Properties

Label 539.2.q.c.361.2
Level $539$
Weight $2$
Character 539.361
Analytic conductor $4.304$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [539,2,Mod(214,539)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(539, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([20, 12]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("539.214");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 539 = 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 539.q (of order \(15\), degree \(8\), not 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: \(4.30393666895\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(2\) over \(\Q(\zeta_{15})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - x^{15} - 5 x^{14} + 16 x^{13} + 4 x^{12} - 29 x^{11} + 10 x^{10} - 156 x^{9} + 251 x^{8} + \cdots + 625 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 77)
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 361.2
Root \(-0.185798 + 1.76775i\) of defining polynomial
Character \(\chi\) \(=\) 539.361
Dual form 539.2.q.c.324.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.760494 - 0.161648i) q^{2} +(-0.0646021 - 0.614648i) q^{3} +(-1.27487 + 0.567608i) q^{4} +(-0.148892 + 0.165361i) q^{5} +(-0.148486 - 0.456994i) q^{6} +(-2.13577 + 1.55173i) q^{8} +(2.56082 - 0.544320i) q^{9} +O(q^{10})\) \(q+(0.760494 - 0.161648i) q^{2} +(-0.0646021 - 0.614648i) q^{3} +(-1.27487 + 0.567608i) q^{4} +(-0.148892 + 0.165361i) q^{5} +(-0.148486 - 0.456994i) q^{6} +(-2.13577 + 1.55173i) q^{8} +(2.56082 - 0.544320i) q^{9} +(-0.0865012 + 0.149825i) q^{10} +(2.48448 + 2.19713i) q^{11} +(0.431239 + 0.746928i) q^{12} +(2.01774 - 6.20997i) q^{13} +(0.111258 + 0.0808336i) q^{15} +(0.494158 - 0.548818i) q^{16} +(4.23989 + 0.901217i) q^{17} +(1.85950 - 0.827904i) q^{18} +(2.66299 + 1.18564i) q^{19} +(0.0959574 - 0.295327i) q^{20} +(2.24459 + 1.26929i) q^{22} +(1.94898 + 3.37573i) q^{23} +(1.09174 + 1.21250i) q^{24} +(0.517467 + 4.92337i) q^{25} +(0.530651 - 5.04881i) q^{26} +(-1.07295 - 3.30220i) q^{27} +(3.05322 + 2.21829i) q^{29} +(0.0976776 + 0.0434889i) q^{30} +(-4.61003 - 5.11996i) q^{31} +(2.92705 - 5.06980i) q^{32} +(1.18996 - 1.66902i) q^{33} +3.37009 q^{34} +(-2.95576 + 2.14748i) q^{36} +(0.590953 - 5.62254i) q^{37} +(2.21685 + 0.471205i) q^{38} +(-3.94730 - 0.839024i) q^{39} +(0.0614035 - 0.584215i) q^{40} +(-1.08255 + 0.786521i) q^{41} -4.70820 q^{43} +(-4.41449 - 1.39084i) q^{44} +(-0.291277 + 0.504506i) q^{45} +(2.02787 + 2.25218i) q^{46} +(5.52287 + 2.45894i) q^{47} +(-0.369254 - 0.268279i) q^{48} +(1.18938 + 3.66055i) q^{50} +(0.280025 - 2.66426i) q^{51} +(0.952474 + 9.06218i) q^{52} +(-1.14951 - 1.27666i) q^{53} +(-1.34977 - 2.33786i) q^{54} +(-0.733239 + 0.0837016i) q^{55} +(0.556717 - 1.71340i) q^{57} +(2.68054 + 1.19345i) q^{58} +(-8.70887 + 3.87744i) q^{59} +(-0.187721 - 0.0399013i) q^{60} +(-6.44334 + 7.15606i) q^{61} +(-4.33353 - 3.14850i) q^{62} +(0.950059 - 2.92398i) q^{64} +(0.726463 + 1.25827i) q^{65} +(0.635163 - 1.46163i) q^{66} +(-0.635774 + 1.10119i) q^{67} +(-5.91685 + 1.25766i) q^{68} +(1.94898 - 1.41602i) q^{69} +(-2.87670 - 8.85357i) q^{71} +(-4.62470 + 5.13625i) q^{72} +(5.10591 - 2.27330i) q^{73} +(-0.459457 - 4.37144i) q^{74} +(2.99271 - 0.636120i) q^{75} -4.06794 q^{76} -3.13752 q^{78} +(4.43056 - 0.941745i) q^{79} +(0.0171771 + 0.163429i) q^{80} +(5.21470 - 2.32174i) q^{81} +(-0.696136 + 0.773138i) q^{82} +(3.48688 + 10.7315i) q^{83} +(-0.780313 + 0.566931i) q^{85} +(-3.58056 + 0.761072i) q^{86} +(1.16623 - 2.01996i) q^{87} +(-8.71563 - 0.837331i) q^{88} +(-3.96078 - 6.86028i) q^{89} +(-0.139962 + 0.430759i) q^{90} +(-4.40079 - 3.19736i) q^{92} +(-2.84916 + 3.16431i) q^{93} +(4.59760 + 0.977249i) q^{94} +(-0.592557 + 0.263824i) q^{95} +(-3.30524 - 1.47159i) q^{96} +(-2.79781 + 8.61078i) q^{97} +(7.55825 + 4.27411i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + q^{2} + 4 q^{3} - 3 q^{4} - 3 q^{5} + 6 q^{6} + 6 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + q^{2} + 4 q^{3} - 3 q^{4} - 3 q^{5} + 6 q^{6} + 6 q^{8} + 2 q^{9} + 28 q^{10} - 5 q^{11} + 14 q^{12} + 10 q^{13} + 12 q^{15} + 3 q^{16} + 11 q^{17} - 4 q^{18} + 9 q^{19} + 42 q^{20} - 2 q^{22} + 16 q^{23} - 21 q^{24} - 5 q^{25} - 21 q^{26} - 44 q^{27} - 18 q^{29} - 14 q^{30} + 11 q^{31} + 20 q^{32} - 10 q^{33} - 48 q^{34} - 4 q^{36} - 6 q^{37} - 35 q^{38} + 5 q^{39} + 16 q^{40} - 44 q^{41} + 32 q^{43} - 29 q^{44} - 18 q^{45} - 29 q^{46} - 7 q^{47} + 8 q^{48} - 68 q^{50} - 3 q^{51} - 21 q^{52} - 2 q^{53} - 4 q^{54} + 52 q^{55} - 6 q^{57} + 39 q^{58} - 25 q^{59} + 38 q^{60} - 7 q^{61} - 10 q^{62} + 2 q^{64} - 24 q^{65} - 18 q^{66} + 30 q^{67} - 8 q^{68} + 16 q^{69} - 28 q^{71} - 3 q^{72} - 3 q^{73} + 9 q^{74} - 5 q^{75} - 104 q^{76} - 36 q^{78} + 9 q^{79} + 33 q^{80} + 28 q^{81} - 31 q^{82} + 46 q^{83} - 20 q^{85} + 17 q^{86} - 12 q^{87} + 7 q^{88} + 34 q^{89} + 4 q^{90} - 68 q^{92} - 8 q^{93} + 30 q^{94} - 24 q^{95} - 10 q^{96} + 60 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/539\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(442\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.760494 0.161648i 0.537751 0.114302i 0.0689729 0.997619i \(-0.478028\pi\)
0.468778 + 0.883316i \(0.344694\pi\)
\(3\) −0.0646021 0.614648i −0.0372981 0.354867i −0.997215 0.0745823i \(-0.976238\pi\)
0.959917 0.280285i \(-0.0904290\pi\)
\(4\) −1.27487 + 0.567608i −0.637435 + 0.283804i
\(5\) −0.148892 + 0.165361i −0.0665866 + 0.0739519i −0.775518 0.631326i \(-0.782511\pi\)
0.708931 + 0.705278i \(0.249178\pi\)
\(6\) −0.148486 0.456994i −0.0606193 0.186567i
\(7\) 0 0
\(8\) −2.13577 + 1.55173i −0.755110 + 0.548620i
\(9\) 2.56082 0.544320i 0.853608 0.181440i
\(10\) −0.0865012 + 0.149825i −0.0273541 + 0.0473787i
\(11\) 2.48448 + 2.19713i 0.749098 + 0.662459i
\(12\) 0.431239 + 0.746928i 0.124488 + 0.215619i
\(13\) 2.01774 6.20997i 0.559620 1.72233i −0.123798 0.992307i \(-0.539507\pi\)
0.683418 0.730027i \(-0.260493\pi\)
\(14\) 0 0
\(15\) 0.111258 + 0.0808336i 0.0287267 + 0.0208711i
\(16\) 0.494158 0.548818i 0.123540 0.137205i
\(17\) 4.23989 + 0.901217i 1.02832 + 0.218577i 0.691033 0.722823i \(-0.257156\pi\)
0.337292 + 0.941400i \(0.390489\pi\)
\(18\) 1.85950 0.827904i 0.438289 0.195139i
\(19\) 2.66299 + 1.18564i 0.610932 + 0.272004i 0.688791 0.724960i \(-0.258142\pi\)
−0.0778590 + 0.996964i \(0.524808\pi\)
\(20\) 0.0959574 0.295327i 0.0214567 0.0660370i
\(21\) 0 0
\(22\) 2.24459 + 1.26929i 0.478549 + 0.270614i
\(23\) 1.94898 + 3.37573i 0.406390 + 0.703888i 0.994482 0.104906i \(-0.0334540\pi\)
−0.588092 + 0.808794i \(0.700121\pi\)
\(24\) 1.09174 + 1.21250i 0.222851 + 0.247502i
\(25\) 0.517467 + 4.92337i 0.103493 + 0.984673i
\(26\) 0.530651 5.04881i 0.104069 0.990153i
\(27\) −1.07295 3.30220i −0.206489 0.635508i
\(28\) 0 0
\(29\) 3.05322 + 2.21829i 0.566969 + 0.411927i 0.834003 0.551760i \(-0.186044\pi\)
−0.267034 + 0.963687i \(0.586044\pi\)
\(30\) 0.0976776 + 0.0434889i 0.0178334 + 0.00793994i
\(31\) −4.61003 5.11996i −0.827986 0.919571i 0.169840 0.985472i \(-0.445675\pi\)
−0.997826 + 0.0659001i \(0.979008\pi\)
\(32\) 2.92705 5.06980i 0.517434 0.896223i
\(33\) 1.18996 1.66902i 0.207145 0.290539i
\(34\) 3.37009 0.577966
\(35\) 0 0
\(36\) −2.95576 + 2.14748i −0.492626 + 0.357914i
\(37\) 0.590953 5.62254i 0.0971521 0.924340i −0.832033 0.554726i \(-0.812823\pi\)
0.929185 0.369614i \(-0.120510\pi\)
\(38\) 2.21685 + 0.471205i 0.359620 + 0.0764396i
\(39\) −3.94730 0.839024i −0.632073 0.134351i
\(40\) 0.0614035 0.584215i 0.00970874 0.0923725i
\(41\) −1.08255 + 0.786521i −0.169066 + 0.122834i −0.669101 0.743171i \(-0.733321\pi\)
0.500035 + 0.866005i \(0.333321\pi\)
\(42\) 0 0
