\) 28.6715 1.08836
\(695\) −4.41324 7.64396i −0.167404 0.289952i
\(696\) −1.08239 + 1.87475i −0.0410277 + 0.0710621i
\(697\) −2.43292 + 4.21394i −0.0921533 + 0.159614i
\(698\) 9.01131 + 15.6081i 0.341083 + 0.590774i
\(699\) −5.26617 −0.199185
\(700\) 6.57847 + 5.05480i 0.248643 + 0.191054i
\(701\) −4.80032 −0.181305 −0.0906527 0.995883i \(-0.528895\pi\)
−0.0906527 + 0.995883i \(0.528895\pi\)
\(702\) −6.11302 10.5881i −0.230721 0.399621i
\(703\) 13.4214 23.2465i 0.506197 0.876758i
\(704\) 5.05709 8.75914i 0.190596 0.330122i
\(705\) 0.633521 + 1.09729i 0.0238598 + 0.0413263i
\(706\) −7.04105 −0.264994
\(707\) 1.38706 10.4819i 0.0521659 0.394211i
\(708\) −0.466766 −0.0175421
\(709\) −24.0138 41.5930i −0.901856 1.56206i −0.825083 0.565011i \(-0.808872\pi\)
−0.0767722 0.997049i \(-0.524461\pi\)
\(710\) −10.6630 + 18.4689i −0.400177 + 0.693127i
\(711\) −12.3762 + 21.4362i −0.464143 + 0.803920i
\(712\) −5.65820 9.80029i −0.212050 0.367281i
\(713\) 13.2383 0.495778
\(714\) −0.601897 + 4.54845i −0.0225254 + 0.170222i
\(715\) 20.3224 0.760015
\(716\) −4.82996 8.36573i −0.180504 0.312642i
\(717\) 2.45500 4.25219i 0.0916837 0.158801i
\(718\) 1.63116 2.82526i 0.0608745 0.105438i
\(719\) 5.92186 + 10.2570i 0.220848 + 0.382520i 0.955066 0.296394i \(-0.0957841\pi\)
−0.734218 + 0.678914i \(0.762451\pi\)
\(720\) 14.6845 0.547260
\(721\) 6.23024 + 4.78723i 0.232026 + 0.178286i
\(722\) 5.71363 0.212639
\(723\) −1.83459 3.17760i −0.0682290 0.118176i
\(724\) 0.706040 1.22290i 0.0262398 0.0454486i
\(725\) −9.98379 + 17.2924i −0.370789 + 0.642225i
\(726\) −0.242332 0.419731i −0.00899378 0.0155777i
\(727\) 48.3049 1.79153 0.895765 0.444527i \(-0.146628\pi\)
0.895765 + 0.444527i \(0.146628\pi\)
\(728\) −28.5581 + 11.8069i −1.05843 + 0.437592i
\(729\) −24.5685 −0.909946
\(730\) −10.2434 17.7422i −0.379127 0.656667i
\(731\) −4.56086 + 7.89963i −0.168689 + 0.292179i
\(732\) 0.269024 0.465964i 0.00994342 0.0172225i
\(733\) −20.0390 34.7086i −0.740159 1.28199i −0.952423 0.304781i \(-0.901417\pi\)
0.212263 0.977212i \(-0.431916\pi\)
\(734\) −3.57591 −0.131989
\(735\) −1.06195 + 1.05912i −0.0391705 + 0.0390663i
\(736\) 16.3769 0.603661
\(737\) 12.9360 + 22.4058i 0.476504 + 0.825329i
\(738\) −2.46530 + 4.27002i −0.0907489 + 0.157182i
\(739\) −5.89362 + 10.2080i −0.216800 + 0.375509i −0.953828 0.300354i \(-0.902895\pi\)
0.737028 + 0.675862i \(0.236229\pi\)
\(740\) −2.67921 4.64053i −0.0984898 0.170589i
\(741\) −4.85569 −0.178378
\(742\) −42.9853 + 17.7716i −1.57804 + 0.652415i
\(743\) 8.89729 0.326410 0.163205 0.986592i \(-0.447817\pi\)
0.163205 + 0.986592i \(0.447817\pi\)
\(744\) 0.737172 + 1.27682i 0.0270260 + 0.0468105i
\(745\) −0.344652 + 0.596954i −0.0126271 + 0.0218707i
