Properties

Label 71.2.c.a.57.5
Level $71$
Weight $2$
Character 71.57
Analytic conductor $0.567$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [71,2,Mod(5,71)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(71, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("71.5");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 71 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 71.c (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.566937854351\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(5\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 6 x^{19} + 28 x^{18} - 91 x^{17} + 268 x^{16} - 604 x^{15} + 1278 x^{14} - 1990 x^{13} + 3162 x^{12} - 4046 x^{11} + 6406 x^{10} - 8426 x^{9} + 12709 x^{8} - 13621 x^{7} + \cdots + 961 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 57.5
Root \(-0.758630 - 2.33482i\) of defining polynomial
Character \(\chi\) \(=\) 71.57
Dual form 71.2.c.a.5.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.758630 - 2.33482i) q^{2} +(-0.252609 + 0.777449i) q^{3} +(-3.25785 - 2.36696i) q^{4} +(-0.0372909 + 0.0270934i) q^{5} +(1.62357 + 1.17959i) q^{6} +(0.331946 - 1.02163i) q^{7} +(-4.02570 + 2.92484i) q^{8} +(1.88643 + 1.37058i) q^{9} +O(q^{10})\) \(q+(0.758630 - 2.33482i) q^{2} +(-0.252609 + 0.777449i) q^{3} +(-3.25785 - 2.36696i) q^{4} +(-0.0372909 + 0.0270934i) q^{5} +(1.62357 + 1.17959i) q^{6} +(0.331946 - 1.02163i) q^{7} +(-4.02570 + 2.92484i) q^{8} +(1.88643 + 1.37058i) q^{9} +(0.0349684 + 0.107622i) q^{10} +(-1.43668 + 4.42163i) q^{11} +(2.66315 - 1.93489i) q^{12} +(1.12919 + 3.47530i) q^{13} +(-2.13349 - 1.55007i) q^{14} +(-0.0116438 - 0.0358358i) q^{15} +(1.28620 + 3.95852i) q^{16} +(-2.33228 - 7.17803i) q^{17} +(4.63116 - 3.36473i) q^{18} +(0.693465 - 2.13426i) q^{19} +0.185617 q^{20} +(0.710409 + 0.516143i) q^{21} +(9.23383 + 6.70877i) q^{22} -6.80205 q^{23} +(-1.25699 - 3.86862i) q^{24} +(-1.54443 + 4.75326i) q^{25} +8.97085 q^{26} +(-3.52610 + 2.56186i) q^{27} +(-3.49958 + 2.54259i) q^{28} +(2.01737 - 1.46571i) q^{29} -0.0925036 q^{30} +(1.02027 - 3.14007i) q^{31} +0.266113 q^{32} +(-3.07468 - 2.23389i) q^{33} -18.5288 q^{34} +(0.0153008 + 0.0470909i) q^{35} +(-2.90161 - 8.93024i) q^{36} +6.40886 q^{37} +(-4.45705 - 3.23823i) q^{38} -2.98711 q^{39} +(0.0708780 - 0.218140i) q^{40} -3.18619 q^{41} +(1.74404 - 1.26712i) q^{42} +(-2.31298 + 1.68048i) q^{43} +(15.1463 - 11.0044i) q^{44} -0.107480 q^{45} +(-5.16024 + 15.8816i) q^{46} +(-1.09406 - 3.36718i) q^{47} -3.40245 q^{48} +(4.72959 + 3.43625i) q^{49} +(9.92638 + 7.21193i) q^{50} +6.16971 q^{51} +(4.54717 - 13.9947i) q^{52} +(11.2897 - 8.20242i) q^{53} +(3.30648 + 10.1763i) q^{54} +(-0.0662223 - 0.203811i) q^{55} +(1.65178 + 5.08365i) q^{56} +(1.48411 + 1.07827i) q^{57} +(-1.89173 - 5.82213i) q^{58} +(-6.15211 + 4.46977i) q^{59} +(-0.0468885 + 0.144308i) q^{60} +(-1.77784 - 5.47162i) q^{61} +(-6.55751 - 4.76431i) q^{62} +(2.02641 - 1.47227i) q^{63} +(-2.37052 + 7.29571i) q^{64} +(-0.136266 - 0.0990033i) q^{65} +(-7.54827 + 5.48414i) q^{66} +(2.96996 + 2.15780i) q^{67} +(-9.39191 + 28.9053i) q^{68} +(1.71826 - 5.28825i) q^{69} +0.121556 q^{70} +(-0.618801 + 8.40340i) q^{71} -11.6029 q^{72} +(4.05110 - 12.4680i) q^{73} +(4.86195 - 14.9635i) q^{74} +(-3.30528 - 2.40143i) q^{75} +(-7.31093 + 5.31170i) q^{76} +(4.04035 + 2.93549i) q^{77} +(-2.26611 + 6.97438i) q^{78} +(-0.376033 + 0.273204i) q^{79} +(-0.155213 - 0.112769i) q^{80} +(1.06067 + 3.26440i) q^{81} +(-2.41714 + 7.43920i) q^{82} +(7.07391 - 5.13949i) q^{83} +(-1.09271 - 3.36302i) q^{84} +(0.281450 + 0.204486i) q^{85} +(2.16893 + 6.67527i) q^{86} +(0.629907 + 1.93865i) q^{87} +(-7.14896 - 22.0022i) q^{88} +(-6.76269 + 4.91338i) q^{89} +(-0.0815379 + 0.250948i) q^{90} +3.92528 q^{91} +(22.1600 + 16.1002i) q^{92} +(2.18352 + 1.58642i) q^{93} -8.69175 q^{94} +(0.0319646 + 0.0983770i) q^{95} +(-0.0672223 + 0.206889i) q^{96} -7.30123 q^{97} +(11.6110 - 8.43591i) q^{98} +(-8.77038 + 6.37205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 6 q^{2} - q^{3} - 10 q^{4} - q^{5} - 8 q^{6} - q^{7} - q^{8} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 6 q^{2} - q^{3} - 10 q^{4} - q^{5} - 8 q^{6} - q^{7} - q^{8} - 10 q^{9} + 15 q^{10} - q^{11} + 4 q^{12} + 3 q^{13} + 5 q^{14} - 5 q^{15} - 16 q^{16} - 2 q^{17} + 36 q^{18} + 3 q^{19} - 72 q^{20} + 25 q^{21} + 10 q^{22} - 22 q^{23} + 19 q^{24} + 14 q^{25} - 42 q^{26} + 2 q^{27} + 4 q^{28} - q^{29} + 20 q^{30} + 6 q^{31} + 52 q^{32} + 10 q^{33} - 34 q^{34} + 3 q^{35} + 20 q^{36} - 6 q^{37} + 25 q^{38} - 86 q^{39} + 65 q^{40} - 60 q^{41} + 27 q^{42} + 23 q^{43} + 37 q^{44} - 44 q^{45} - 19 q^{46} + 29 q^{47} - 96 q^{48} + 22 q^{49} + 36 q^{50} + 34 q^{51} + 43 q^{52} + 2 q^{53} + 4 q^{54} + 10 q^{55} + 31 q^{56} - 18 q^{57} - 33 q^{58} + 31 q^{59} - 38 q^{60} - 2 q^{61} + 5 q^{62} + 23 q^{63} - 65 q^{64} + 54 q^{65} - 94 q^{66} - 38 q^{67} - 3 q^{68} + 11 q^{69} - 34 q^{70} + 45 q^{71} - 10 q^{72} - 21 q^{73} + 21 q^{74} + 13 q^{75} - q^{76} - 12 q^{77} - 6 q^{78} - 59 q^{79} - 16 q^{80} - 35 q^{81} + 53 q^{82} - 15 q^{83} - 33 q^{84} + 13 q^{85} - 19 q^{86} + 49 q^{87} - 64 q^{88} + 16 q^{89} + 86 q^{90} - 18 q^{91} + 86 q^{92} - 62 q^{94} + 15 q^{95} + 107 q^{96} - 58 q^{97} - 30 q^{98} + 30 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/71\mathbb{Z}\right)^\times\).