\(43\) −4.70820 −0.717994 −0.358997 0.933339i \(-0.616881\pi\)
−0.358997 + 0.933339i \(0.616881\pi\)
\(44\) −4.41449 1.39084i −0.665510 0.209677i
\(45\) −0.291277 + 0.504506i −0.0434210 + 0.0752074i
\(46\) 2.02787 + 2.25218i 0.298993 + 0.332065i
\(47\) 5.52287 + 2.45894i 0.805594 + 0.358673i 0.767863 0.640615i \(-0.221320\pi\)
0.0377310 + 0.999288i \(0.487987\pi\)
\(48\) −0.369254 0.268279i −0.0532972 0.0387227i
\(49\) 0 0
\(50\) 1.18938 + 3.66055i 0.168204 + 0.517679i
\(51\) 0.280025 2.66426i 0.0392114 0.373071i
\(52\) 0.952474 + 9.06218i 0.132084 + 1.25670i
\(53\) −1.14951 1.27666i −0.157897 0.175363i 0.659005 0.752138i \(-0.270977\pi\)
−0.816903 + 0.576775i \(0.804311\pi\)
\(54\) −1.34977 2.33786i −0.183680 0.318143i
\(55\) −0.733239 + 0.0837016i −0.0988700 + 0.0112863i
\(56\) 0 0
\(57\) 0.556717 1.71340i 0.0737389 0.226945i
\(58\) 2.68054 + 1.19345i 0.351972 + 0.156708i
\(59\) −8.70887 + 3.87744i −1.13380 + 0.504799i −0.885849 0.463974i \(-0.846423\pi\)
−0.247949 + 0.968773i \(0.579756\pi\)
\(60\) −0.187721 0.0399013i −0.0242347 0.00515124i
\(61\) −6.44334 + 7.15606i −0.824986 + 0.916239i −0.997634 0.0687442i \(-0.978101\pi\)
0.172649 + 0.984983i \(0.444767\pi\)
\(62\) −4.33353 3.14850i −0.550359 0.399859i
\(63\) 0 0
\(64\) 0.950059 2.92398i 0.118757 0.365498i
\(65\) 0.726463 + 1.25827i 0.0901067 + 0.156069i
\(66\) 0.635163 1.46163i 0.0781832 0.179915i
\(67\) −0.635774 + 1.10119i −0.0776722 + 0.134532i −0.902245 0.431223i \(-0.858082\pi\)
0.824573 + 0.565756i \(0.191415\pi\)
\(68\) −5.91685 + 1.25766i −0.717523 + 0.152514i
\(69\) 1.94898 1.41602i 0.234629 0.170468i
\(70\) 0 0
\(71\) −2.87670 8.85357i −0.341401 1.05072i −0.963482 0.267772i \(-0.913713\pi\)
0.622081 0.782953i \(-0.286287\pi\)
\(72\) −4.62470 + 5.13625i −0.545026 + 0.605313i
\(73\) 5.10591 2.27330i 0.597601 0.266069i −0.0855643 0.996333i \(-0.527269\pi\)
0.683166 + 0.730263i \(0.260603\pi\)
\(74\) −0.459457 4.37144i −0.0534108 0.508169i
\(75\) 2.99271 0.636120i 0.345568 0.0734528i
\(76\) −4.06794 −0.466625
\(77\) 0 0
\(78\) −3.13752 −0.355254
\(79\) 4.43056 0.941745i 0.498477 0.105955i 0.0481897 0.998838i \(-0.484655\pi\)
0.450288 + 0.892884i \(0.351321\pi\)
\(80\) 0.0171771 + 0.163429i 0.00192046 + 0.0182720i
\(81\) 5.21470 2.32174i 0.579412 0.257971i
\(82\) −0.696136 + 0.773138i −0.0768754 + 0.0853788i
\(83\) 3.48688 + 10.7315i 0.382734 + 1.17793i 0.938111 + 0.346336i \(0.112574\pi\)
−0.555376 + 0.831599i \(0.687426\pi\)
\(84\) 0 0
\(85\) −0.780313 + 0.566931i −0.0846368 + 0.0614922i
\(86\) −3.58056 + 0.761072i −0.386102 + 0.0820685i
\(87\) 1.16623 2.01996i 0.125033 0.216563i
\(88\) −8.71563 0.837331i −0.929090 0.0892598i
\(89\) −3.96078 6.86028i −0.419842 0.727188i 0.576081 0.817393i \(-0.304581\pi\)
−0.995923 + 0.0902046i \(0.971248\pi\)
\(90\) −0.139962 + 0.430759i −0.0147533 + 0.0454059i
\(91\) 0 0
\(92\) −4.40079 3.19736i −0.458814 0.333348i
\(93\) −2.84916 + 3.16431i −0.295444 + 0.328123i
\(94\) 4.59760 + 0.977249i 0.474206 + 0.100796i
\(95\) −0.592557 + 0.263824i −0.0607951 + 0.0270677i
\(96\) −3.30524 1.47159i −0.337339 0.150193i
\(97\) −2.79781 + 8.61078i −0.284075 + 0.874292i 0.702600 + 0.711585i \(0.252023\pi\)
−0.986674 + 0.162707i \(0.947977\pi\)
\(98\) 0 0
\(99\) 7.55825 + 4.27411i 0.759633 + 0.429564i
\(100\) −3.45425 5.98293i −0.345425 0.598293i
\(101\) −12.8541 14.2759i −1.27903 1.42051i −0.858155 0.513390i \(-0.828389\pi\)
−0.420876 0.907118i \(-0.638277\pi\)
\(102\) −0.217715 2.07142i −0.0215570 0.205101i
\(103\) −1.69737 + 16.1494i −0.167246 + 1.59124i 0.513085 + 0.858338i \(0.328503\pi\)
−0.680331 + 0.732905i \(0.738164\pi\)
\(104\) 5.32676 + 16.3941i 0.522332 + 1.60757i
\(105\) 0 0
\(106\) −1.08057 0.785077i −0.104954 0.0762534i
\(107\) −4.92708 2.19368i −0.476319 0.212071i 0.154513 0.987991i \(-0.450619\pi\)
−0.630831 + 0.775920i \(0.717286\pi\)
\(108\) 3.24222 + 3.60086i 0.311983 + 0.346492i
\(109\) −2.69951 + 4.67568i −0.258566 + 0.447849i −0.965858 0.259072i \(-0.916583\pi\)
0.707292 + 0.706921i \(0.249917\pi\)
\(110\) −0.544094 + 0.182181i −0.0518773 + 0.0173703i
\(111\) −3.49406 −0.331642
\(112\) 0 0
\(113\) 13.3457 9.69624i 1.25546 0.912145i 0.256935 0.966429i \(-0.417287\pi\)
0.998526 + 0.0542834i \(0.0172875\pi\)
\(114\) 0.146412 1.39302i 0.0137128 0.130468i
\(115\) −0.848403 0.180334i −0.0791140 0.0168162i
\(116\) −5.15158 1.09500i −0.478312 0.101668i
\(117\) 1.78687 17.0009i 0.165196 1.57174i
\(118\) −5.99626 + 4.35654i −0.552001 + 0.401052i
\(119\) 0 0
\(120\) −0.363054 −0.0331421
\(121\) 1.34525 + 10.9174i 0.122296 + 0.992494i
\(122\) −3.74336 + 6.48370i −0.338908 + 0.587006i
\(123\) 0.553369 + 0.614579i 0.0498956 + 0.0554147i
\(124\) 8.78332 + 3.91058i 0.788765 + 0.351181i
\(125\) −1.79128 1.30144i −0.160217 0.116404i
\(126\) 0 0
\(127\) 0.617194 + 1.89953i 0.0547671 + 0.168556i 0.974699 0.223523i \(-0.0717559\pi\)
−0.919931 + 0.392079i \(0.871756\pi\)
\(128\) −0.973982 + 9.26682i −0.0860886 + 0.819079i
\(129\) 0.304160 + 2.89389i 0.0267798 + 0.254793i
\(130\) 0.755868 + 0.839477i 0.0662940 + 0.0736270i
\(131\) −0.685047 1.18654i −0.0598528 0.103668i 0.834546 0.550938i \(-0.185730\pi\)
−0.894399 + 0.447270i \(0.852396\pi\)
\(132\) −0.569693 + 2.80321i −0.0495854 + 0.243988i
\(133\) 0 0
\(134\) −0.305497 + 0.940223i −0.0263909 + 0.0812229i
\(135\) 0.705810 + 0.314247i 0.0607464 + 0.0270461i
\(136\) −10.4539 + 4.65437i −0.896414 + 0.399109i
\(137\) −2.44463 0.519621i −0.208858 0.0443942i 0.102294 0.994754i \(-0.467382\pi\)
−0.311153 + 0.950360i \(0.600715\pi\)
\(138\) 1.25329 1.39192i 0.106687 0.118488i
\(139\) 3.85302 + 2.79938i 0.326809 + 0.237441i 0.739075 0.673623i \(-0.235263\pi\)
−0.412266 + 0.911063i \(0.635263\pi\)
\(140\) 0 0
\(141\) 1.15459 3.55348i 0.0972344 0.299257i
\(142\) −3.61887 6.26807i −0.303689 0.526005i
\(143\) 18.6571 10.9953i 1.56019 0.919472i
\(144\) 0.966719 1.67441i 0.0805599 0.139534i
\(145\) −0.821421 + 0.174598i −0.0682153 + 0.0144996i
\(146\) 3.51554 2.55419i 0.290948 0.211386i
\(147\) 0 0
\(148\) 2.43801 + 7.50344i 0.200404 + 0.616779i
\(149\) −4.83772 + 5.37283i −0.396321 + 0.440159i −0.907970 0.419036i \(-0.862368\pi\)
0.511649 + 0.859195i \(0.329035\pi\)
\(150\) 2.17311 0.967532i 0.177434 0.0789986i
\(151\) −0.850829 8.09509i −0.0692394 0.658769i −0.973012 0.230756i \(-0.925880\pi\)
0.903772 0.428014i \(-0.140786\pi\)
\(152\) −7.52734 + 1.59999i −0.610548 + 0.129776i
\(153\) 11.3482 0.917445
\(154\) 0 0
\(155\) 1.53304 0.123137
\(156\) 5.50852 1.17087i 0.441035 0.0937448i
\(157\) −2.10640 20.0410i −0.168109 1.59945i −0.675253 0.737587i \(-0.735965\pi\)
0.507144 0.861861i \(-0.330701\pi\)
\(158\) 3.21719 1.43238i 0.255946 0.113954i
\(159\) −0.710436 + 0.789019i −0.0563412 + 0.0625733i
\(160\) 0.402535 + 1.23887i 0.0318232 + 0.0979416i
\(161\) 0 0
\(162\) 3.59045 2.60861i 0.282092 0.204952i
\(163\) −7.27203 + 1.54572i −0.569590 + 0.121070i −0.483699 0.875235i \(-0.660707\pi\)
−0.0858908 + 0.996305i \(0.527374\pi\)
\(164\) 0.933679 1.61718i 0.0729080 0.126280i
\(165\) 0.0988159 + 0.445277i 0.00769280 + 0.0346648i
\(166\) 4.38647 + 7.59760i 0.340456 + 0.589688i
\(167\) −0.683275 + 2.10290i −0.0528734 + 0.162728i −0.974006 0.226520i \(-0.927265\pi\)
0.921133 + 0.389248i \(0.127265\pi\)
\(168\) 0 0
\(169\) −23.9752 17.4190i −1.84424 1.33992i
\(170\) −0.501780 + 0.557284i −0.0384848 + 0.0427417i
\(171\) 7.46482 + 1.58670i 0.570849 + 0.121338i
\(172\) 6.00234 2.67242i 0.457675 0.203770i
\(173\) −9.46634 4.21469i −0.719712 0.320437i 0.0139950 0.999902i \(-0.495545\pi\)
−0.733708 + 0.679465i \(0.762212\pi\)
\(174\) 0.560385 1.72469i 0.0424827 0.130748i
\(175\) 0 0
\(176\) 2.43355 0.277797i 0.183436 0.0209398i
\(177\) 2.94587 + 5.10240i 0.221425 + 0.383520i