\(746\) −7.50030 + 12.9909i −0.274605 + 0.475631i
\(747\) −22.1227 38.3177i −0.809429 1.40197i
\(748\) −13.4327 −0.491147
\(749\) −24.5598 18.8714i −0.897397 0.689547i
\(750\) −3.21583 −0.117426
\(751\) −20.0914 34.7993i −0.733145 1.26985i −0.955532 0.294887i \(-0.904718\pi\)
0.222387 0.974958i \(-0.428615\pi\)
\(752\) 14.6475 25.3702i 0.534139 0.925156i
\(753\) 2.50657 4.34151i 0.0913446 0.158214i
\(754\) 24.0388 + 41.6365i 0.875443 + 1.51631i
\(755\) 8.93611 0.325218
\(756\) −0.346553 + 2.61885i −0.0126040 + 0.0952467i
\(757\) −36.7228 −1.33471 −0.667357 0.744738i \(-0.732574\pi\)
−0.667357 + 0.744738i \(0.732574\pi\)
\(758\) 21.1662 + 36.6609i 0.768791 + 1.33158i
\(759\) −1.45925 + 2.52749i −0.0529672 + 0.0917420i
\(760\) 4.01397 6.95240i 0.145602 0.252190i
\(761\) 19.0594 + 33.0119i 0.690904 + 1.19668i 0.971542 + 0.236867i \(0.0761204\pi\)
−0.280639 + 0.959813i \(0.590546\pi\)
\(762\) 4.30699 0.156026
\(763\) −5.05281 + 38.1834i −0.182924 + 1.38233i
\(764\) −1.70047 −0.0615207
\(765\) 7.21178 + 12.4912i 0.260742 + 0.451619i
\(766\) 20.4926 35.4942i 0.740427 1.28246i
\(767\) 8.01857 13.8886i 0.289534 0.501487i
\(768\) 1.74263 + 3.01833i 0.0628819 + 0.108915i
\(769\) −3.22533 −0.116308 −0.0581541 0.998308i \(-0.518521\pi\)
−0.0581541 + 0.998308i \(0.518521\pi\)
\(770\) −12.3503 9.48981i −0.445075 0.341989i
\(771\) 2.97113 0.107003
\(772\) −2.76210 4.78410i −0.0994102 0.172184i
\(773\) 21.8124 37.7801i 0.784536 1.35886i −0.144740 0.989470i \(-0.546234\pi\)
0.929276 0.369387i \(-0.120432\pi\)
\(774\) −4.62156 + 8.00478i −0.166119 + 0.287726i
\(775\) 6.79958 + 11.7772i 0.244248 + 0.423050i
\(776\) 37.1367 1.33313
\(777\) −3.55119 + 1.46818i −0.127398 + 0.0526707i
\(778\) 38.9308 1.39574
\(779\) 1.97335 + 3.41794i 0.0707025 + 0.122460i
\(780\) −0.484654 + 0.839445i −0.0173534 + 0.0300569i
\(781\) −22.3878 + 38.7769i −0.801100 + 1.38755i
\(782\) 15.7838 + 27.3384i 0.564428 + 0.977618i
\(783\) −6.35807 −0.227219
\(784\) 33.4835 + 9.01970i 1.19584 + 0.322132i
\(785\) −15.9580 −0.569565
\(786\) 1.53419 + 2.65730i 0.0547229 + 0.0947829i
\(787\) −4.17525 + 7.23174i −0.148832 + 0.257784i −0.930796 0.365539i \(-0.880885\pi\)
0.781964 + 0.623323i \(0.214218\pi\)
\(788\) 3.71967 6.44266i 0.132508 0.229510i
\(789\) 2.27776 + 3.94519i 0.0810904 + 0.140453i
\(790\) 14.0289 0.499127
\(791\) 24.8364 10.2682i 0.883081 0.365095i
\(792\) 21.0572 0.748236
\(793\) 9.24313 + 16.0096i 0.328233 + 0.568516i
\(794\) −14.9214 + 25.8447i −0.529541 + 0.917192i
\(795\) 1.12854 1.95469i 0.0400253 0.0693258i
\(796\) −1.39674 2.41923i −0.0495063 0.0857473i
\(797\) −11.5618 −0.409539 −0.204769 0.978810i \(-0.565644\pi\)
−0.204769 + 0.978810i \(0.565644\pi\)
\(798\) 2.95090 + 2.26743i 0.104461 + 0.0802661i
\(799\) 28.7744 1.01796