\(n\) \(7\)
\(\chi(n)\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.758630 2.33482i 0.536432 1.65097i −0.204101 0.978950i \(-0.565427\pi\)
0.740534 0.672019i \(-0.234573\pi\)
\(3\) −0.252609 + 0.777449i −0.145844 + 0.448860i −0.997119 0.0758595i \(-0.975830\pi\)
0.851275 + 0.524720i \(0.175830\pi\)
\(4\) −3.25785 2.36696i −1.62892 1.18348i
\(5\) −0.0372909 + 0.0270934i −0.0166770 + 0.0121165i −0.596093 0.802916i \(-0.703281\pi\)
0.579416 + 0.815032i \(0.303281\pi\)
\(6\) 1.62357 + 1.17959i 0.662820 + 0.481567i
\(7\) 0.331946 1.02163i 0.125464 0.386138i −0.868521 0.495652i \(-0.834929\pi\)
0.993985 + 0.109514i \(0.0349293\pi\)
\(8\) −4.02570 + 2.92484i −1.42330 + 1.03409i
\(9\) 1.88643 + 1.37058i 0.628812 + 0.456858i
\(10\) 0.0349684 + 0.107622i 0.0110580 + 0.0340329i
\(11\) −1.43668 + 4.42163i −0.433174 + 1.33317i 0.461772 + 0.886999i \(0.347214\pi\)
−0.894946 + 0.446174i \(0.852786\pi\)
\(12\) 2.66315 1.93489i 0.768786 0.558556i
\(13\) 1.12919 + 3.47530i 0.313182 + 0.963875i 0.976496 + 0.215534i \(0.0691491\pi\)
−0.663315 + 0.748341i \(0.730851\pi\)
\(14\) −2.13349 1.55007i −0.570199 0.414274i
\(15\) −0.0116438 0.0358358i −0.00300641 0.00925276i
\(16\) 1.28620 + 3.95852i 0.321550 + 0.989630i
\(17\) −2.33228 7.17803i −0.565662 1.74093i −0.665977 0.745972i \(-0.731985\pi\)
0.100315 0.994956i \(-0.468015\pi\)
\(18\) 4.63116 3.36473i 1.09157 0.793075i
\(19\) 0.693465 2.13426i 0.159092 0.489634i −0.839461 0.543420i \(-0.817129\pi\)
0.998552 + 0.0537864i \(0.0171290\pi\)
\(20\) 0.185617 0.0415052
\(21\) 0.710409 + 0.516143i 0.155024 + 0.112632i
\(22\) 9.23383 + 6.70877i 1.96866 + 1.43031i
\(23\) −6.80205 −1.41832 −0.709162 0.705045i \(-0.750927\pi\)
−0.709162 + 0.705045i \(0.750927\pi\)
\(24\) −1.25699 3.86862i −0.256582 0.789678i
\(25\) −1.54443 + 4.75326i −0.308886 + 0.950652i
\(26\) 8.97085 1.75933
\(27\) −3.52610 + 2.56186i −0.678597 + 0.493030i
\(28\) −3.49958 + 2.54259i −0.661358 + 0.480505i
\(29\) 2.01737 1.46571i 0.374617 0.272175i −0.384506 0.923122i \(-0.625628\pi\)
0.759123 + 0.650948i \(0.225628\pi\)
\(30\) −0.0925036 −0.0168888
\(31\) 1.02027 3.14007i 0.183246 0.563974i −0.816667 0.577109i \(-0.804181\pi\)
0.999914 + 0.0131345i \(0.00418095\pi\)
\(32\) 0.266113 0.0470425
\(33\) −3.07468 2.23389i −0.535233 0.388869i
\(34\) −18.5288 −3.17766
\(35\) 0.0153008 + 0.0470909i 0.00258630 + 0.00795981i
\(36\) −2.90161 8.93024i −0.483602 1.48837i
\(37\) 6.40886 1.05361 0.526805 0.849986i \(-0.323390\pi\)
0.526805 + 0.849986i \(0.323390\pi\)
\(38\) −4.45705 3.23823i −0.723029 0.525311i
\(39\) −2.98711 −0.478321
\(40\) 0.0708780 0.218140i 0.0112068 0.0344910i
\(41\) −3.18619 −0.497600 −0.248800 0.968555i \(-0.580036\pi\)
−0.248800 + 0.968555i \(0.580036\pi\)
\(42\) 1.74404 1.26712i 0.269111 0.195521i
\(43\) −2.31298 + 1.68048i −0.352727 + 0.256271i −0.750012 0.661424i \(-0.769952\pi\)
0.397285 + 0.917695i \(0.369952\pi\)
\(44\) 15.1463 11.0044i 2.28339 1.65898i
\(45\) −0.107480 −0.0160222
\(46\) −5.16024 + 15.8816i −0.760835 + 2.34161i
\(47\) −1.09406 3.36718i −0.159585 0.491153i 0.839011 0.544114i \(-0.183134\pi\)
−0.998597 + 0.0529608i \(0.983134\pi\)
\(48\) −3.40245 −0.491102
\(49\) 4.72959 + 3.43625i 0.675656 + 0.490893i
\(50\) 9.92638 + 7.21193i 1.40380 + 1.01992i
\(51\) 6.16971 0.863932
\(52\) 4.54717 13.9947i 0.630579 1.94072i
\(53\) 11.2897 8.20242i 1.55075 1.12669i 0.607644 0.794210i \(-0.292115\pi\)
0.943110 0.332480i \(-0.107885\pi\)
\(54\) 3.30648 + 10.1763i 0.449955 + 1.38482i
\(55\) −0.0662223 0.203811i −0.00892941 0.0274819i
\(56\) 1.65178 + 5.08365i 0.220728 + 0.679331i
\(57\) 1.48411 + 1.07827i 0.196575 + 0.142820i
\(58\) −1.89173 5.82213i −0.248396 0.764484i
\(59\) −6.15211 + 4.46977i −0.800936 + 0.581914i −0.911189 0.411990i \(-0.864834\pi\)
0.110253 + 0.993904i \(0.464834\pi\)
\(60\) −0.0468885 + 0.144308i −0.00605327 + 0.0186301i
\(61\) −1.77784 5.47162i −0.227629 0.700569i −0.998014 0.0629908i \(-0.979936\pi\)
0.770385 0.637579i \(-0.220064\pi\)
\(62\) −6.55751 4.76431i −0.832805 0.605068i
\(63\) 2.02641 1.47227i 0.255304 0.185489i
\(64\) −2.37052 + 7.29571i −0.296315 + 0.911964i
\(65\) −0.136266 0.0990033i −0.0169018 0.0122798i
\(66\) −7.54827 + 5.48414i −0.929128 + 0.675051i