\(178\) −4.12110 4.57695i −0.308890 0.343057i
\(179\) 2.44695 + 23.2812i 0.182894 + 1.74012i 0.573186 + 0.819426i \(0.305707\pi\)
−0.390292 + 0.920691i \(0.627626\pi\)
\(180\) 0.0849779 0.808511i 0.00633388 0.0602628i
\(181\) −4.23851 13.0448i −0.315046 0.969611i −0.975736 0.218952i \(-0.929736\pi\)
0.660690 0.750659i \(-0.270264\pi\)
\(182\) 0 0
\(183\) 4.81471 + 3.49809i 0.355914 + 0.258587i
\(184\) −9.40080 4.18551i −0.693036 0.308560i
\(185\) 0.841764 + 0.934873i 0.0618877 + 0.0687332i
\(186\) −1.65526 + 2.86700i −0.121370 + 0.210219i
\(187\) 8.55382 + 11.5546i 0.625518 + 0.844959i
\(188\) −8.43666 −0.615306
\(189\) 0 0
\(190\) −0.407990 + 0.296422i −0.0295987 + 0.0215047i
\(191\) 1.25695 11.9591i 0.0909496 0.865328i −0.850000 0.526782i \(-0.823398\pi\)
0.940950 0.338546i \(-0.109935\pi\)
\(192\) −1.85860 0.395057i −0.134133 0.0285108i
\(193\) −15.5368 3.30245i −1.11836 0.237716i −0.388595 0.921409i \(-0.627039\pi\)
−0.729770 + 0.683693i \(0.760373\pi\)
\(194\) −0.735804 + 7.00071i −0.0528277 + 0.502622i
\(195\) 0.726463 0.527806i 0.0520231 0.0377970i
\(196\) 0 0
\(197\) 12.3035 0.876590 0.438295 0.898831i \(-0.355582\pi\)
0.438295 + 0.898831i \(0.355582\pi\)
\(198\) 6.43891 + 2.02866i 0.457593 + 0.144171i
\(199\) −7.63075 + 13.2168i −0.540929 + 0.936917i 0.457922 + 0.888993i \(0.348594\pi\)
−0.998851 + 0.0479244i \(0.984739\pi\)
\(200\) −8.74493 9.71223i −0.618360 0.686758i
\(201\) 0.717919 + 0.319638i 0.0506381 + 0.0225455i
\(202\) −12.0832 8.77892i −0.850168 0.617683i
\(203\) 0 0
\(204\) 1.15526 + 3.55553i 0.0808845 + 0.248937i
\(205\) 0.0311234 0.296119i 0.00217375 0.0206819i
\(206\) 1.31967 + 12.5559i 0.0919461 + 0.874809i
\(207\) 6.82847 + 7.58378i 0.474611 + 0.527109i
\(208\) −2.41106 4.17608i −0.167177 0.289559i
\(209\) 4.01114 + 8.79663i 0.277456 + 0.608476i
\(210\) 0 0
\(211\) 2.76058 8.49620i 0.190046 0.584903i −0.809952 0.586496i \(-0.800507\pi\)
0.999999 + 0.00159295i \(0.000507051\pi\)
\(212\) 2.19012 + 0.975103i 0.150418 + 0.0669704i
\(213\) −5.25599 + 2.34012i −0.360134 + 0.160342i
\(214\) −4.10162 0.871826i −0.280381 0.0595968i
\(215\) 0.701014 0.778555i 0.0478088 0.0530970i
\(216\) 7.41570 + 5.38782i 0.504574 + 0.366595i
\(217\) 0 0
\(218\) −1.29714 + 3.99220i −0.0878537 + 0.270386i
\(219\) −1.72713 2.99148i −0.116709 0.202145i
\(220\) 0.887275 0.522901i 0.0598200 0.0352540i
\(221\) 14.1515 24.5112i 0.951935 1.64880i
\(222\) −2.65722 + 0.564809i −0.178341 + 0.0379075i
\(223\) −0.578645 + 0.420410i −0.0387489 + 0.0281527i −0.606991 0.794709i \(-0.707624\pi\)
0.568242 + 0.822861i \(0.307624\pi\)
\(224\) 0 0
\(225\) 4.00503 + 12.3262i 0.267002 + 0.821747i
\(226\) 8.58197 9.53124i 0.570864 0.634009i
\(227\) −4.86154 + 2.16450i −0.322672 + 0.143663i −0.561679 0.827355i \(-0.689845\pi\)
0.239008 + 0.971018i \(0.423178\pi\)
\(228\) 0.262798 + 2.50036i 0.0174042 + 0.165590i
\(229\) 6.46392 1.37395i 0.427148 0.0907930i 0.0106786 0.999943i \(-0.496601\pi\)
0.416469 + 0.909150i \(0.363267\pi\)
\(230\) −0.674356 −0.0444657
\(231\) 0 0
\(232\) −9.96318 −0.654115
\(233\) 9.34828 1.98704i 0.612426 0.130175i 0.108752 0.994069i \(-0.465315\pi\)
0.503674 + 0.863894i \(0.331981\pi\)
\(234\) −1.38926 13.2179i −0.0908189 0.864084i
\(235\) −1.22893 + 0.547153i −0.0801663 + 0.0356923i
\(236\) 8.90180 9.88645i 0.579458 0.643553i
\(237\) −0.865066 2.66240i −0.0561921 0.172941i
\(238\) 0 0
\(239\) −21.7194 + 15.7801i −1.40491 + 1.02073i −0.410872 + 0.911693i \(0.634776\pi\)
−0.994038 + 0.109034i \(0.965224\pi\)
\(240\) 0.0993419 0.0211158i 0.00641249 0.00136302i
\(241\) −9.43316 + 16.3387i −0.607643 + 1.05247i 0.383985 + 0.923340i \(0.374552\pi\)
−0.991628 + 0.129129i \(0.958782\pi\)
\(242\) 2.78784 + 8.08519i 0.179209 + 0.519736i
\(243\) −6.97214 12.0761i −0.447263 0.774682i
\(244\) 4.15258 12.7803i 0.265842 0.818177i
\(245\) 0 0
\(246\) 0.520180 + 0.377933i 0.0331654 + 0.0240961i
\(247\) 12.7360 14.1448i 0.810373 0.900010i
\(248\) 17.7908 + 3.78155i 1.12972 + 0.240128i
\(249\) 6.37084 2.83648i 0.403735 0.179755i
\(250\) −1.57263 0.700180i −0.0994619 0.0442833i
\(251\) 9.07680 27.9355i 0.572923 1.76328i −0.0702229 0.997531i \(-0.522371\pi\)
0.643146 0.765744i \(-0.277629\pi\)
\(252\) 0 0
\(253\) −2.57472 + 12.6691i −0.161871 + 0.796498i
\(254\) 0.776427 + 1.34481i 0.0487174 + 0.0843810i
\(255\) 0.398873 + 0.442993i 0.0249784 + 0.0277413i
\(256\) 1.39999 + 13.3200i 0.0874995 + 0.832502i
\(257\) 1.76824 16.8237i 0.110300 1.04943i −0.789685 0.613513i \(-0.789756\pi\)
0.899985 0.435922i \(-0.143578\pi\)
\(258\) 0.699104 + 2.15162i 0.0435243 + 0.133954i
\(259\) 0 0
\(260\) −1.64035 1.19178i −0.101730 0.0739114i
\(261\) 9.02622 + 4.01873i 0.558709 + 0.248753i
\(262\) −0.712776 0.791617i −0.0440354 0.0489063i
\(263\) 4.09017 7.08438i 0.252211 0.436842i −0.711923 0.702257i \(-0.752176\pi\)
0.964134 + 0.265415i \(0.0855091\pi\)
\(264\) 0.0483844 + 5.41114i 0.00297785 + 0.333033i
\(265\) 0.382263 0.0234822
\(266\) 0 0
\(267\) −3.96078 + 2.87768i −0.242396 + 0.176111i
\(268\) 0.185482 1.76475i 0.0113301 0.107799i
\(269\) 6.11065 + 1.29886i 0.372573 + 0.0791928i 0.390393 0.920648i \(-0.372339\pi\)
−0.0178200 + 0.999841i \(0.505673\pi\)
\(270\) 0.587562 + 0.124890i 0.0357579 + 0.00760057i
\(271\) −0.822312 + 7.82378i −0.0499519 + 0.475261i 0.940739 + 0.339131i \(0.110133\pi\)
−0.990691 + 0.136130i \(0.956534\pi\)
\(272\) 2.58978 1.88159i 0.157029 0.114088i
\(273\) 0 0
\(274\) −1.94312 −0.117388
\(275\) −9.53164 + 13.3689i −0.574779 + 0.806177i
\(276\) −1.68095 + 2.91149i −0.101181 + 0.175251i
\(277\) 8.06145 + 8.95315i 0.484366 + 0.537943i 0.934944 0.354794i \(-0.115449\pi\)
−0.450579 + 0.892737i \(0.648782\pi\)
\(278\) 3.38272 + 1.50608i 0.202882 + 0.0903288i
\(279\) −14.5924 10.6020i −0.873622 0.634724i
\(280\) 0 0
\(281\) 6.53723 + 20.1195i 0.389978 + 1.20023i 0.932804 + 0.360384i \(0.117354\pi\)
−0.542826 + 0.839846i \(0.682646\pi\)
\(282\) 0.303650 2.88904i 0.0180821 0.172040i
\(283\) 2.61356 + 24.8664i 0.155360 + 1.47815i 0.743142 + 0.669134i \(0.233335\pi\)
−0.587782 + 0.809020i \(0.699999\pi\)
\(284\) 8.69277 + 9.65430i 0.515821 + 0.572877i
\(285\) 0.200439 + 0.347171i 0.0118730 + 0.0205646i
\(286\) 12.4113 11.3777i 0.733894 0.672780i
\(287\) 0 0
\(288\) 4.73607 14.5761i 0.279075 0.858906i
\(289\) 1.63422 + 0.727601i 0.0961305 + 0.0428001i
\(290\) −0.596462 + 0.265562i −0.0350255 + 0.0155943i
\(291\) 5.47335 + 1.16340i 0.320853 + 0.0681995i
\(292\) −5.21902 + 5.79631i −0.305420 + 0.339204i
\(293\) 0.368173 + 0.267494i 0.0215089 + 0.0156271i 0.598488 0.801132i \(-0.295769\pi\)
−0.576979 + 0.816759i \(0.695769\pi\)
\(294\) 0 0
\(295\) 0.655503 2.01743i 0.0381648 0.117459i
\(296\) 7.46253 + 12.9255i 0.433751 + 0.751278i
\(297\) 4.58964 10.5616i 0.266318 0.612849i
\(298\) −2.81055 + 4.86801i −0.162811 + 0.281996i
\(299\) 24.8957 5.29175i 1.43976 0.306030i
\(300\) −3.45425 + 2.50966i −0.199431 + 0.144895i
\(301\) 0 0
\(302\) −1.95561 6.01874i −0.112533 0.346339i
\(303\) −7.94428 + 8.82301i −0.456387 + 0.506869i
\(304\) 1.96664 0.875604i 0.112794 0.0502193i
\(305\) −0.223973 2.13096i −0.0128247 0.122018i
\(306\) 8.63022 1.83441i 0.493357 0.104866i
\(307\) −8.03578 −0.458626 −0.229313 0.973353i \(-0.573648\pi\)
−0.229313 + 0.973353i \(0.573648\pi\)
\(308\) 0 0
\(309\) 10.0358 0.570918
\(310\) 1.16587 0.247813i 0.0662169 0.0140748i
\(311\) −0.0143167 0.136214i −0.000811827 0.00772401i 0.994108 0.108390i \(-0.0345694\pi\)
−0.994920 + 0.100666i \(0.967903\pi\)
\(312\) 9.73247 4.33317i 0.550993 0.245318i
\(313\) −10.2310 + 11.3626i −0.578288 + 0.642254i −0.959324 0.282306i \(-0.908901\pi\)
0.381036 + 0.924560i \(0.375567\pi\)
\(314\) −4.84150 14.9006i −0.273221 0.840889i
\(315\) 0 0