\(800\) 8.41166 + 14.5694i 0.297397 + 0.515107i
\(801\) 8.24561 14.2818i 0.291344 0.504623i
\(802\) −18.2616 + 31.6301i −0.644840 + 1.11690i
\(803\) −21.5069 37.2510i −0.758961 1.31456i
\(804\) −1.23400 −0.0435199
\(805\) −1.35375 + 10.2301i −0.0477134 + 0.360564i
\(806\) 32.7439 1.15335
\(807\) −2.91196 5.04366i −0.102506 0.177545i
\(808\) 4.05091 7.01639i 0.142511 0.246836i
\(809\) −24.3994 + 42.2609i −0.857836 + 1.48582i 0.0161531 + 0.999870i \(0.494858\pi\)
−0.873989 + 0.485946i \(0.838475\pi\)
\(810\) 7.19322 + 12.4590i 0.252744 + 0.437766i
\(811\) 13.8738 0.487176 0.243588 0.969879i \(-0.421676\pi\)
0.243588 + 0.969879i \(0.421676\pi\)
\(812\) 1.36278 10.2984i 0.0478243 0.361402i
\(813\) 5.19481 0.182190
\(814\) −19.9527 34.5591i −0.699342 1.21130i
\(815\) −10.1614 + 17.6000i −0.355937 + 0.616502i
\(816\) −2.57376 + 4.45789i −0.0900997 + 0.156057i
\(817\) 3.69933 + 6.40742i 0.129423 + 0.224167i
\(818\) −29.2068 −1.02119
\(819\) −35.7095 27.4387i −1.24779 0.958785i
\(820\) 0.787850 0.0275129
\(821\) −18.5968 32.2107i −0.649034 1.12416i −0.983354 0.181700i \(-0.941840\pi\)
0.334320 0.942460i \(-0.391493\pi\)
\(822\) 0.0307319 0.0532291i 0.00107190 0.00185658i
\(823\) 15.8277 27.4143i 0.551718 0.955604i −0.446433 0.894817i \(-0.647306\pi\)
0.998151 0.0607866i \(-0.0193609\pi\)
\(824\) 3.01027 + 5.21394i 0.104868 + 0.181636i
\(825\) −2.99804 −0.104378
\(826\) −11.3585 + 4.69598i −0.395212 + 0.163394i
\(827\) 18.2232 0.633683 0.316842 0.948478i \(-0.397378\pi\)
0.316842 + 0.948478i \(0.397378\pi\)
\(828\) 4.50911 + 7.81000i 0.156702 + 0.271416i
\(829\) −3.96544 + 6.86834i −0.137725 + 0.238547i −0.926635 0.375962i \(-0.877312\pi\)
0.788910 + 0.614509i \(0.210646\pi\)
\(830\) −12.5385 + 21.7174i −0.435219 + 0.753822i
\(831\) −0.130421 0.225895i −0.00452424 0.00783622i
\(832\) −16.5746 −0.574622
\(833\) 8.77177 + 32.9120i 0.303924 + 1.14033i
\(834\) 3.13522 0.108564
\(835\) −8.50940 14.7387i −0.294480 0.510054i
\(836\) −5.44765 + 9.43560i −0.188411 + 0.326337i
\(837\) −2.16512 + 3.75010i −0.0748375 + 0.129622i
\(838\) 6.03462 + 10.4523i 0.208462 + 0.361068i
\(839\) −3.16668 −0.109326 −0.0546630 0.998505i \(-0.517408\pi\)
−0.0546630 + 0.998505i \(0.517408\pi\)
\(840\) −1.06206 + 0.439093i −0.0366447 + 0.0151502i
\(841\) −3.99752 −0.137845
\(842\) 2.92264 + 5.06216i 0.100721 + 0.174454i
\(843\) −1.79330 + 3.10609i −0.0617645 + 0.106979i
\(844\) −8.50793 + 14.7362i −0.292855 + 0.507240i
\(845\) −10.1300 17.5457i −0.348484 0.603591i
\(846\) 29.1573 1.00245
\(847\) −2.85304 2.19223i −0.0980315 0.0753260i
\(848\) −52.1855 −1.79206
\(849\) 0.292408 + 0.506465i 0.0100354 + 0.0173818i
\(850\) −16.2141 + 28.0836i −0.556138 + 0.963259i
\(851\) −13.2196 + 22.8970i −0.453161 + 0.784898i