\(67\) 2.96996 + 2.15780i 0.362839 + 0.263618i 0.754235 0.656604i \(-0.228008\pi\)
−0.391396 + 0.920222i \(0.628008\pi\)
\(68\) −9.39191 + 28.9053i −1.13894 + 3.50529i
\(69\) 1.71826 5.28825i 0.206854 0.636630i
\(70\) 0.121556 0.0145288
\(71\) −0.618801 + 8.40340i −0.0734382 + 0.997300i
\(72\) −11.6029 −1.36742
\(73\) 4.05110 12.4680i 0.474146 1.45927i −0.372961 0.927847i \(-0.621657\pi\)
0.847106 0.531423i \(-0.178343\pi\)
\(74\) 4.86195 14.9635i 0.565190 1.73948i
\(75\) −3.30528 2.40143i −0.381661 0.277293i
\(76\) −7.31093 + 5.31170i −0.838621 + 0.609294i
\(77\) 4.04035 + 2.93549i 0.460441 + 0.334530i
\(78\) −2.26611 + 6.97438i −0.256587 + 0.789693i
\(79\) −0.376033 + 0.273204i −0.0423070 + 0.0307379i −0.608738 0.793371i \(-0.708324\pi\)
0.566431 + 0.824109i \(0.308324\pi\)
\(80\) −0.155213 0.112769i −0.0173534 0.0126080i
\(81\) 1.06067 + 3.26440i 0.117852 + 0.362712i
\(82\) −2.41714 + 7.43920i −0.266929 + 0.821522i
\(83\) 7.07391 5.13949i 0.776462 0.564133i −0.127453 0.991845i \(-0.540680\pi\)
0.903915 + 0.427712i \(0.140680\pi\)
\(84\) −1.09271 3.36302i −0.119225 0.366936i
\(85\) 0.281450 + 0.204486i 0.0305276 + 0.0221796i
\(86\) 2.16893 + 6.67527i 0.233881 + 0.719813i
\(87\) 0.629907 + 1.93865i 0.0675331 + 0.207846i
\(88\) −7.14896 22.0022i −0.762081 2.34545i
\(89\) −6.76269 + 4.91338i −0.716844 + 0.520818i −0.885374 0.464879i \(-0.846098\pi\)
0.168530 + 0.985696i \(0.446098\pi\)
\(90\) −0.0815379 + 0.250948i −0.00859485 + 0.0264522i
\(91\) 3.92528 0.411482
\(92\) 22.1600 + 16.1002i 2.31034 + 1.67856i
\(93\) 2.18352 + 1.58642i 0.226420 + 0.164504i
\(94\) −8.69175 −0.896486
\(95\) 0.0319646 + 0.0983770i 0.00327950 + 0.0100933i
\(96\) −0.0672223 + 0.206889i −0.00686085 + 0.0211155i
\(97\) −7.30123 −0.741328 −0.370664 0.928767i \(-0.620870\pi\)
−0.370664 + 0.928767i \(0.620870\pi\)
\(98\) 11.6110 8.43591i 1.17289 0.852156i
\(99\) −8.77038 + 6.37205i −0.881456 + 0.640415i
\(100\) 16.2823 11.8298i 1.62823 1.18298i
\(101\) −1.71025 −0.170177 −0.0850883 0.996373i \(-0.527117\pi\)
−0.0850883 + 0.996373i \(0.527117\pi\)
\(102\) 4.68053 14.4052i 0.463441 1.42632i
\(103\) 14.0771 1.38706 0.693528 0.720430i \(-0.256056\pi\)
0.693528 + 0.720430i \(0.256056\pi\)
\(104\) −14.7105 10.6878i −1.44248 1.04803i
\(105\) −0.0404759 −0.00395004
\(106\) −10.5865 32.5820i −1.02825 3.16464i
\(107\) −3.48065 10.7123i −0.336487 1.03560i −0.965985 0.258598i \(-0.916740\pi\)
0.629498 0.777002i \(-0.283260\pi\)
\(108\) 17.5513 1.68887
\(109\) 2.03044 + 1.47520i 0.194481 + 0.141299i 0.680764 0.732502i \(-0.261648\pi\)
−0.486283 + 0.873801i \(0.661648\pi\)
\(110\) −0.526101 −0.0501618
\(111\) −1.61893 + 4.98256i −0.153662 + 0.472924i
\(112\) 4.47107 0.422477
\(113\) −1.65362 + 1.20143i −0.155560 + 0.113021i −0.662842 0.748759i \(-0.730650\pi\)
0.507283 + 0.861780i \(0.330650\pi\)
\(114\) 3.64345 2.64712i 0.341240 0.247926i
\(115\) 0.253654 0.184291i 0.0236534 0.0171852i
\(116\) −10.0416 −0.932335
\(117\) −2.63301 + 8.10357i −0.243422 + 0.749175i
\(118\) 5.76894 + 17.7550i 0.531074 + 1.63448i
\(119\) −8.10745 −0.743209
\(120\) 0.151688 + 0.110208i 0.0138472 + 0.0100606i
\(121\) −8.58762 6.23927i −0.780693 0.567207i
\(122\) −14.1240 −1.27873
\(123\) 0.804860 2.47710i 0.0725718 0.223353i
\(124\) −10.7563 + 7.81493i −0.965947 + 0.701802i
\(125\) −0.142408 0.438288i −0.0127374 0.0392016i
\(126\) −1.90020 5.84822i −0.169283 0.521000i
\(127\) 0.769988 + 2.36978i 0.0683254 + 0.210284i 0.979389 0.201981i \(-0.0647379\pi\)
−0.911064 + 0.412265i \(0.864738\pi\)
\(128\) 15.6664 + 11.3823i 1.38473 + 1.00607i
\(129\) −0.722209 2.22273i −0.0635870 0.195701i
\(130\) −0.334531 + 0.243051i −0.0293403 + 0.0213170i
\(131\) 1.52870 4.70485i 0.133563 0.411065i −0.861801 0.507247i \(-0.830663\pi\)
0.995364 + 0.0961824i \(0.0306632\pi\)
\(132\) 4.72930 + 14.5553i 0.411633 + 1.26688i
\(133\) −1.95023 1.41692i −0.169106 0.122863i
\(134\) 7.29120 5.29736i 0.629863 0.457623i
\(135\) 0.0620817 0.191068i 0.00534315 0.0164445i
\(136\) 30.3837 + 22.0750i 2.60538 + 1.89292i
\(137\) −6.29737 + 4.57531i −0.538021 + 0.390895i −0.823349 0.567535i \(-0.807897\pi\)
0.285329 + 0.958430i \(0.407897\pi\)
\(138\) −11.0436 8.02364i −0.940094 0.683018i