\(316\) −5.11385 + 3.71543i −0.287676 + 0.209009i
\(317\) 32.2716 6.85953i 1.81255 0.385270i 0.828051 0.560653i \(-0.189450\pi\)
0.984500 + 0.175383i \(0.0561163\pi\)
\(318\) −0.412739 + 0.714885i −0.0231453 + 0.0400888i
\(319\) 2.71178 + 12.2196i 0.151830 + 0.684167i
\(320\) 0.342058 + 0.592461i 0.0191216 + 0.0331196i
\(321\) −1.03004 + 3.17014i −0.0574912 + 0.176940i
\(322\) 0 0
\(323\) 10.2223 + 7.42692i 0.568783 + 0.413245i
\(324\) −5.33023 + 5.91982i −0.296124 + 0.328879i
\(325\) 31.6181 + 6.72063i 1.75385 + 0.372793i
\(326\) −5.28048 + 2.35102i −0.292459 + 0.130211i
\(327\) 3.04830 + 1.35719i 0.168571 + 0.0750527i
\(328\) 1.09162 3.35966i 0.0602747 0.185506i
\(329\) 0 0
\(330\) 0.147127 + 0.322657i 0.00809908 + 0.0177617i
\(331\) −14.7667 25.5767i −0.811653 1.40582i −0.911707 0.410842i \(-0.865235\pi\)
0.100054 0.994982i \(-0.468099\pi\)
\(332\) −10.5366 11.7021i −0.578271 0.642235i
\(333\) −1.54714 14.7200i −0.0847825 0.806652i
\(334\) −0.179696 + 1.70970i −0.00983255 + 0.0935505i
\(335\) −0.0874331 0.269091i −0.00477698 0.0147020i
\(336\) 0 0
\(337\) −4.55497 3.30938i −0.248125 0.180273i 0.456770 0.889585i \(-0.349006\pi\)
−0.704895 + 0.709311i \(0.749006\pi\)
\(338\) −21.0487 9.37150i −1.14490 0.509742i
\(339\) −6.82194 7.57653i −0.370517 0.411501i
\(340\) 0.673002 1.16567i 0.0364987 0.0632176i
\(341\) −0.204309 22.8492i −0.0110640 1.23736i
\(342\) 5.93344 0.320844
\(343\) 0 0
\(344\) 10.0557 7.30586i 0.542165 0.393906i
\(345\) −0.0560331 + 0.533120i −0.00301672 + 0.0287022i
\(346\) −7.88039 1.67503i −0.423653 0.0900501i
\(347\) −8.53983 1.81520i −0.458442 0.0974449i −0.0270988 0.999633i \(-0.508627\pi\)
−0.431343 + 0.902188i \(0.641960\pi\)
\(348\) −0.340238 + 3.23715i −0.0182387 + 0.173529i
\(349\) −14.9401 + 10.8546i −0.799724 + 0.581034i −0.910833 0.412774i \(-0.864560\pi\)
0.111109 + 0.993808i \(0.464560\pi\)
\(350\) 0 0
\(351\) −22.6715 −1.21011
\(352\) 18.4112 6.16470i 0.981320 0.328579i
\(353\) 11.7428 20.3392i 0.625009 1.08255i −0.363531 0.931582i \(-0.618429\pi\)
0.988539 0.150964i \(-0.0482379\pi\)
\(354\) 3.06511 + 3.40415i 0.162909 + 0.180929i
\(355\) 1.89236 + 0.842531i 0.100436 + 0.0447169i
\(356\) 8.94343 + 6.49778i 0.474001 + 0.344382i
\(357\) 0 0
\(358\) 5.62425 + 17.3097i 0.297251 + 0.914844i
\(359\) −1.55551 + 14.7997i −0.0820967 + 0.781098i 0.873580 + 0.486680i \(0.161792\pi\)
−0.955677 + 0.294417i \(0.904874\pi\)
\(360\) −0.160756 1.52949i −0.00847261 0.0806115i
\(361\) −7.02770 7.80505i −0.369879 0.410792i
\(362\) −5.33203 9.23534i −0.280245 0.485399i
\(363\) 6.62347 1.53215i 0.347642 0.0804168i
\(364\) 0 0
\(365\) −0.384314 + 1.18280i −0.0201159 + 0.0619104i
\(366\) 4.22702 + 1.88199i 0.220950 + 0.0983733i
\(367\) −31.2669 + 13.9209i −1.63212 + 0.726667i −0.998881 0.0472889i \(-0.984942\pi\)
−0.633240 + 0.773956i \(0.718275\pi\)
\(368\) 2.81577 + 0.598509i 0.146782 + 0.0311995i
\(369\) −2.34411 + 2.60340i −0.122030 + 0.135527i
\(370\) 0.791277 + 0.574896i 0.0411365 + 0.0298874i
\(371\) 0 0
\(372\) 1.83621 5.65128i 0.0952032 0.293005i
\(373\) −1.50870 2.61314i −0.0781173 0.135303i 0.824320 0.566124i \(-0.191558\pi\)
−0.902438 + 0.430820i \(0.858224\pi\)
\(374\) 8.37292 + 7.40453i 0.432953 + 0.382879i
\(375\) −0.684207 + 1.18508i −0.0353323 + 0.0611973i
\(376\) −15.6112 + 3.31827i −0.805087 + 0.171127i
\(377\) 19.9361 14.4845i 1.02676 0.745987i
\(378\) 0 0
\(379\) −1.89252 5.82457i −0.0972121 0.299188i 0.890612 0.454764i \(-0.150277\pi\)
−0.987824 + 0.155576i \(0.950277\pi\)
\(380\) 0.605685 0.672681i 0.0310710 0.0345078i
\(381\) 1.12767 0.502071i 0.0577723 0.0257219i
\(382\) −0.977258 9.29799i −0.0500009 0.475726i
\(383\) −4.29503 + 0.912937i −0.219466 + 0.0466489i −0.316332 0.948649i \(-0.602451\pi\)
0.0968663 + 0.995297i \(0.469118\pi\)
\(384\) 5.75876 0.293875
\(385\) 0 0
\(386\) −12.3495 −0.628573
\(387\) −12.0569 + 2.56277i −0.612886 + 0.130273i
\(388\) −1.32071 12.5657i −0.0670487 0.637926i
\(389\) 9.58858 4.26911i 0.486160 0.216452i −0.148994 0.988838i \(-0.547603\pi\)
0.635154 + 0.772386i \(0.280937\pi\)
\(390\) 0.467152 0.518825i 0.0236552 0.0262717i
\(391\) 5.22119 + 16.0692i 0.264047 + 0.812654i
\(392\) 0 0
\(393\) −0.685047 + 0.497716i −0.0345560 + 0.0251064i
\(394\) 9.35677 1.98884i 0.471387 0.100196i
\(395\) −0.503947 + 0.872863i −0.0253563 + 0.0439185i
\(396\) −12.0618 1.15881i −0.606128 0.0582321i
\(397\) −5.69441 9.86301i −0.285794 0.495010i 0.687007 0.726651i \(-0.258924\pi\)
−0.972801 + 0.231640i \(0.925591\pi\)
\(398\) −3.66666 + 11.2848i −0.183793 + 0.565657i
\(399\) 0 0
\(400\) 2.95774 + 2.14893i 0.147887 + 0.107446i
\(401\) −3.16161 + 3.51133i −0.157883 + 0.175347i −0.816897 0.576784i \(-0.804307\pi\)
0.659013 + 0.752131i \(0.270974\pi\)
\(402\) 0.597642 + 0.127033i 0.0298077 + 0.00633582i
\(403\) −41.0966 + 18.2974i −2.04717 + 0.911458i
\(404\) 24.4904 + 10.9038i 1.21845 + 0.542487i
\(405\) −0.392503 + 1.20800i −0.0195036 + 0.0600260i
\(406\) 0 0
\(407\) 13.8217 12.6707i 0.685114 0.628062i
\(408\) 3.53615 + 6.12479i 0.175065 + 0.303222i
\(409\) 1.64970 + 1.83218i 0.0815725 + 0.0905954i 0.782549 0.622589i \(-0.213919\pi\)
−0.700977 + 0.713184i \(0.747252\pi\)
\(410\) −0.0241980 0.230228i −0.00119505 0.0113702i
\(411\) −0.161456 + 1.53615i −0.00796405 + 0.0757729i
\(412\) −7.00259 21.5518i −0.344993 1.06178i
\(413\) 0 0
\(414\) 6.41892 + 4.66362i 0.315472 + 0.229204i
\(415\) −2.29374 1.02124i −0.112595 0.0501307i
\(416\) −25.5773 28.4064i −1.25403 1.39274i
\(417\) 1.47172 2.54910i 0.0720706 0.124830i
\(418\) 4.47240 + 6.04139i 0.218752 + 0.295494i
\(419\) −14.3399 −0.700548 −0.350274 0.936647i \(-0.613912\pi\)
−0.350274 + 0.936647i \(0.613912\pi\)
\(420\) 0 0
\(421\) 14.0087 10.1779i 0.682744 0.496043i −0.191523 0.981488i \(-0.561343\pi\)
0.874267 + 0.485446i \(0.161343\pi\)
\(422\) 0.726014 6.90756i 0.0353418 0.336255i
\(423\) 15.4816 + 3.29071i 0.752739 + 0.160000i
\(424\) 4.43613 + 0.942927i 0.215437 + 0.0457926i
\(425\) −2.24302 + 21.3409i −0.108802 + 1.03519i
\(426\) −3.61887 + 2.62927i −0.175335 + 0.127388i
\(427\) 0 0
\(428\) 7.52653 0.363808
\(429\) −7.96352 10.7573i −0.384482 0.519365i
\(430\) 0.407266 0.705405i 0.0196401 0.0340176i
\(431\) 18.6636 + 20.7280i 0.898994 + 0.998434i 0.999994 + 0.00354712i \(0.00112909\pi\)
−0.101000 + 0.994886i \(0.532204\pi\)
\(432\) −2.34251 1.04295i −0.112704 0.0501791i
\(433\) 23.9040 + 17.3673i 1.14875 + 0.834619i 0.988315 0.152426i \(-0.0487087\pi\)
0.160440 + 0.987046i \(0.448709\pi\)
\(434\) 0 0
\(435\) 0.160382 + 0.493605i 0.00768973 + 0.0236666i
\(436\) 0.787562 7.49315i 0.0377174 0.358857i
\(437\) 1.18771 + 11.3003i 0.0568160 + 0.540568i
\(438\) −1.79704 1.99582i −0.0858659 0.0953637i
\(439\) 16.8328 + 29.1552i 0.803384 + 1.39150i 0.917376 + 0.398021i \(0.130303\pi\)
−0.113992 + 0.993482i \(0.536364\pi\)
\(440\) 1.43615 1.31656i 0.0684658 0.0627644i
\(441\) 0 0
\(442\) 6.79997 20.9282i 0.323442 0.995451i
\(443\) 9.43393 + 4.20025i 0.448219 + 0.199560i 0.618417 0.785850i \(-0.287774\pi\)
−0.170198 + 0.985410i \(0.554441\pi\)
\(444\) 4.45447 1.98326i 0.211400 0.0941214i
\(445\) 1.72415 + 0.366480i 0.0817328 + 0.0173728i
\(446\) −0.372098 + 0.413256i −0.0176193 + 0.0195682i
\(447\) 3.61493 + 2.62640i 0.170980 + 0.124224i
\(448\) 0 0
\(449\) −0.852224 + 2.62287i −0.0402189 + 0.123781i −0.969150 0.246471i \(-0.920729\pi\)
0.928931 + 0.370253i \(0.120729\pi\)
\(450\) 5.03831 + 8.72661i 0.237508 + 0.411376i
\(451\) −4.41767 0.424416i −0.208020 0.0199850i
\(452\) −11.5104 + 19.9366i −0.541403 + 0.937738i
\(453\) −4.92067 + 1.04592i −0.231193 + 0.0491416i
\(454\) −3.34729 + 2.43195i −0.157096 + 0.114137i
\(455\) 0 0
\(456\) 1.46971 + 4.52331i 0.0688255 + 0.211823i