\(852\) −1.06782 1.84952i −0.0365829 0.0633635i
\(853\) −39.5683 −1.35479 −0.677396 0.735618i \(-0.736892\pi\)
−0.677396 + 0.735618i \(0.736892\pi\)
\(854\) 1.85864 14.0455i 0.0636015 0.480628i
\(855\) 11.6990 0.400097
\(856\) −11.8666 20.5535i −0.405592 0.702505i
\(857\) 13.6357 23.6177i 0.465785 0.806764i −0.533451 0.845831i \(-0.679105\pi\)
0.999237 + 0.0390669i \(0.0124385\pi\)
\(858\) −3.60933 + 6.25154i −0.123220 + 0.213424i
\(859\) 14.8438 + 25.7103i 0.506465 + 0.877224i 0.999972 + 0.00748180i \(0.00238155\pi\)
−0.493507 + 0.869742i \(0.664285\pi\)
\(860\) 1.47694 0.0503632
\(861\) 0.0741198 0.560113i 0.00252600 0.0190886i
\(862\) −18.4460 −0.628275
\(863\) −15.2252 26.3708i −0.518271 0.897671i −0.999775 0.0212274i \(-0.993243\pi\)
0.481504 0.876444i \(-0.340091\pi\)
\(864\) −2.67844 + 4.63920i −0.0911224 + 0.157829i
\(865\) 6.95729 12.0504i 0.236555 0.409725i
\(866\) −27.1536 47.0315i −0.922718 1.59819i
\(867\) −1.42572 −0.0484200
\(868\) −5.61008 4.31071i −0.190419 0.146315i
\(869\) 29.4548 0.999185
\(870\) 0.893994 + 1.54844i 0.0303092 + 0.0524971i
\(871\) 21.1989 36.7176i 0.718298 1.24413i
\(872\) −14.7567 + 25.5594i −0.499725 + 0.865549i
\(873\) 27.0594 + 46.8682i 0.915821 + 1.58625i
\(874\) 25.6046 0.866090
\(875\) −22.0623 + 9.12128i −0.745841 + 0.308356i
\(876\) 2.05160 0.0693172
\(877\) 7.68523 + 13.3112i 0.259512 + 0.449487i 0.966111 0.258126i \(-0.0831051\pi\)
−0.706600 + 0.707614i \(0.749772\pi\)
\(878\) 14.6834 25.4325i 0.495542 0.858304i
\(879\) 0.784043 1.35800i 0.0264451 0.0458043i
\(880\) −8.73714 15.1332i −0.294529 0.510139i
\(881\) 1.78454 0.0601226 0.0300613 0.999548i \(-0.490430\pi\)
0.0300613 + 0.999548i \(0.490430\pi\)
\(882\) 8.88852 + 33.3500i 0.299292 + 1.12295i
\(883\) −16.3164 −0.549090 −0.274545 0.961574i \(-0.588527\pi\)
−0.274545 + 0.961574i \(0.588527\pi\)
\(884\) 11.0064 + 19.0637i 0.370186 + 0.641181i
\(885\) 0.298207 0.516510i 0.0100241 0.0173623i
\(886\) −19.6572 + 34.0473i −0.660397 + 1.14384i
\(887\) 11.7016 + 20.2678i 0.392903 + 0.680528i 0.992831 0.119526i \(-0.0381375\pi\)
−0.599928 + 0.800054i \(0.704804\pi\)
\(888\) −2.94451 −0.0988114
\(889\) 29.5482 12.2162i 0.991015 0.409719i
\(890\) −9.34676 −0.313304
\(891\) 15.1027 + 26.1586i 0.505959 + 0.876348i
\(892\) −3.36564 + 5.82945i −0.112690 + 0.195185i
\(893\) 11.6695 20.2122i 0.390505 0.676374i
\(894\) −0.122422 0.212042i −0.00409442 0.00709174i
\(895\) 12.3430 0.412582
\(896\) 27.7494 + 21.3223i 0.927044 + 0.712327i
\(897\) 4.78269 0.159689
\(898\) −6.83076 11.8312i −0.227946 0.394813i
\(899\) 8.51412 14.7469i 0.283962 0.491836i
\(900\) −4.63202 + 8.02289i −0.154401 + 0.267430i
\(901\) −25.6290 44.3908i −0.853827 1.47887i
\(902\) 5.86730 0.195360