\(139\) −4.21743 + 12.9799i −0.357718 + 1.10094i 0.596699 + 0.802465i \(0.296479\pi\)
−0.954417 + 0.298477i \(0.903521\pi\)
\(140\) 0.0616149 0.189631i 0.00520741 0.0160268i
\(141\) 2.89418 0.243734
\(142\) 19.1510 + 7.81986i 1.60712 + 0.656228i
\(143\) −16.9888 −1.42067
\(144\) −2.99911 + 9.23032i −0.249926 + 0.769194i
\(145\) −0.0355186 + 0.109315i −0.00294966 + 0.00907812i
\(146\) −26.0373 18.9172i −2.15486 1.56560i
\(147\) −3.86624 + 2.80899i −0.318882 + 0.231682i
\(148\) −20.8791 15.1695i −1.71625 1.24693i
\(149\) −2.25571 + 6.94237i −0.184795 + 0.568741i −0.999945 0.0105093i \(-0.996655\pi\)
0.815150 + 0.579251i \(0.196655\pi\)
\(150\) −8.11440 + 5.89546i −0.662538 + 0.481362i
\(151\) 4.84062 + 3.51692i 0.393924 + 0.286203i 0.767062 0.641573i \(-0.221718\pi\)
−0.373138 + 0.927776i \(0.621718\pi\)
\(152\) 3.45071 + 10.6202i 0.279889 + 0.861411i
\(153\) 5.43833 16.7375i 0.439663 1.35314i
\(154\) 9.91898 7.20656i 0.799294 0.580721i
\(155\) 0.0470285 + 0.144739i 0.00377742 + 0.0116257i
\(156\) 9.73155 + 7.07038i 0.779147 + 0.566084i
\(157\) 4.92371 + 15.1536i 0.392955 + 1.20939i 0.930543 + 0.366183i \(0.119335\pi\)
−0.537588 + 0.843207i \(0.680665\pi\)
\(158\) 0.352613 + 1.08523i 0.0280524 + 0.0863364i
\(159\) 3.52510 + 10.8491i 0.279559 + 0.860393i
\(160\) −0.00992358 + 0.00720990i −0.000784528 + 0.000569993i
\(161\) −2.25791 + 6.94914i −0.177948 + 0.547669i
\(162\) 8.42646 0.662045
\(163\) −15.1771 11.0268i −1.18876 0.863687i −0.195631 0.980678i \(-0.562675\pi\)
−0.993133 + 0.116990i \(0.962675\pi\)
\(164\) 10.3801 + 7.54160i 0.810552 + 0.588900i
\(165\) 0.175181 0.0136378
\(166\) −6.63333 20.4153i −0.514846 1.58453i
\(167\) 6.67072 20.5304i 0.516196 1.58869i −0.264900 0.964276i \(-0.585339\pi\)
0.781096 0.624411i \(-0.214661\pi\)
\(168\) −4.36953 −0.337117
\(169\) −0.285405 + 0.207359i −0.0219542 + 0.0159507i
\(170\) 0.690954 0.502008i 0.0529938 0.0385022i
\(171\) 4.23335 3.07571i 0.323732 0.235205i
\(172\) 11.5130 0.877857
\(173\) −4.16355 + 12.8141i −0.316549 + 0.974238i 0.658563 + 0.752526i \(0.271165\pi\)
−0.975112 + 0.221713i \(0.928835\pi\)
\(174\) 5.00428 0.379373
\(175\) 4.34338 + 3.15565i 0.328329 + 0.238545i
\(176\) −19.3510 −1.45863
\(177\) −1.92094 5.91205i −0.144387 0.444377i
\(178\) 6.34150 + 19.5171i 0.475316 + 1.46287i
\(179\) −2.78978 −0.208518 −0.104259 0.994550i \(-0.533247\pi\)
−0.104259 + 0.994550i \(0.533247\pi\)
\(180\) 0.350155 + 0.254402i 0.0260990 + 0.0189620i
\(181\) 5.97431 0.444067 0.222033 0.975039i \(-0.428731\pi\)
0.222033 + 0.975039i \(0.428731\pi\)
\(182\) 2.97784 9.16484i 0.220732 0.679343i
\(183\) 4.70300 0.347656
\(184\) 27.3830 19.8949i 2.01870 1.46667i
\(185\) −0.238992 + 0.173638i −0.0175710 + 0.0127661i
\(186\) 5.36049 3.89463i 0.393050 0.285568i
\(187\) 35.0894 2.56599
\(188\) −4.40570 + 13.5594i −0.321319 + 0.988917i
\(189\) 1.44679 + 4.45275i 0.105238 + 0.323890i
\(190\) 0.253942 0.0184229
\(191\) −2.87909 2.09178i −0.208324 0.151356i 0.478731 0.877962i \(-0.341097\pi\)
−0.687055 + 0.726605i \(0.741097\pi\)
\(192\) −5.07323 3.68592i −0.366129 0.266008i
\(193\) −14.1397 −1.01780 −0.508900 0.860826i \(-0.669948\pi\)
−0.508900 + 0.860826i \(0.669948\pi\)
\(194\) −5.53893 + 17.0471i −0.397672 + 1.22391i
\(195\) 0.111392 0.0809311i 0.00797695 0.00579560i
\(196\) −7.27480 22.3895i −0.519628 1.59925i
\(197\) 5.49417 + 16.9093i 0.391443 + 1.20474i 0.931697 + 0.363237i \(0.118328\pi\)
−0.540253 + 0.841502i \(0.681672\pi\)
\(198\) 8.22414 + 25.3113i 0.584464 + 1.79880i
\(199\) −0.658239 0.478239i −0.0466613 0.0339014i 0.564210 0.825631i \(-0.309181\pi\)
−0.610871 + 0.791730i \(0.709181\pi\)
\(200\) −7.68514 23.6524i −0.543421 1.67248i
\(201\) −2.42782 + 1.76392i −0.171245 + 0.124417i
\(202\) −1.29745 + 3.99314i −0.0912883 + 0.280956i
\(203\) −0.827744 2.54753i −0.0580962 0.178802i
\(204\) −20.1000 14.6035i −1.40728 1.02245i
\(205\) 0.118816 0.0863249i 0.00829847 0.00602919i
\(206\) 10.6793 32.8675i 0.744061 2.28999i
\(207\) −12.8316 9.32272i −0.891859 0.647974i
\(208\) −12.3047 + 8.93987i −0.853175 + 0.619868i
\(209\) 8.44065 + 6.13249i 0.583852 + 0.424193i
\(210\) −0.0307062 + 0.0945040i −0.00211893 + 0.00652139i
\(211\) −0.899500 + 2.76838i −0.0619241 + 0.190583i −0.977233 0.212171i \(-0.931947\pi\)