\(457\) −26.9864 + 29.9714i −1.26237 + 1.40200i −0.384484 + 0.923132i \(0.625621\pi\)
−0.877885 + 0.478872i \(0.841046\pi\)
\(458\) 4.69367 2.08976i 0.219321 0.0976480i
\(459\) −1.57319 14.9679i −0.0734303 0.698643i
\(460\) 1.18396 0.251659i 0.0552025 0.0117337i
\(461\) −34.2251 −1.59402 −0.797011 0.603965i \(-0.793587\pi\)
−0.797011 + 0.603965i \(0.793587\pi\)
\(462\) 0 0
\(463\) 0.707349 0.0328733 0.0164367 0.999865i \(-0.494768\pi\)
0.0164367 + 0.999865i \(0.494768\pi\)
\(464\) 2.72621 0.579475i 0.126561 0.0269014i
\(465\) −0.0990377 0.942281i −0.00459276 0.0436972i
\(466\) 6.78812 3.02226i 0.314453 0.140004i
\(467\) −19.1321 + 21.2483i −0.885326 + 0.983255i −0.999948 0.0101545i \(-0.996768\pi\)
0.114622 + 0.993409i \(0.463434\pi\)
\(468\) 7.37184 + 22.6882i 0.340764 + 1.04876i
\(469\) 0 0
\(470\) −0.846145 + 0.614760i −0.0390298 + 0.0283568i
\(471\) −12.1821 + 2.58939i −0.561322 + 0.119313i
\(472\) 12.5834 21.7951i 0.579199 1.00320i
\(473\) −11.6974 10.3445i −0.537848 0.475642i
\(474\) −1.08825 1.88490i −0.0499850 0.0865765i
\(475\) −4.45933 + 13.7244i −0.204608 + 0.629719i
\(476\) 0 0
\(477\) −3.63860 2.64360i −0.166600 0.121042i
\(478\) −13.9666 + 15.5115i −0.638820 + 0.709481i
\(479\) 4.98578 + 1.05976i 0.227806 + 0.0484217i 0.320400 0.947282i \(-0.396183\pi\)
−0.0925942 + 0.995704i \(0.529516\pi\)
\(480\) 0.735468 0.327451i 0.0335694 0.0149460i
\(481\) −33.7234 15.0146i −1.53766 0.684608i
\(482\) −4.53274 + 13.9503i −0.206461 + 0.635421i
\(483\) 0 0
\(484\) −7.91185 13.1547i −0.359629 0.597942i
\(485\) −1.00732 1.74473i −0.0457400 0.0792240i
\(486\) −7.25435 8.05677i −0.329064 0.365462i
\(487\) −3.05101 29.0284i −0.138254 1.31540i −0.815119 0.579294i \(-0.803328\pi\)
0.676864 0.736108i \(-0.263338\pi\)
\(488\) 2.65725 25.2821i 0.120288 1.14446i
\(489\) 1.41986 + 4.36989i 0.0642084 + 0.197613i
\(490\) 0 0
\(491\) −24.3870 17.7182i −1.10057 0.799610i −0.119416 0.992844i \(-0.538102\pi\)
−0.981153 + 0.193235i \(0.938102\pi\)
\(492\) −1.05431 0.469411i −0.0475321 0.0211627i
\(493\) 10.9462 + 12.1569i 0.492990 + 0.547521i
\(494\) 7.39919 12.8158i 0.332905 0.576609i
\(495\) −1.83214 + 0.613462i −0.0823484 + 0.0275731i
\(496\) −5.08801 −0.228458
\(497\) 0 0
\(498\) 4.38647 3.18696i 0.196563 0.142811i
\(499\) −0.622054 + 5.91844i −0.0278469 + 0.264946i 0.971736 + 0.236070i \(0.0758595\pi\)
−0.999583 + 0.0288760i \(0.990807\pi\)
\(500\) 3.02235 + 0.642421i 0.135164 + 0.0287299i
\(501\) 1.33669 + 0.284122i 0.0597188 + 0.0126936i
\(502\) 2.38713 22.7121i 0.106543 1.01369i
\(503\) 4.02773 2.92632i 0.179588 0.130478i −0.494360 0.869257i \(-0.664597\pi\)
0.673947 + 0.738779i \(0.264597\pi\)
\(504\) 0 0
\(505\) 4.27456 0.190216
\(506\) 0.0898719 + 10.0510i 0.00399529 + 0.446820i
\(507\) −9.15770 + 15.8616i −0.406708 + 0.704439i
\(508\) −1.86503 2.07133i −0.0827473 0.0919002i
\(509\) −19.4846 8.67509i −0.863639 0.384517i −0.0733902 0.997303i \(-0.523382\pi\)
−0.790248 + 0.612787i \(0.790049\pi\)
\(510\) 0.374949 + 0.272417i 0.0166030 + 0.0120628i
\(511\) 0 0
\(512\) −2.54091 7.82012i −0.112293 0.345604i
\(513\) 1.05796 10.0659i 0.0467102 0.444418i
\(514\) −1.37478 13.0802i −0.0606390 0.576942i
\(515\) −2.41776 2.68519i −0.106539 0.118324i
\(516\) −2.03036 3.51669i −0.0893816 0.154814i
\(517\) 8.31884 + 18.2436i 0.365862 + 0.802354i
\(518\) 0 0
\(519\) −1.97900 + 6.09075i −0.0868686 + 0.267354i
\(520\) −3.50406 1.56011i −0.153663 0.0684152i
\(521\) −20.2244 + 9.00448i −0.886046 + 0.394493i −0.798732 0.601687i \(-0.794495\pi\)
−0.0873149 + 0.996181i \(0.527829\pi\)
\(522\) 7.51401 + 1.59715i 0.328879 + 0.0699054i
\(523\) 3.28641 3.64993i 0.143705 0.159600i −0.666996 0.745062i \(-0.732420\pi\)
0.810700 + 0.585462i \(0.199087\pi\)
\(524\) 1.54683 + 1.12384i 0.0675737 + 0.0490952i
\(525\) 0 0
\(526\) 1.96537 6.04880i 0.0856944 0.263740i
\(527\) −14.9318 25.8627i −0.650441 1.12660i
\(528\) −0.327960 1.47783i −0.0142726 0.0643143i
\(529\) 3.90296 6.76013i 0.169694 0.293919i
\(530\) 0.290709 0.0617921i 0.0126276 0.00268408i
\(531\) −20.1913 + 14.6698i −0.876228 + 0.636617i
\(532\) 0 0
\(533\) 2.69996 + 8.30962i 0.116948 + 0.359929i
\(534\) −2.54698 + 2.82871i −0.110219 + 0.122410i
\(535\) 1.09635 0.488127i 0.0473994 0.0211036i
\(536\) −0.350885 3.33845i −0.0151559 0.144199i
\(537\) 14.1517 3.00803i 0.610689 0.129806i
\(538\) 4.85707 0.209403
\(539\) 0 0
\(540\) −1.07818 −0.0463977
\(541\) −18.9609 + 4.03026i −0.815192 + 0.173274i −0.596597 0.802541i \(-0.703481\pi\)
−0.218595 + 0.975816i \(0.570147\pi\)
\(542\) 0.639335 + 6.08287i 0.0274618 + 0.261281i
\(543\) −7.74414 + 3.44791i −0.332333 + 0.147964i
\(544\) 16.9794 18.8575i 0.727984 0.808509i
\(545\) −0.371242 1.14257i −0.0159023 0.0489422i
\(546\) 0 0
\(547\) −11.6904 + 8.49354i −0.499843 + 0.363158i −0.808957 0.587868i \(-0.799968\pi\)
0.309114 + 0.951025i \(0.399968\pi\)
\(548\) 3.41152 0.725141i 0.145733 0.0309765i
\(549\) −12.6051 + 21.8326i −0.537972 + 0.931794i
\(550\) −5.08769 + 11.7078i −0.216940 + 0.499221i
\(551\) 5.50060 + 9.52732i 0.234333 + 0.405877i
\(552\) −1.96530 + 6.04858i −0.0836489 + 0.257445i
\(553\) 0 0
\(554\) 7.57795 + 5.50570i 0.321956 + 0.233915i
\(555\) 0.520239 0.577783i 0.0220829 0.0245255i
\(556\) −6.50105 1.38184i −0.275706 0.0586031i
\(557\) 16.8739 7.51276i 0.714972 0.318326i −0.0168159 0.999859i \(-0.505353\pi\)
0.731788 + 0.681533i \(0.238686\pi\)
\(558\) −12.8112 5.70392i −0.542341 0.241466i
\(559\) −9.49993 + 29.2378i −0.401804 + 1.23663i
\(560\) 0 0
\(561\) 6.54945 6.00405i 0.276518 0.253491i
\(562\) 8.22381 + 14.2441i 0.346900 + 0.600849i
\(563\) 20.9330 + 23.2484i 0.882220 + 0.979804i 0.999912 0.0132458i \(-0.00421639\pi\)
−0.117693 + 0.993050i \(0.537550\pi\)
\(564\) 0.545026 + 5.18558i 0.0229497 + 0.218352i
\(565\) −0.383689 + 3.65056i −0.0161419 + 0.153580i
\(566\) 6.00720 + 18.4883i 0.252502 + 0.777120i
\(567\) 0 0
\(568\) 19.8823 + 14.4454i 0.834244 + 0.606114i
\(569\) 1.58596 + 0.706115i 0.0664869 + 0.0296019i 0.439711 0.898139i \(-0.355081\pi\)
−0.373224 + 0.927741i \(0.621748\pi\)
\(570\) 0.208552 + 0.231621i 0.00873530 + 0.00970153i
\(571\) −6.26546 + 10.8521i −0.262201 + 0.454146i −0.966827 0.255433i \(-0.917782\pi\)
0.704625 + 0.709580i \(0.251115\pi\)
\(572\) −17.5444 + 24.6075i −0.733567 + 1.02889i
\(573\) −7.43182 −0.310469
\(574\) 0 0
\(575\) −15.6114 + 11.3424i −0.651042 + 0.473009i
\(576\) 0.841353 8.00494i 0.0350564 0.333539i
\(577\) −19.7484 4.19766i −0.822138 0.174751i −0.222408 0.974954i \(-0.571392\pi\)
−0.599729 + 0.800203i \(0.704725\pi\)
\(578\) 1.36043 + 0.289168i 0.0565864 + 0.0120278i
\(579\) −1.02614 + 9.76303i −0.0426447 + 0.405738i
\(580\) 0.948101 0.688835i 0.0393677 0.0286023i
\(581\) 0 0
\(582\) 4.35051 0.180334
\(583\) −0.0509445 5.69745i −0.00210990 0.235964i
\(584\) −7.37752 + 12.7782i −0.305284 + 0.528768i
\(585\) 2.54525 + 2.82678i 0.105233 + 0.116873i
\(586\) 0.323234 + 0.143913i 0.0133527 + 0.00594499i
\(587\) 0.00677611 + 0.00492314i 0.000279680 + 0.000203200i 0.587925 0.808915i \(-0.299945\pi\)
−0.587645 + 0.809119i \(0.699945\pi\)
\(588\) 0 0
\(589\) −6.20604 19.1002i −0.255716 0.787012i
\(590\) 0.172392 1.64021i 0.00709729 0.0675262i
\(591\) −0.794835 7.56235i −0.0326951 0.311073i
\(592\) −2.79373 3.10275i −0.114822 0.127522i
\(593\) 0.219649 + 0.380443i 0.00901989 + 0.0156229i 0.870500 0.492168i \(-0.163796\pi\)
−0.861480 + 0.507791i \(0.830462\pi\)
\(594\) 1.78312 8.77397i 0.0731624 0.360001i
\(595\) 0 0
\(596\) 3.11779 9.59558i 0.127710 0.393050i
\(597\) 8.61667 + 3.83639i 0.352657 + 0.157013i
\(598\) 18.0776 8.04868i 0.739250 0.329135i
\(599\) −44.1794 9.39061i −1.80512 0.383690i −0.822418 0.568884i \(-0.807375\pi\)
−0.982702 + 0.185194i \(0.940709\pi\)