\(903\) 0.138948 1.05001i 0.00462391 0.0349423i
\(904\) 20.5934 0.684928
\(905\) 0.902149 + 1.56257i 0.0299884 + 0.0519415i
\(906\) −1.58708 + 2.74890i −0.0527272 + 0.0913262i
\(907\) −27.2790 + 47.2485i −0.905783 + 1.56886i −0.0859196 + 0.996302i \(0.527383\pi\)
−0.819863 + 0.572560i \(0.805951\pi\)
\(908\) 4.93395 + 8.54585i 0.163739 + 0.283604i
\(909\) 11.8067 0.391603
\(910\) −3.34839 + 25.3033i −0.110998 + 0.838797i
\(911\) −6.08564 −0.201626 −0.100813 0.994905i \(-0.532144\pi\)
−0.100813 + 0.994905i \(0.532144\pi\)
\(912\) 2.08759 + 3.61581i 0.0691270 + 0.119731i
\(913\) −26.3256 + 45.5973i −0.871250 + 1.50905i
\(914\) −8.23635 + 14.2658i −0.272434 + 0.471870i
\(915\) 0.343748 + 0.595389i 0.0113640 + 0.0196830i
\(916\) 15.5632 0.514224
\(917\) 18.0625 + 13.8789i 0.596475 + 0.458323i
\(918\) −10.3258 −0.340801
\(919\) 6.07391 + 10.5203i 0.200360 + 0.347034i 0.948644 0.316344i \(-0.102456\pi\)
−0.748284 + 0.663378i \(0.769122\pi\)
\(920\) −3.95362 + 6.84787i −0.130347 + 0.225767i
\(921\) −3.24008 + 5.61198i −0.106764 + 0.184921i
\(922\) −5.20664 9.01816i −0.171472 0.296997i
\(923\) 73.3763 2.41521
\(924\) 1.44140 0.595925i 0.0474187 0.0196045i
\(925\) −27.1598 −0.893010
\(926\) −26.2716 45.5038i −0.863340 1.49535i
\(927\) −4.38683 + 7.59820i −0.144082 + 0.249558i
\(928\) 10.5327 18.2432i 0.345753 0.598861i
\(929\) −0.362326 0.627568i −0.0118875 0.0205898i 0.860020 0.510260i \(-0.170451\pi\)
−0.871908 + 0.489670i \(0.837117\pi\)
\(930\) 1.21773 0.0399310
\(931\) 26.6760 + 7.18590i 0.874269 + 0.235508i
\(932\) 19.3641 0.634291
\(933\) 0.739183 + 1.28030i 0.0241998 + 0.0419152i
\(934\) 0.350940 0.607846i 0.0114831 0.0198893i
\(935\) 8.58186 14.8642i 0.280657 0.486112i
\(936\) −17.2538 29.8844i −0.563958 0.976803i
\(937\) 54.0177 1.76468 0.882341 0.470610i \(-0.155966\pi\)
0.882341 + 0.470610i \(0.155966\pi\)
\(938\) −30.0287 + 12.4149i −0.980473 + 0.405360i
\(939\) −6.56778 −0.214332
\(940\) −2.32950 4.03481i −0.0759798 0.131601i
\(941\) 27.0814 46.9063i 0.882828 1.52910i 0.0346444 0.999400i \(-0.488970\pi\)
0.848183 0.529703i \(-0.177697\pi\)
\(942\) 2.83419 4.90896i 0.0923428 0.159942i
\(943\) −1.94368 3.36655i −0.0632948 0.109630i
\(944\) −13.7896 −0.448812
\(945\) −2.67654 2.05662i −0.0870679 0.0669017i
\(946\) 10.9991 0.357612
\(947\) −20.5106 35.5255i −0.666506 1.15442i −0.978875 0.204461i \(-0.934456\pi\)
0.312369 0.949961i \(-0.398878\pi\)
\(948\) −0.702444 + 1.21667i −0.0228143 + 0.0395156i
\(949\) −35.2444 + 61.0452i −1.14408 + 1.98161i
\(950\) 13.1513 + 22.7787i 0.426684 + 0.739038i
\(951\) −0.620579 −0.0201237
\(952\) −3.42389 + 25.8738i −0.110969 + 0.838576i
\(953\) −50.6204 −1.63976 −0.819879 0.572537i \(-0.805959\pi\)
−0.819879 + 0.572537i \(0.805959\pi\)