0.915309 + 0.402753i \(0.131947\pi\)
\(212\) −56.1948 −3.85947
\(213\) −6.37690 2.60386i −0.436938 0.178413i
\(214\) −27.6519 −1.89025
\(215\) 0.0407233 0.125333i 0.00277730 0.00854766i
\(216\) 6.70197 20.6266i 0.456011 1.40346i
\(217\) −2.86930 2.08467i −0.194781 0.141517i
\(218\) 4.98469 3.62159i 0.337606 0.245285i
\(219\) 8.66990 + 6.29905i 0.585858 + 0.425651i
\(220\) −0.266672 + 0.820731i −0.0179790 + 0.0553337i
\(221\) 22.3122 16.2108i 1.50088 1.09045i
\(222\) 10.4052 + 7.55984i 0.698353 + 0.507383i
\(223\) −7.04003 21.6670i −0.471436 1.45093i −0.850705 0.525643i \(-0.823825\pi\)
0.379269 0.925286i \(-0.376175\pi\)
\(224\) 0.0883351 0.271867i 0.00590214 0.0181649i
\(225\) −9.42817 + 6.84996i −0.628544 + 0.456664i
\(226\) 1.55063 + 4.77235i 0.103146 + 0.317452i
\(227\) 14.6971 + 10.6781i 0.975481 + 0.708728i 0.956694 0.291095i \(-0.0940196\pi\)
0.0187868 + 0.999824i \(0.494020\pi\)
\(228\) −2.28277 7.02565i −0.151180 0.465285i
\(229\) −4.81678 14.8245i −0.318302 0.979632i −0.974374 0.224934i \(-0.927783\pi\)
0.656072 0.754698i \(-0.272217\pi\)
\(230\) −0.237856 0.732047i −0.0156838 0.0482697i
\(231\) −3.30282 + 2.39964i −0.217310 + 0.157885i
\(232\) −3.83437 + 11.8010i −0.251739 + 0.774773i
\(233\) −17.6339 −1.15524 −0.577618 0.816307i \(-0.696018\pi\)
−0.577618 + 0.816307i \(0.696018\pi\)
\(234\) 16.9229 + 12.2952i 1.10629 + 0.803764i
\(235\) 0.132027 + 0.0959232i 0.00861249 + 0.00625734i
\(236\) 30.6224 1.99335
\(237\) −0.117413 0.361360i −0.00762680 0.0234729i
\(238\) −6.15055 + 18.9295i −0.398681 + 1.22701i
\(239\) 27.5931 1.78485 0.892426 0.451193i \(-0.149002\pi\)
0.892426 + 0.451193i \(0.149002\pi\)
\(240\) 0.126881 0.0921841i 0.00819010 0.00595046i
\(241\) −2.92979 + 2.12862i −0.188725 + 0.137116i −0.678136 0.734937i \(-0.737212\pi\)
0.489411 + 0.872053i \(0.337212\pi\)
\(242\) −21.0824 + 15.3173i −1.35523 + 0.984632i
\(243\) −15.8813 −1.01879
\(244\) −7.15921 + 22.0338i −0.458321 + 1.41057i
\(245\) −0.269470 −0.0172158
\(246\) −5.17301 3.75841i −0.329819 0.239627i
\(247\) 8.20026 0.521770
\(248\) 5.07691 + 15.6251i 0.322384 + 0.992197i
\(249\) 2.20877 + 6.79788i 0.139975 + 0.430798i
\(250\) −1.13136 −0.0715534
\(251\) 23.8825 + 17.3516i 1.50745 + 1.09523i 0.967293 + 0.253661i \(0.0816349\pi\)
0.540156 + 0.841565i \(0.318365\pi\)
\(252\) −10.0865 −0.635392
\(253\) 9.77234 30.0762i 0.614382 1.89087i
\(254\) 6.11715 0.383824
\(255\) −0.230074 + 0.167158i −0.0144078 + 0.0104679i
\(256\) 26.0485 18.9254i 1.62803 1.18284i
\(257\) −13.8636 + 10.0725i −0.864790 + 0.628307i −0.929184 0.369618i \(-0.879489\pi\)
0.0643938 + 0.997925i \(0.479489\pi\)
\(258\) −5.73757 −0.357206
\(259\) 2.12740 6.54745i 0.132190 0.406839i
\(260\) 0.209598 + 0.645075i 0.0129987 + 0.0400058i
\(261\) 5.81450 0.359909
\(262\) −9.82527 7.13848i −0.607007 0.441017i
\(263\) 19.8893 + 14.4504i 1.22643 + 0.891052i 0.996617 0.0821828i \(-0.0261891\pi\)
0.229811 + 0.973235i \(0.426189\pi\)
\(264\) 18.9115 1.16392
\(265\) −0.198770 + 0.611751i −0.0122103 + 0.0375796i
\(266\) −4.78776 + 3.47851i −0.293556 + 0.213281i
\(267\) −2.11159 6.49881i −0.129227 0.397721i
\(268\) −4.56824 14.0596i −0.279050 0.858826i
\(269\) −3.76723 11.5944i −0.229692 0.706920i −0.997781 0.0665771i \(-0.978792\pi\)
0.768089 0.640343i \(-0.221208\pi\)
\(270\) −0.399013 0.289900i −0.0242831 0.0176427i
\(271\) −5.84872 18.0005i −0.355284 1.09345i −0.955845 0.293873i \(-0.905056\pi\)
0.600560 0.799579i \(-0.294944\pi\)
\(272\) 25.4146 18.4648i 1.54099 1.11959i
\(273\) −0.991560 + 3.05171i −0.0600120 + 0.184698i
\(274\) 5.90516 + 18.1742i 0.356744 + 1.09794i
\(275\) −18.7983 13.6578i −1.13358 0.823596i
\(276\) −18.1149 + 13.1612i −1.09039 + 0.792214i
\(277\) −0.320186 + 0.985432i −0.0192381 + 0.0592089i −0.960215 0.279263i \(-0.909910\pi\)
0.940977 + 0.338472i \(0.109910\pi\)
\(278\) 27.1063 + 19.6939i 1.62573 + 1.18116i
\(279\) 6.22839 4.52519i 0.372884 0.270916i
\(280\) −0.199330 0.144821i −0.0119122 0.00865474i
\(281\) 3.40318 10.4739i 0.203017 0.624821i −0.796772 0.604279i \(-0.793461\pi\)
0.999789 0.0205412i \(-0.00653893\pi\)
\(282\) 2.19561 6.75740i 0.130747 0.402397i
\(283\) 0.0206694 0.00122867 0.000614335 1.00000i \(-0.499804\pi\)