\(600\) −5.40467 + 6.00249i −0.220645 + 0.245051i
\(601\) −9.01541 6.55008i −0.367746 0.267183i 0.388529 0.921436i \(-0.372983\pi\)
−0.756276 + 0.654253i \(0.772983\pi\)
\(602\) 0 0
\(603\) −1.02870 + 3.16603i −0.0418921 + 0.128931i
\(604\) 5.67954 + 9.83725i 0.231097 + 0.400272i
\(605\) −2.00562 1.40307i −0.0815400 0.0570428i
\(606\) −4.61535 + 7.99403i −0.187486 + 0.324735i
\(607\) 34.9196 7.42240i 1.41734 0.301266i 0.565365 0.824841i \(-0.308735\pi\)
0.851980 + 0.523575i \(0.175402\pi\)
\(608\) 13.8057 10.0304i 0.559894 0.406787i
\(609\) 0 0
\(610\) −0.514796 1.58438i −0.0208435 0.0641496i
\(611\) 26.4137 29.3353i 1.06858 1.18678i
\(612\) −14.4674 + 6.44131i −0.584811 + 0.260375i
\(613\) −1.79768 17.1038i −0.0726076 0.690815i −0.968917 0.247386i \(-0.920428\pi\)
0.896309 0.443429i \(-0.146238\pi\)
\(614\) −6.11116 + 1.29897i −0.246626 + 0.0524221i
\(615\) −0.184020 −0.00742040
\(616\) 0 0
\(617\) −16.8852 −0.679774 −0.339887 0.940466i \(-0.610389\pi\)
−0.339887 + 0.940466i \(0.610389\pi\)
\(618\) 7.63219 1.62227i 0.307012 0.0652573i
\(619\) −3.24762 30.8990i −0.130533 1.24194i −0.842101 0.539320i \(-0.818681\pi\)
0.711568 0.702617i \(-0.247985\pi\)
\(620\) −1.95443 + 0.870167i −0.0784917 + 0.0349467i
\(621\) 9.05617 10.0579i 0.363412 0.403610i
\(622\) −0.0329066 0.101276i −0.00131943 0.00406080i
\(623\) 0 0
\(624\) −2.41106 + 1.75174i −0.0965196 + 0.0701256i
\(625\) −23.7296 + 5.04389i −0.949185 + 0.201755i
\(626\) −5.94384 + 10.2950i −0.237564 + 0.411472i
\(627\) 5.14771 3.03372i 0.205580 0.121155i
\(628\) 14.0608 + 24.3541i 0.561088 + 0.971834i
\(629\) 7.57271 23.3064i 0.301944 0.929287i
\(630\) 0 0
\(631\) −5.86832 4.26359i −0.233614 0.169731i 0.464819 0.885406i \(-0.346119\pi\)
−0.698434 + 0.715675i \(0.746119\pi\)
\(632\) −8.00135 + 8.88640i −0.318276 + 0.353482i
\(633\) −5.40052 1.14792i −0.214651 0.0456255i
\(634\) 23.4335 10.4333i 0.930664 0.414358i
\(635\) −0.406004 0.180765i −0.0161118 0.00717342i
\(636\) 0.457859 1.40915i 0.0181553 0.0558763i
\(637\) 0 0
\(638\) 4.03757 + 8.85460i 0.159849 + 0.350557i
\(639\) −12.1859 21.1066i −0.482066 0.834963i
\(640\) −1.38736 1.54081i −0.0548401 0.0609061i
\(641\) 2.16896 + 20.6362i 0.0856686 + 0.815082i 0.950019 + 0.312192i \(0.101063\pi\)
−0.864350 + 0.502890i \(0.832270\pi\)
\(642\) −0.270893 + 2.57737i −0.0106913 + 0.101721i
\(643\) 2.19750 + 6.76322i 0.0866611 + 0.266715i 0.984991 0.172606i \(-0.0552188\pi\)
−0.898330 + 0.439322i \(0.855219\pi\)
\(644\) 0 0
\(645\) −0.523825 0.380581i −0.0206256 0.0149854i
\(646\) 8.97453 + 3.99572i 0.353098 + 0.157209i
\(647\) 18.4539 + 20.4951i 0.725496 + 0.805745i 0.987214 0.159399i \(-0.0509556\pi\)
−0.261718 + 0.965144i \(0.584289\pi\)
\(648\) −7.53472 + 13.0505i −0.295992 + 0.512673i
\(649\) −30.1562 9.50110i −1.18373 0.372951i
\(650\) 25.1317 0.985748
\(651\) 0 0
\(652\) 8.39353 6.09826i 0.328716 0.238826i
\(653\) −1.68857 + 16.0656i −0.0660787 + 0.628697i 0.910496 + 0.413518i \(0.135700\pi\)
−0.976575 + 0.215179i \(0.930966\pi\)
\(654\) 2.53760 + 0.539383i 0.0992279 + 0.0210916i
\(655\) 0.298205 + 0.0633855i 0.0116518 + 0.00247668i
\(656\) −0.103295 + 0.982791i −0.00403301 + 0.0383715i
\(657\) 11.8379 8.60076i 0.461842 0.335548i
\(658\) 0 0
\(659\) −13.2085 −0.514531 −0.257266 0.966341i \(-0.582822\pi\)
−0.257266 + 0.966341i \(0.582822\pi\)
\(660\) −0.378720 0.511581i −0.0147417 0.0199133i
\(661\) 2.45330 4.24924i 0.0954223 0.165276i −0.814362 0.580357i \(-0.802913\pi\)
0.909785 + 0.415080i \(0.136247\pi\)
\(662\) −15.3644 17.0639i −0.597156 0.663209i
\(663\) −15.9800 7.11474i −0.620610 0.276314i
\(664\) −24.0996 17.5094i −0.935245 0.679495i
\(665\) 0 0
\(666\) −3.55605 10.9444i −0.137794 0.424087i
\(667\) −1.53770 + 14.6303i −0.0595401 + 0.566486i
\(668\) −0.322540 3.06876i −0.0124794 0.118734i
\(669\) 0.295786 + 0.328504i 0.0114357 + 0.0127007i
\(670\) −0.109991 0.190509i −0.00424930 0.00736001i
\(671\) −31.7311 + 3.62221i −1.22497 + 0.139834i
\(672\) 0 0
\(673\) −9.26654 + 28.5195i −0.357199 + 1.09935i 0.597524 + 0.801851i \(0.296151\pi\)
−0.954723 + 0.297495i \(0.903849\pi\)
\(674\) −3.99898 1.78046i −0.154035 0.0685808i
\(675\) 15.7027 6.99130i 0.604398 0.269095i
\(676\) 40.4524 + 8.59842i 1.55586 + 0.330708i
\(677\) 8.42364 9.35540i 0.323747 0.359557i −0.559198 0.829034i \(-0.688891\pi\)
0.882945 + 0.469477i \(0.155558\pi\)
\(678\) −6.41278 4.65916i −0.246281 0.178934i
\(679\) 0 0
\(680\) 0.786849 2.42167i 0.0301743 0.0928668i
\(681\) 1.64447 + 2.84831i 0.0630163 + 0.109147i
\(682\) −3.84891 17.3437i −0.147382 0.664124i
\(683\) 14.2671 24.7114i 0.545916 0.945554i −0.452633 0.891697i \(-0.649515\pi\)
0.998549 0.0538567i \(-0.0171514\pi\)
\(684\) −10.4173 + 2.21426i −0.398315 + 0.0846645i
\(685\) 0.449911 0.326879i 0.0171902 0.0124894i
\(686\) 0 0
\(687\) −1.26208 3.88427i −0.0481513 0.148194i
\(688\) −2.32660 + 2.58395i −0.0887007 + 0.0985121i
\(689\) −10.2474 + 4.56245i −0.390396 + 0.173815i
\(690\) 0.0435649 + 0.414492i 0.00165849 + 0.0157794i
\(691\) −24.8197 + 5.27560i −0.944188 + 0.200693i −0.654187 0.756333i \(-0.726989\pi\)
−0.290001 + 0.957026i \(0.593656\pi\)
\(692\) 14.4606 0.549711
\(693\) 0 0
\(694\) −6.78791 −0.257666
\(695\) −1.03659 + 0.220335i −0.0393203 + 0.00835778i
\(696\) 0.643643 + 6.12385i 0.0243972 + 0.232124i
\(697\) −5.29874 + 2.35915i −0.200704 + 0.0893592i
\(698\) −9.60722 + 10.6699i −0.363639 + 0.403862i
\(699\) −1.82525 5.61754i −0.0690373 0.212475i
\(700\) 0 0
\(701\) 36.9738 26.8630i 1.39648 1.01460i 0.401363 0.915919i \(-0.368537\pi\)
0.995119 0.0986843i \(-0.0314634\pi\)
\(702\) −17.2415 + 3.66480i −0.650739 + 0.138319i
\(703\) 8.24002 14.2721i 0.310778 0.538283i
\(704\) 8.78477 5.17716i 0.331088 0.195122i
\(705\) 0.415698 + 0.720010i 0.0156561 + 0.0271171i
\(706\) 5.64257 17.3661i 0.212361 0.653580i
\(707\) 0 0
\(708\) −6.65177 4.83279i −0.249989 0.181627i
\(709\) 25.7819 28.6337i 0.968258 1.07536i −0.0288664 0.999583i \(-0.509190\pi\)
0.997125 0.0757766i \(-0.0241436\pi\)
\(710\) 1.57532 + 0.334844i 0.0591207 + 0.0125665i
\(711\) 10.8333 4.82329i 0.406280 0.180887i
\(712\) 19.1046 + 8.50593i 0.715977 + 0.318773i
\(713\) 8.29874 25.5409i 0.310790 0.956515i
\(714\) 0 0
\(715\) −0.959703 + 4.72228i −0.0358908 + 0.176603i
\(716\) −16.3341 28.2915i −0.610435 1.05730i
\(717\) 11.1023 + 12.3304i 0.414623 + 0.460486i
\(718\) 1.20938 + 11.5065i 0.0451338 + 0.429420i
\(719\) −0.596034 + 5.67089i −0.0222283 + 0.211488i 0.977770 + 0.209680i \(0.0672423\pi\)
−0.999998 + 0.00180831i \(0.999424\pi\)
\(720\) 0.132945 + 0.409164i 0.00495458 + 0.0152486i
\(721\) 0 0
\(722\) −6.60620 4.79969i −0.245857 0.178626i
\(723\) 10.6520 + 4.74256i 0.396151 + 0.176378i
\(724\) 12.8079 + 14.2246i 0.476001 + 0.528653i
\(725\) −9.34154 + 16.1800i −0.346936 + 0.600911i
\(726\) 4.78945 2.23586i 0.177753 0.0829806i
\(727\) 11.8221 0.438458 0.219229 0.975673i \(-0.429646\pi\)
0.219229 + 0.975673i \(0.429646\pi\)
\(728\) 0 0
\(729\) 6.88197 5.00004i 0.254888 0.185187i
\(730\) −0.101072 + 0.961634i −0.00374083 + 0.0355917i
\(731\) −19.9623 4.24311i −0.738331 0.156937i
\(732\) −8.12368 1.72674i −0.300260 0.0638222i
\(733\) −0.921097 + 8.76365i −0.0340215 + 0.323693i 0.964253 + 0.264981i \(0.0853659\pi\)
−0.998275 + 0.0587114i \(0.981301\pi\)
\(734\) −21.5280 + 15.6410i −0.794614 + 0.577321i
\(735\) 0 0
\(736\) 22.8190 0.841121
\(737\) −3.99903 + 1.33901i −0.147306 + 0.0493231i
\(738\) −1.36185 + 2.35879i −0.0501303 + 0.0868283i
\(739\) 0.321724 + 0.357311i 0.0118348 + 0.0131439i 0.749033 0.662532i \(-0.230518\pi\)
−0.737198 + 0.675676i \(0.763852\pi\)
\(740\) −1.60378 0.714049i −0.0589561 0.0262490i
\(741\) −9.51683 6.91438i −0.349610 0.254006i
\(742\) 0 0