\(954\) −25.9702 44.9816i −0.840815 1.45633i
\(955\) 1.08639 1.88169i 0.0351548 0.0608899i
\(956\) −9.02719 + 15.6356i −0.291960 + 0.505690i
\(957\) 1.87701 + 3.25107i 0.0606750 + 0.105092i
\(958\) −46.6049 −1.50574
\(959\) 0.0598590 0.452346i 0.00193295 0.0146070i
\(960\) −0.616404 −0.0198944
\(961\) 9.70136 + 16.8032i 0.312947 + 0.542040i
\(962\) −32.6975 + 56.6338i −1.05421 + 1.82595i
\(963\) 17.2930 29.9524i 0.557259 0.965202i
\(964\) 6.74589 + 11.6842i 0.217271 + 0.376324i
\(965\) 7.05860 0.227224
\(966\) −2.90653 2.23334i −0.0935160 0.0718564i
\(967\) 56.5914 1.81986 0.909928 0.414766i \(-0.136137\pi\)
0.909928 + 0.414766i \(0.136137\pi\)
\(968\) −1.37850 2.38764i −0.0443068 0.0767416i
\(969\) −2.05049 + 3.55155i −0.0658712 + 0.114092i
\(970\) 15.3365 26.5636i 0.492425 0.852905i
\(971\) 18.6801 + 32.3549i 0.599473 + 1.03832i 0.992899 + 0.118962i \(0.0379566\pi\)
−0.393425 + 0.919357i \(0.628710\pi\)
\(972\) −4.43608 −0.142287
\(973\) 21.5093 8.89266i 0.689556 0.285086i
\(974\) −30.5890 −0.980134
\(975\) 2.45653 + 4.25483i 0.0786718 + 0.136264i
\(976\) 7.94772 13.7659i 0.254400 0.440634i
\(977\) 2.59379 4.49257i 0.0829826 0.143730i −0.821547 0.570141i \(-0.806889\pi\)
0.904530 + 0.426410i \(0.140222\pi\)
\(978\) −3.60938 6.25164i −0.115415 0.199905i
\(979\) −19.6242 −0.627192
\(980\) 3.90485 3.89446i 0.124736 0.124404i
\(981\) −43.0094 −1.37319
\(982\) −7.04195 12.1970i −0.224718 0.389222i
\(983\) 23.1340 40.0693i 0.737860 1.27801i −0.215597 0.976482i \(-0.569170\pi\)
0.953457 0.301529i \(-0.0974969\pi\)
\(984\) 0.216466 0.374931i 0.00690070 0.0119524i
\(985\) 4.75284 + 8.23217i 0.151438 + 0.262299i
\(986\) 40.6050 1.29313
\(987\) −3.08765 + 1.27654i −0.0982811 + 0.0406327i
\(988\) 17.8547 0.568034
\(989\) −3.64371 6.31108i −0.115863 0.200681i
\(990\) 8.69608 15.0621i 0.276380 0.478704i
\(991\) −8.46781 + 14.6667i −0.268989 + 0.465902i −0.968601 0.248621i \(-0.920023\pi\)
0.699612 + 0.714523i \(0.253356\pi\)
\(992\) −7.17342 12.4247i −0.227756 0.394485i
\(993\) −0.994014 −0.0315441
\(994\) −44.5922 34.2640i −1.41438 1.08679i
\(995\) 3.56940 0.113158
\(996\) −1.25564 2.17483i −0.0397864 0.0689120i
\(997\) 11.1719 19.3503i 0.353818 0.612831i −0.633097 0.774073i \(-0.718217\pi\)
0.986915 + 0.161242i \(0.0515499\pi\)
\(998\) 5.27395 9.13474i 0.166944 0.289155i
\(999\) −4.32412 7.48959i −0.136809 0.236960i
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 287.2.e.d.165.13 34
7.2 even 3 inner 287.2.e.d.247.13 yes 34
7.3 odd 6 2009.2.a.r.1.5 17
7.4 even 3 2009.2.a.s.1.5 17
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
287.2.e.d.165.13 34 1.1 even 1 trivial
287.2.e.d.247.13 yes 34 7.2 even 3 inner
2009.2.a.r.1.5 17 7.3 odd 6
2009.2.a.s.1.5 17 7.4 even 3