0.000614335 1.00000i \(0.499804\pi\)
\(284\) 21.9065 25.9123i 1.29991 1.53761i
\(285\) −0.0845576 −0.00500876
\(286\) −12.8882 + 39.6658i −0.762095 + 2.34549i
\(287\) −1.05764 + 3.25510i −0.0624308 + 0.192142i
\(288\) 0.502004 + 0.364727i 0.0295809 + 0.0214918i
\(289\) −32.3313 + 23.4900i −1.90184 + 1.38177i
\(290\) 0.228286 + 0.165859i 0.0134054 + 0.00973959i
\(291\) 1.84435 5.67634i 0.108118 0.332753i
\(292\) −42.7092 + 31.0300i −2.49937 + 1.81590i
\(293\) 19.8023 + 14.3872i 1.15686 + 0.840511i 0.989378 0.145364i \(-0.0464352\pi\)
0.167486 + 0.985875i \(0.446435\pi\)
\(294\) 3.62545 + 11.1580i 0.211440 + 0.650746i
\(295\) 0.108316 0.333363i 0.00630642 0.0194092i
\(296\) −25.8001 + 18.7449i −1.49960 + 1.08953i
\(297\) −6.26174 19.2717i −0.363343 1.11826i
\(298\) 14.4980 + 10.5334i 0.839844 + 0.610183i
\(299\) −7.68082 23.6391i −0.444194 1.36709i
\(300\) 5.08401 + 15.6470i 0.293525 + 0.903378i
\(301\) 0.949036 + 2.92083i 0.0547015 + 0.168354i
\(302\) 11.8836 8.63395i 0.683825 0.496828i
\(303\) 0.432025 1.32964i 0.0248192 0.0763856i
\(304\) 9.34046 0.535712
\(305\) 0.214542 + 0.155874i 0.0122846 + 0.00892532i
\(306\) −34.9533 25.3951i −1.99815 1.45174i
\(307\) 8.69769 0.496403 0.248202 0.968708i \(-0.420160\pi\)
0.248202 + 0.968708i \(0.420160\pi\)
\(308\) −6.21465 19.1267i −0.354113 1.08985i
\(309\) −3.55599 + 10.9442i −0.202293 + 0.622594i
\(310\) 0.373617 0.0212200
\(311\) −15.8249 + 11.4975i −0.897349 + 0.651963i −0.937784 0.347220i \(-0.887126\pi\)
0.0404344 + 0.999182i \(0.487126\pi\)
\(312\) 12.0252 8.73683i 0.680794 0.494626i
\(313\) −18.1030 + 13.1526i −1.02324 + 0.743427i −0.966944 0.254987i \(-0.917929\pi\)
−0.0562953 + 0.998414i \(0.517929\pi\)
\(314\) 39.1163 2.20746
\(315\) −0.0356777 + 0.109805i −0.00201021 + 0.00618679i
\(316\) 1.87172 0.105293
\(317\) −0.0186102 0.0135211i −0.00104525 0.000759420i 0.587263 0.809397i \(-0.300206\pi\)
−0.588308 + 0.808637i \(0.700206\pi\)
\(318\) 28.0051 1.57045
\(319\) 3.58251 + 11.0258i 0.200582 + 0.617328i
\(320\) −0.109267 0.336289i −0.00610821 0.0187991i
\(321\) 9.20753 0.513914
\(322\) 14.5121 + 10.5437i 0.808728 + 0.587575i
\(323\) −16.9372 −0.942409
\(324\) 4.27123 13.1455i 0.237290 0.730305i
\(325\) −18.2630 −1.01305
\(326\) −37.2595 + 27.0706i −2.06361 + 1.49930i
\(327\) −1.65980 + 1.20592i −0.0917872 + 0.0666873i
\(328\) 12.8267 9.31912i 0.708234 0.514562i
\(329\) −3.80316 −0.209675
\(330\) 0.132898 0.409017i 0.00731577 0.0225156i
\(331\) −3.25188 10.0083i −0.178739 0.550103i 0.821045 0.570863i \(-0.193391\pi\)
−0.999784 + 0.0207601i \(0.993391\pi\)
\(332\) −35.2107 −1.93244
\(333\) 12.0899 + 8.78382i 0.662522 + 0.481350i
\(334\) −42.8741 31.1499i −2.34597 1.70445i
\(335\) −0.169215 −0.00924520
\(336\) −1.12943 + 3.47603i −0.0616155 + 0.189633i
\(337\) −1.60117 + 1.16332i −0.0872212 + 0.0633699i −0.630541 0.776156i \(-0.717167\pi\)
0.543320 + 0.839526i \(0.317167\pi\)
\(338\) 0.267629 + 0.823678i 0.0145571 + 0.0448022i
\(339\) −0.516329 1.58910i −0.0280431 0.0863079i
\(340\) −0.432912 1.33236i −0.0234779 0.0722576i
\(341\) 12.4185 + 9.02254i 0.672497 + 0.488598i
\(342\) −3.96969 12.2174i −0.214656 0.660643i
\(343\) 11.1638 8.11101i 0.602791 0.437953i
\(344\) 4.39624 13.5302i 0.237029 0.729501i
\(345\) 0.0792014 + 0.243757i 0.00426406 + 0.0131234i
\(346\) 26.7601 + 19.4423i 1.43863 + 1.04523i
\(347\) 5.02508 3.65094i 0.269761 0.195993i −0.444678 0.895690i \(-0.646682\pi\)
0.714439 + 0.699698i \(0.246682\pi\)
\(348\) 2.53658 7.80680i 0.135975 0.418488i
\(349\) −17.0779 12.4078i −0.914159 0.664175i 0.0279044 0.999611i \(-0.491117\pi\)
−0.942063 + 0.335435i \(0.891117\pi\)
\(350\) 10.6629 7.74706i 0.569957 0.414098i
\(351\) −12.8849 9.36140i −0.687743 0.499675i
\(352\) −0.382318 + 1.17665i −0.0203776 + 0.0627158i
\(353\) 6.60892 20.3402i 0.351757 1.08260i −0.606109 0.795382i \(-0.707270\pi\)
0.957866 0.287216i \(-0.0927296\pi\)
\(354\) −15.2609 −0.811106
\(355\) −0.204601 0.330136i −0.0108591 0.0175218i
\(356\) 33.6616 1.78406
\(357\) 2.04801 6.30313i 0.108392 0.333597i
\(358\) −2.11641 + 6.51363i −0.111856 + 0.344256i
\(359\) 7.96414 + 5.78629i 0.420331 + 0.305389i 0.777771 0.628548i \(-0.216350\pi\)
−0.357440 + 0.933936i \(0.616350\pi\)