\(743\) 10.2730 + 31.6172i 0.376881 + 1.15992i 0.942201 + 0.335049i \(0.108753\pi\)
−0.565319 + 0.824872i \(0.691247\pi\)
\(744\) 1.17500 11.1794i 0.0430776 0.409856i
\(745\) −0.168161 1.59994i −0.00616094 0.0586174i
\(746\) −1.56976 1.74340i −0.0574731 0.0638304i
\(747\) 14.7706 + 25.5835i 0.540429 + 0.936051i
\(748\) −17.4635 9.87543i −0.638530 0.361082i
\(749\) 0 0
\(750\) −0.328769 + 1.01185i −0.0120050 + 0.0369475i
\(751\) 25.5853 + 11.3913i 0.933622 + 0.415675i 0.816437 0.577435i \(-0.195946\pi\)
0.117185 + 0.993110i \(0.462613\pi\)
\(752\) 4.07868 1.81595i 0.148734 0.0662208i
\(753\) −17.7569 3.77435i −0.647098 0.137545i
\(754\) 12.8199 14.2380i 0.466875 0.518517i
\(755\) 1.46530 + 1.06460i 0.0533276 + 0.0387448i
\(756\) 0 0
\(757\) −6.87465 + 21.1580i −0.249863 + 0.769001i 0.744935 + 0.667137i \(0.232481\pi\)
−0.994798 + 0.101864i \(0.967519\pi\)
\(758\) −2.38078 4.12363i −0.0864738 0.149777i
\(759\) 7.95336 + 0.764098i 0.288689 + 0.0277350i
\(760\) 0.856186 1.48296i 0.0310571 0.0537925i
\(761\) 47.1716 10.0266i 1.70997 0.363465i 0.753986 0.656891i \(-0.228129\pi\)
0.955982 + 0.293426i \(0.0947954\pi\)
\(762\) 0.776427 0.564108i 0.0281270 0.0204355i
\(763\) 0 0
\(764\) 5.18562 + 15.9597i 0.187609 + 0.577402i
\(765\) −1.68965 + 1.87655i −0.0610895 + 0.0678468i
\(766\) −3.11877 + 1.38857i −0.112686 + 0.0501709i
\(767\) 6.50652 + 61.9054i 0.234937 + 2.23528i
\(768\) 8.09669 1.72101i 0.292164 0.0621014i
\(769\) 43.6883 1.57544 0.787721 0.616032i \(-0.211261\pi\)
0.787721 + 0.616032i \(0.211261\pi\)
\(770\) 0 0
\(771\) −10.4549 −0.376524
\(772\) 21.6819 4.60863i 0.780349 0.165868i
\(773\) 0.0612087 + 0.582362i 0.00220152 + 0.0209461i 0.995568 0.0940496i \(-0.0299812\pi\)
−0.993366 + 0.114996i \(0.963315\pi\)
\(774\) −8.75492 + 3.89794i −0.314689 + 0.140109i
\(775\) 22.8219 25.3463i 0.819787 0.910465i
\(776\) −7.38612 22.7321i −0.265146 0.816036i
\(777\) 0 0
\(778\) 6.60197 4.79661i 0.236692 0.171967i
\(779\) −3.81536 + 0.810980i −0.136700 + 0.0290564i
\(780\) −0.626558 + 1.08523i −0.0224344 + 0.0388575i
\(781\) 12.3053 28.3170i 0.440319 1.01326i
\(782\) 6.56824 + 11.3765i 0.234880 + 0.406824i
\(783\) 4.04930 12.4625i 0.144710 0.445372i
\(784\) 0 0
\(785\) 3.62764 + 2.63563i 0.129476 + 0.0940698i
\(786\) −0.440520 + 0.489247i −0.0157128 + 0.0174508i
\(787\) −30.0453 6.38634i −1.07100 0.227648i −0.361514 0.932367i \(-0.617740\pi\)
−0.709487 + 0.704718i \(0.751073\pi\)
\(788\) −15.6854 + 6.98359i −0.558769 + 0.248780i
\(789\) −4.61864 2.05635i −0.164428 0.0732080i
\(790\) −0.242153 + 0.745269i −0.00861540 + 0.0265155i
\(791\) 0 0
\(792\) −22.7750 + 2.59984i −0.809274 + 0.0923811i
\(793\) 31.4379 + 54.4520i 1.11639 + 1.93365i
\(794\) −5.92490 6.58027i −0.210267 0.233525i
\(795\) −0.0246950 0.234957i −0.000875842 0.00833308i
\(796\) 2.22621 21.1810i 0.0789061 0.750741i
\(797\) −3.34767 10.3031i −0.118581 0.364953i 0.874096 0.485752i \(-0.161454\pi\)
−0.992677 + 0.120799i \(0.961454\pi\)
\(798\) 0 0
\(799\) 21.2003 + 15.4029i 0.750014 + 0.544917i
\(800\) 26.4751 + 11.7875i 0.936038 + 0.416751i
\(801\) −13.8771 15.4120i −0.490322 0.544557i
\(802\) −1.83679 + 3.18141i −0.0648593 + 0.112340i
\(803\) 17.6802 + 5.57038i 0.623922 + 0.196575i
\(804\) −1.09668 −0.0386770
\(805\) 0 0
\(806\) −28.2960 + 20.5582i −0.996684 + 0.724133i
\(807\) 0.403580 3.83981i 0.0142067 0.135168i
\(808\) 49.6059 + 10.5441i 1.74513 + 0.370939i
\(809\) 37.7468 + 8.02332i 1.32711 + 0.282085i 0.816308 0.577616i \(-0.196017\pi\)
0.510797 + 0.859701i \(0.329350\pi\)
\(810\) −0.103225 + 0.982124i −0.00362697 + 0.0345083i
\(811\) 41.1737 29.9144i 1.44580 1.05044i 0.459015 0.888428i \(-0.348202\pi\)
0.986789 0.162010i \(-0.0517977\pi\)
\(812\) 0 0
\(813\) 4.86200 0.170518
\(814\) 8.46310 11.8702i 0.296632 0.416051i
\(815\) 0.827146 1.43266i 0.0289737 0.0501839i
\(816\) −1.32382 1.47025i −0.0463429 0.0514690i
\(817\) −12.5379 5.58223i −0.438646 0.195298i
\(818\) 1.55076 + 1.12669i 0.0542209 + 0.0393938i
\(819\) 0 0
\(820\) 0.128402 + 0.395180i 0.00448398 + 0.0138003i
\(821\) 4.21348 40.0886i 0.147052 1.39910i −0.633370 0.773849i \(-0.718329\pi\)
0.780422 0.625253i \(-0.215004\pi\)
\(822\) 0.125530 + 1.19434i 0.00437835 + 0.0416572i
\(823\) 17.1844 + 19.0853i 0.599012 + 0.665270i 0.964050 0.265723i \(-0.0856105\pi\)
−0.365038 + 0.930993i \(0.618944\pi\)
\(824\) −21.4343 37.1252i −0.746698 1.29332i
\(825\) 8.83296 + 4.99494i 0.307524 + 0.173902i
\(826\) 0 0
\(827\) −9.87486 + 30.3917i −0.343382 + 1.05682i 0.619062 + 0.785342i \(0.287513\pi\)
−0.962444 + 0.271480i \(0.912487\pi\)
\(828\) −13.0100 5.79244i −0.452130 0.201301i
\(829\) 44.2158 19.6861i 1.53568 0.683728i 0.547467 0.836827i \(-0.315592\pi\)
0.988211 + 0.153099i \(0.0489254\pi\)
\(830\) −1.90946 0.405868i −0.0662784 0.0140879i
\(831\) 4.98225 5.53335i 0.172832 0.191950i
\(832\) −16.2409 11.7997i −0.563050 0.409080i
\(833\) 0 0
\(834\) 0.707180 2.17648i 0.0244876 0.0753652i
\(835\) −0.246005 0.426093i −0.00851335 0.0147456i
\(836\) −10.1067 8.93780i −0.349548 0.309120i
\(837\) −11.9608 + 20.7167i −0.413425 + 0.716073i
\(838\) −10.9054 + 2.31801i −0.376720 + 0.0800744i
\(839\) 30.5133 22.1692i 1.05344 0.765366i 0.0805734 0.996749i \(-0.474325\pi\)
0.972863 + 0.231382i \(0.0743249\pi\)
\(840\) 0 0
\(841\) −4.56017 14.0348i −0.157247 0.483957i
\(842\) 9.00832 10.0048i 0.310447 0.344787i
\(843\) 11.9441 5.31786i 0.411377 0.183157i
\(844\) 1.30313 + 12.3985i 0.0448557 + 0.426773i
\(845\) 6.45014 1.37102i 0.221892 0.0471645i
\(846\) 12.3056 0.423074
\(847\) 0 0
\(848\) −1.26869 −0.0435671
\(849\) 15.1152 3.21284i 0.518754 0.110265i
\(850\) 1.74391 + 16.5922i 0.0598157 + 0.569108i
\(851\) 20.1319 8.96332i 0.690114 0.307259i
\(852\) 5.37243 5.96669i 0.184056 0.204415i
\(853\) 2.87035 + 8.83403i 0.0982789 + 0.302471i 0.988094 0.153849i \(-0.0491670\pi\)
−0.889815 + 0.456321i \(0.849167\pi\)
\(854\) 0 0
\(855\) −1.37383 + 0.998146i −0.0469840 + 0.0341359i
\(856\) 13.9271 2.96030i 0.476019 0.101181i
\(857\) 14.8822 25.7767i 0.508365 0.880515i −0.491588 0.870828i \(-0.663583\pi\)
0.999953 0.00968670i \(-0.00308342\pi\)
\(858\) −7.79510 6.89354i −0.266120 0.235342i
\(859\) −16.6305 28.8050i −0.567427 0.982812i −0.996819 0.0796943i \(-0.974606\pi\)
0.429392 0.903118i \(-0.358728\pi\)
\(860\) −0.451787 + 1.39046i −0.0154058 + 0.0474142i
\(861\) 0 0
\(862\) 17.5442 + 12.7466i 0.597558 + 0.434151i
\(863\) −12.4242 + 13.7985i −0.422924 + 0.469705i −0.916521 0.399986i \(-0.869015\pi\)
0.493597 + 0.869691i \(0.335682\pi\)
\(864\) −19.8821 4.22606i −0.676401 0.143774i
\(865\) 2.10641 0.937834i 0.0716201 0.0318873i
\(866\) 20.9863 + 9.34369i 0.713143 + 0.317512i
\(867\) 0.341645 1.05147i 0.0116029 0.0357100i
\(868\) 0 0
\(869\) 13.0768 + 7.39477i 0.443599 + 0.250850i
\(870\) 0.201760 + 0.349459i 0.00684031 + 0.0118478i
\(871\) 5.55554 + 6.17006i 0.188242 + 0.209064i
\(872\) −1.48986 14.1751i −0.0504532 0.480030i
\(873\) −2.47769 + 23.5736i −0.0838569 + 0.797845i
\(874\) 2.72992 + 8.40184i 0.0923411 + 0.284197i
\(875\) 0 0
\(876\) 3.89985 + 2.83341i 0.131764 + 0.0957321i
\(877\) −20.5476 9.14837i −0.693842 0.308918i 0.0293463 0.999569i \(-0.490657\pi\)
−0.723188 + 0.690651i \(0.757324\pi\)
\(878\) 17.5141 + 19.4514i 0.591073 + 0.656453i
\(879\) 0.140630 0.243578i 0.00474332 0.00821568i
\(880\) −0.316399 + 0.443777i −0.0106658 + 0.0149597i
\(881\) 7.06565 0.238048 0.119024 0.992891i \(-0.462023\pi\)
0.119024 + 0.992891i \(0.462023\pi\)
\(882\) 0 0
\(883\) 16.1304 11.7194i 0.542830 0.394389i −0.282305 0.959325i \(-0.591099\pi\)
0.825135 + 0.564936i \(0.191099\pi\)
\(884\) −4.12861 + 39.2811i −0.138860 + 1.32116i
\(885\) −1.28236 0.272573i −0.0431060 0.00916245i
\(886\) 7.85341 + 1.66929i 0.263841 + 0.0560810i