\(360\) 0.432684 0.314363i 0.0228044 0.0165684i
\(361\) 11.2971 + 8.20785i 0.594586 + 0.431992i
\(362\) 4.53229 13.9490i 0.238212 0.733141i
\(363\) 7.02002 5.10035i 0.368456 0.267699i
\(364\) −12.7880 9.29100i −0.670272 0.486981i
\(365\) 0.186732 + 0.574701i 0.00977399 + 0.0300812i
\(366\) 3.56784 10.9807i 0.186494 0.573970i
\(367\) 1.51466 1.10046i 0.0790645 0.0574437i −0.547551 0.836772i \(-0.684440\pi\)
0.626615 + 0.779329i \(0.284440\pi\)
\(368\) −8.74880 26.9260i −0.456063 1.40362i
\(369\) −6.01055 4.36692i −0.312897 0.227333i
\(370\) 0.224107 + 0.689731i 0.0116508 + 0.0358574i
\(371\) −4.63224 14.2566i −0.240494 0.740164i
\(372\) −3.35857 10.3366i −0.174134 0.535929i
\(373\) −8.95874 + 6.50891i −0.463866 + 0.337018i −0.795046 0.606549i \(-0.792553\pi\)
0.331180 + 0.943568i \(0.392553\pi\)
\(374\) 26.6198 81.9274i 1.37648 4.23637i
\(375\) 0.376720 0.0194537
\(376\) 14.2528 + 10.3553i 0.735034 + 0.534033i
\(377\) 7.37177 + 5.35590i 0.379665 + 0.275843i
\(378\) 11.4940 0.591185
\(379\) 9.51931 + 29.2974i 0.488974 + 1.50491i 0.826141 + 0.563463i \(0.190531\pi\)
−0.337167 + 0.941445i \(0.609469\pi\)
\(380\) 0.128719 0.396156i 0.00660314 0.0203224i
\(381\) −2.03689 −0.104353
\(382\) −7.06811 + 5.13528i −0.361636 + 0.262744i
\(383\) −6.47388 + 4.70355i −0.330800 + 0.240340i −0.740770 0.671759i \(-0.765539\pi\)
0.409970 + 0.912099i \(0.365539\pi\)
\(384\) −12.8067 + 9.30458i −0.653537 + 0.474822i
\(385\) −0.230201 −0.0117321
\(386\) −10.7268 + 33.0137i −0.545980 + 1.68035i
\(387\) −6.66652 −0.338878
\(388\) 23.7863 + 17.2817i 1.20757 + 0.877348i
\(389\) 5.76622 0.292359 0.146179 0.989258i \(-0.453302\pi\)
0.146179 + 0.989258i \(0.453302\pi\)
\(390\) −0.104454 0.321478i −0.00528925 0.0162786i
\(391\) 15.8643 + 48.8253i 0.802292 + 2.46920i
\(392\) −29.0904 −1.46929
\(393\) 3.27162 + 2.37697i 0.165031 + 0.119902i
\(394\) 43.6483 2.19897
\(395\) 0.00662058 0.0203760i 0.000333117 0.00102523i
\(396\) 43.6549 2.19374
\(397\) −1.21396 + 0.881991i −0.0609267 + 0.0442659i −0.617832 0.786310i \(-0.711989\pi\)
0.556905 + 0.830576i \(0.311989\pi\)
\(398\) −1.61596 + 1.17407i −0.0810009 + 0.0588506i
\(399\) 1.59423 1.15827i 0.0798112 0.0579863i
\(400\) −20.8023 −1.04012
\(401\) 5.94498 18.2968i 0.296878 0.913697i −0.685706 0.727879i \(-0.740506\pi\)
0.982584 0.185818i \(-0.0594935\pi\)
\(402\) 2.27661 + 7.00669i 0.113547 + 0.349462i
\(403\) 12.0648 0.600990
\(404\) 5.57174 + 4.04811i 0.277205 + 0.201401i
\(405\) −0.127997 0.0929954i −0.00636023 0.00462098i
\(406\) −6.57599 −0.326361
\(407\) −9.20745 + 28.3376i −0.456396 + 1.40464i
\(408\) −24.8374 + 18.0454i −1.22963 + 0.893382i
\(409\) −7.78862 23.9709i −0.385123 1.18529i −0.936391 0.350958i \(-0.885856\pi\)
0.551269 0.834328i \(-0.314144\pi\)
\(410\) −0.111416 0.342903i −0.00550244 0.0169348i
\(411\) −1.96630 6.05165i −0.0969904 0.298506i
\(412\) −45.8609 33.3199i −2.25941 1.64155i
\(413\) 2.52426 + 7.76887i 0.124211 + 0.382281i
\(414\) −31.5013 + 22.8871i −1.54821 + 1.12484i
\(415\) −0.124546 + 0.383313i −0.00611371 + 0.0188161i
\(416\) 0.300493 + 0.924821i 0.0147329 + 0.0453431i
\(417\) −9.02587 6.55768i −0.441999 0.321131i
\(418\) 20.7216 15.0551i 1.01353 0.736371i
\(419\) −5.78535 + 17.8055i −0.282633 + 0.869854i 0.704466 + 0.709738i \(0.251187\pi\)
−0.987098 + 0.160116i \(0.948813\pi\)
\(420\) 0.131864 + 0.0958049i 0.00643431 + 0.00467480i
\(421\) −18.5039 + 13.4439i −0.901825 + 0.655214i −0.938934 0.344097i \(-0.888185\pi\)
0.0371089 + 0.999311i \(0.488185\pi\)
\(422\) 5.78128 + 4.20034i 0.281428 + 0.204470i
\(423\) 2.55109 7.85146i 0.124038 0.381751i
\(424\) −21.4580 + 66.0410i −1.04209 + 3.20723i
\(425\) 37.7211 1.82974
\(426\) −10.9173 + 12.9136i −0.528943 + 0.625664i
\(427\) −6.18009 −0.299076
\(428\) −14.0163 + 43.1377i −0.677502 + 2.08514i
\(429\) 4.29151 13.2079i 0.207196 0.637684i
\(430\) −0.261737 0.190163i −0.0126221 0.00917048i
\(431\) −4.99972 + 3.63251i −0.240828 + 0.174972i −0.701652 0.712520i \(-0.747554\pi\)
0.460824 + 0.887491i \(0.347554\pi\)
\(432\) −14.6764 10.6631i −0.706120 0.513026i
\(433\) 4.91298 15.1206i 0.236103 0.726650i −0.760870 0.648904i \(-0.775228\pi\)
0.996973 0.0777457i \(-0.0247722\pi\)