\(887\) −0.726975 + 6.91671i −0.0244094 + 0.232240i 0.975515 + 0.219934i \(0.0705841\pi\)
−0.999924 + 0.0123067i \(0.996083\pi\)
\(888\) 7.46253 5.42185i 0.250426 0.181945i
\(889\) 0 0
\(890\) 1.37045 0.0459376
\(891\) 18.0570 + 5.68908i 0.604931 + 0.190591i
\(892\) 0.499068 0.864411i 0.0167100 0.0289426i
\(893\) 11.7919 + 13.0963i 0.394602 + 0.438250i
\(894\) 3.17368 + 1.41301i 0.106144 + 0.0472583i
\(895\) −4.21414 3.06175i −0.140863 0.102343i
\(896\) 0 0
\(897\) −4.86088 14.9602i −0.162300 0.499508i
\(898\) −0.224129 + 2.13244i −0.00747927 + 0.0711605i
\(899\) −2.71787 25.8588i −0.0906459 0.862438i
\(900\) −12.1023 13.4410i −0.403412 0.448034i
\(901\) −3.72325 6.44886i −0.124039 0.214843i
\(902\) −3.42822 + 0.391342i −0.114147 + 0.0130303i
\(903\) 0 0
\(904\) −13.4575 + 41.4179i −0.447590 + 1.37754i
\(905\) 2.78818 + 1.24138i 0.0926824 + 0.0412649i
\(906\) −3.57307 + 1.59083i −0.118707 + 0.0528519i
\(907\) 22.9279 + 4.87348i 0.761309 + 0.161821i 0.572177 0.820130i \(-0.306099\pi\)
0.189132 + 0.981952i \(0.439432\pi\)
\(908\) 4.96924 5.51890i 0.164910 0.183151i
\(909\) −40.6878 29.5614i −1.34953 0.980490i
\(910\) 0 0
\(911\) 14.4650 44.5186i 0.479246 1.47497i −0.360899 0.932605i \(-0.617530\pi\)
0.840145 0.542362i \(-0.182470\pi\)
\(912\) −0.665238 1.15223i −0.0220282 0.0381540i
\(913\) −14.9154 + 34.3233i −0.493628 + 1.13593i
\(914\) −15.6782 + 27.1554i −0.518588 + 0.898220i
\(915\) −1.29532 + 0.275329i −0.0428220 + 0.00910211i
\(916\) −7.46078 + 5.42058i −0.246511 + 0.179101i
\(917\) 0 0
\(918\) −3.61594 11.1287i −0.119344 0.367302i
\(919\) 7.11106 7.89763i 0.234572 0.260519i −0.614354 0.789031i \(-0.710583\pi\)
0.848926 + 0.528512i \(0.177250\pi\)
\(920\) 2.09183 0.931341i 0.0689655 0.0307054i
\(921\) 0.519128 + 4.93918i 0.0171059 + 0.162751i
\(922\) −26.0280 + 5.53242i −0.857186 + 0.182201i
\(923\) −60.7848 −2.00075
\(924\) 0 0
\(925\) 27.9876 0.920228
\(926\) 0.537935 0.114342i 0.0176776 0.00375750i
\(927\) 4.44376 + 42.2795i 0.145952 + 1.38864i
\(928\) 20.1832 8.98616i 0.662547 0.294985i
\(929\) −24.5377 + 27.2518i −0.805054 + 0.894104i −0.996168 0.0874645i \(-0.972124\pi\)
0.191113 + 0.981568i \(0.438790\pi\)
\(930\) −0.227635 0.700590i −0.00746446 0.0229733i
\(931\) 0 0
\(932\) −10.7900 + 7.83938i −0.353438 + 0.256787i
\(933\) −0.0827991 + 0.0175995i −0.00271072 + 0.000576182i
\(934\) −11.1151 + 19.2519i −0.363697 + 0.629941i
\(935\) −3.18429 0.305922i −0.104137 0.0100047i
\(936\) 22.5645 + 39.0829i 0.737544 + 1.27746i
\(937\) −12.4278 + 38.2490i −0.406000 + 1.24954i 0.514057 + 0.857756i \(0.328142\pi\)
−0.920057 + 0.391784i \(0.871858\pi\)
\(938\) 0 0
\(939\) 7.64497 + 5.55439i 0.249484 + 0.181261i
\(940\) 1.25615 1.39510i 0.0409711 0.0455031i
\(941\) −24.3653 5.17901i −0.794287 0.168831i −0.207140 0.978311i \(-0.566416\pi\)
−0.587147 + 0.809480i \(0.699749\pi\)
\(942\) −8.84585 + 3.93843i −0.288213 + 0.128321i
\(943\) −4.76496 2.12150i −0.155168 0.0690854i
\(944\) −2.17555 + 6.69565i −0.0708081 + 0.217925i
\(945\) 0 0
\(946\) −10.5680 5.97609i −0.343595 0.194299i
\(947\) 16.1031 + 27.8913i 0.523279 + 0.906347i 0.999633 + 0.0270927i \(0.00862493\pi\)
−0.476353 + 0.879254i \(0.658042\pi\)
\(948\) 2.61405 + 2.90319i 0.0849003 + 0.0942913i
\(949\) −3.81470 36.2944i −0.123830 1.17817i
\(950\) −1.17277 + 11.1582i −0.0380497 + 0.362019i
\(951\) −6.30101 19.3925i −0.204324 0.628846i
\(952\) 0 0
\(953\) −36.4552 26.4863i −1.18090 0.857975i −0.188628 0.982049i \(-0.560404\pi\)
−0.992273 + 0.124074i \(0.960404\pi\)
\(954\) −3.19447 1.42227i −0.103425 0.0460477i
\(955\) 1.79042 + 1.98846i 0.0579366 + 0.0643451i
\(956\) 18.7325 32.4456i 0.605852 1.04937i
\(957\) 7.33558 2.45620i 0.237126 0.0793978i
\(958\) 3.96296 0.128038
\(959\) 0 0
\(960\) 0.342058 0.248519i 0.0110399 0.00802093i
\(961\) −1.72120 + 16.3761i −0.0555226 + 0.528263i
\(962\) −28.0736 5.96722i −0.905128 0.192391i
\(963\) −13.8114 2.93571i −0.445067 0.0946020i
\(964\) 2.75206 26.1841i 0.0886378 0.843332i
\(965\) 2.85941 2.07748i 0.0920476 0.0668765i
\(966\) 0 0
\(967\) 1.81387 0.0583300 0.0291650 0.999575i \(-0.490715\pi\)
0.0291650 + 0.999575i \(0.490715\pi\)
\(968\) −19.8141 21.2297i −0.636848 0.682348i
\(969\) 3.90456 6.76290i 0.125433 0.217256i
\(970\) −1.04809 1.16402i −0.0336522 0.0373746i
\(971\) 21.0608 + 9.37687i 0.675873 + 0.300918i 0.715821 0.698284i \(-0.246053\pi\)
−0.0399480 + 0.999202i \(0.512719\pi\)
\(972\) 15.7431 + 11.4380i 0.504959 + 0.366874i
\(973\) 0 0
\(974\) −7.01266 21.5827i −0.224700 0.691555i
\(975\) 2.08823 19.8682i 0.0668768 0.636290i
\(976\) 0.743344 + 7.07245i 0.0237939 + 0.226384i
\(977\) −4.74714 5.27223i −0.151875 0.168674i 0.662407 0.749145i \(-0.269535\pi\)
−0.814281 + 0.580471i \(0.802869\pi\)
\(978\) 1.78618 + 3.09376i 0.0571158 + 0.0989274i
\(979\) 5.23244 25.7466i 0.167229 0.822863i
\(980\) 0 0
\(981\) −4.36789 + 13.4430i −0.139456 + 0.429202i
\(982\) −21.4103 9.53246i −0.683229 0.304193i
\(983\) 35.0347 15.5984i 1.11743 0.497513i 0.236917 0.971530i \(-0.423863\pi\)
0.880516 + 0.474017i \(0.157196\pi\)
\(984\) −2.13553 0.453922i −0.0680783 0.0144705i
\(985\) −1.83190 + 2.03453i −0.0583691 + 0.0648255i
\(986\) 10.2896 + 7.47586i 0.327689 + 0.238080i
\(987\) 0 0
\(988\) −8.20806 + 25.2618i −0.261133 + 0.803685i
\(989\) −9.17619 15.8936i −0.291786 0.505388i
\(990\) −1.29416 + 0.762695i −0.0411312 + 0.0242401i
\(991\) −10.1361 + 17.5562i −0.321984 + 0.557692i −0.980897 0.194527i \(-0.937683\pi\)
0.658914 + 0.752219i \(0.271016\pi\)
\(992\) −39.4510 + 8.38556i −1.25257 + 0.266242i
\(993\) −14.7667 + 10.7287i −0.468608 + 0.340464i
\(994\) 0 0
\(995\) −1.04940 3.22971i −0.0332681 0.102389i
\(996\) −6.51198 + 7.23228i −0.206340 + 0.229164i
\(997\) 14.0784 6.26810i 0.445867 0.198513i −0.171506 0.985183i \(-0.554863\pi\)
0.617373 + 0.786670i \(0.288197\pi\)
\(998\) 0.483637 + 4.60150i 0.0153093 + 0.145658i
\(999\) −19.2008 + 4.08126i −0.607487 + 0.129125i
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 539.2.q.c.361.2 16
7.2 even 3 inner 539.2.q.c.471.1 16
7.3 odd 6 539.2.f.d.295.1 8
7.4 even 3 77.2.f.a.64.1 8
7.5 odd 6 539.2.q.b.471.1 16
7.6 odd 2 539.2.q.b.361.2 16
11.5 even 5 inner 539.2.q.c.214.1 16
21.11 odd 6 693.2.m.g.64.2 8
77.4 even 15 847.2.a.l.1.2 4
77.5 odd 30 539.2.q.b.324.2 16
77.16 even 15 inner 539.2.q.c.324.2 16
77.18 odd 30 847.2.a.k.1.3 4
77.25 even 15 847.2.f.p.323.2 8
77.27 odd 10 539.2.q.b.214.1 16
77.32 odd 6 847.2.f.q.372.2 8
77.38 odd 30 539.2.f.d.148.1 8
77.39 odd 30 847.2.f.q.148.2 8
77.46 odd 30 847.2.f.s.729.1 8
77.53 even 15 847.2.f.p.729.2 8
77.59 odd 30 5929.2.a.bi.1.2 4
77.60 even 15 77.2.f.a.71.1 yes 8
77.73 even 30 5929.2.a.bb.1.3 4
77.74 odd 30 847.2.f.s.323.1 8
231.95 even 30 7623.2.a.co.1.2 4
231.137 odd 30 693.2.m.g.379.2 8
231.158 odd 30 7623.2.a.ch.1.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
77.2.f.a.64.1 8 7.4 even 3
77.2.f.a.71.1 yes 8 77.60 even 15
539.2.f.d.148.1 8 77.38 odd 30
539.2.f.d.295.1 8 7.3 odd 6
539.2.q.b.214.1 16 77.27 odd 10
539.2.q.b.324.2 16 77.5 odd 30
539.2.q.b.361.2 16 7.6 odd 2
539.2.q.b.471.1 16 7.5 odd 6
539.2.q.c.214.1 16 11.5 even 5 inner
539.2.q.c.324.2 16 77.16 even 15 inner
539.2.q.c.361.2 16 1.1 even 1 trivial
539.2.q.c.471.1 16 7.2 even 3 inner
693.2.m.g.64.2 8 21.11 odd 6
693.2.m.g.379.2 8 231.137 odd 30
847.2.a.k.1.3 4 77.18 odd 30
847.2.a.l.1.2 4 77.4 even 15
847.2.f.p.323.2 8 77.25 even 15
847.2.f.p.729.2 8 77.53 even 15
847.2.f.q.148.2 8 77.39 odd 30
847.2.f.q.372.2 8 77.32 odd 6
847.2.f.s.323.1 8 77.74 odd 30
847.2.f.s.729.1 8 77.46 odd 30
5929.2.a.bb.1.3 4 77.73 even 30
5929.2.a.bi.1.2 4 77.59 odd 30
7623.2.a.ch.1.3 4 231.158 odd 30
7623.2.a.co.1.2 4 231.95 even 30