\(434\) −7.04408 + 5.11782i −0.338127 + 0.245663i
\(435\) −0.0760145 0.0552278i −0.00364462 0.00264797i
\(436\) −3.12311 9.61196i −0.149570 0.460329i
\(437\) −4.71698 + 14.5174i −0.225644 + 0.694460i
\(438\) 21.2844 15.4640i 1.01701 0.738900i
\(439\) 3.36789 + 10.3653i 0.160741 + 0.494708i 0.998697 0.0510283i \(-0.0162499\pi\)
−0.837957 + 0.545737i \(0.816250\pi\)
\(440\) 0.862707 + 0.626793i 0.0411279 + 0.0298812i
\(441\) 4.21243 + 12.9645i 0.200592 + 0.617358i
\(442\) −20.9226 64.3930i −0.995185 3.06286i
\(443\) 2.31867 + 7.13613i 0.110163 + 0.339048i 0.990908 0.134544i \(-0.0429571\pi\)
−0.880744 + 0.473592i \(0.842957\pi\)
\(444\) 17.0678 12.4005i 0.810000 0.588500i
\(445\) 0.119067 0.366449i 0.00564429 0.0173713i
\(446\) −55.9294 −2.64833
\(447\) −4.82753 3.50741i −0.228334 0.165895i
\(448\) 6.66660 + 4.84357i 0.314967 + 0.228837i
\(449\) −13.1622 −0.621162 −0.310581 0.950547i \(-0.600524\pi\)
−0.310581 + 0.950547i \(0.600524\pi\)
\(450\) 8.84096 + 27.2097i 0.416767 + 1.28268i
\(451\) 4.57753 14.0882i 0.215547 0.663387i
\(452\) 8.23097 0.387152
\(453\) −3.95701 + 2.87493i −0.185916 + 0.135076i
\(454\) 36.0811 26.2144i 1.69337 1.23030i
\(455\) −0.146377 + 0.106349i −0.00686228 + 0.00498574i
\(456\) −9.12833 −0.427473
\(457\) −4.99366 + 15.3689i −0.233594 + 0.718927i 0.763711 + 0.645558i \(0.223375\pi\)
−0.997305 + 0.0733691i \(0.976625\pi\)
\(458\) −38.2668 −1.78809
\(459\) 26.6129 + 19.3354i 1.24219 + 0.902501i
\(460\) −1.26258 −0.0588679
\(461\) 2.19559 + 6.75732i 0.102259 + 0.314720i 0.989077 0.147398i \(-0.0470898\pi\)
−0.886819 + 0.462118i \(0.847090\pi\)
\(462\) 3.09712 + 9.53194i 0.144091 + 0.443466i
\(463\) −7.46619 −0.346983 −0.173492 0.984835i \(-0.555505\pi\)
−0.173492 + 0.984835i \(0.555505\pi\)
\(464\) 8.39677 + 6.10061i 0.389810 + 0.283214i
\(465\) −0.124407 −0.00576923
\(466\) −13.3776 + 41.1721i −0.619706 + 1.90726i
\(467\) −17.5885 −0.813898 −0.406949 0.913451i \(-0.633407\pi\)
−0.406949 + 0.913451i \(0.633407\pi\)
\(468\) 27.7588 20.1679i 1.28315 0.932263i
\(469\) 3.19034 2.31791i 0.147316 0.107031i
\(470\) 0.324123 0.235489i 0.0149507 0.0108623i
\(471\) −13.0249 −0.600157
\(472\) 11.6932 35.9879i 0.538222 1.65648i
\(473\) −4.10746 12.6415i −0.188861 0.581256i
\(474\) −0.932785 −0.0428442
\(475\) 9.07371 + 6.59244i 0.416330 + 0.302482i
\(476\) 26.4128 + 19.1900i 1.21063 + 0.879574i
\(477\) 32.5392 1.48987
\(478\) 20.9330 64.4251i 0.957453 2.94674i
\(479\) 20.9233 15.2016i 0.956008 0.694581i 0.00378806 0.999993i \(-0.498794\pi\)
0.952220 + 0.305412i \(0.0987942\pi\)
\(480\) −0.00309855 0.00953636i −0.000141429 0.000435273i
\(481\) 7.23684 + 22.2727i 0.329971 + 1.01555i
\(482\) 2.74732 + 8.45538i 0.125137 + 0.385132i
\(483\) −4.83224 3.51083i −0.219874 0.159748i
\(484\) 13.2090 + 40.6532i 0.600410 + 1.84787i
\(485\) 0.272269 0.197815i 0.0123631 0.00898233i
\(486\) −12.0480 + 37.0801i −0.546511 + 1.68199i
\(487\) −7.47523 23.0064i −0.338735 1.04252i −0.964853 0.262790i \(-0.915357\pi\)
0.626118 0.779728i \(-0.284643\pi\)
\(488\) 23.1607 + 16.8272i 1.04843 + 0.761732i
\(489\) 12.4067 9.01397i 0.561049 0.407626i
\(490\) −0.204428 + 0.629165i −0.00923513 + 0.0284228i
\(491\) 8.75437 + 6.36042i 0.395079 + 0.287042i 0.767534 0.641009i \(-0.221484\pi\)
−0.372455 + 0.928050i \(0.621484\pi\)
\(492\) −8.48532 + 6.16495i −0.382548 + 0.277937i
\(493\) −15.2260 11.0623i −0.685743 0.498221i
\(494\) 6.22097 19.1462i 0.279894 0.861427i
\(495\) 0.154415 0.475239i 0.00694042 0.0213604i
\(496\) 13.7423 0.617048
\(497\) 8.37971 + 3.42166i 0.375882 + 0.153482i
\(498\) 17.5475 0.786322
\(499\) 10.3666 31.9050i 0.464071 1.42826i −0.396077 0.918217i \(-0.629629\pi\)
0.860148 0.510045i \(-0.170371\pi\)
\(500\) −0.573466 + 1.76495i −0.0256462 + 0.0789309i
\(501\) 14.2762 + 10.3723i 0.637815 + 0.463400i
\(502\) 58.6310 42.5979i 2.61683 1.90124i
\(503\) −7.73870 5.62250i −0.345052 0.250695i 0.401739 0.915754i \(-0.368406\pi\)
−0.746790 + 0.665060i \(0.768406\pi\)
\(504\) −3.85155 + 11.8539i −0.171562 + 0.528013i
\(505\) 0.0637769 0.0463366i 0.00283804 0.00206195i
\(506\) −62.8089 45.6334i −2.79220 2.02865i
\(507\) −0.0891152 0.274268i −0.00395774 0.0121807i
\(508\) 3.10068 9.54291i 0.137570 0.423398i
\(509\) −25.2645 + 18.3558i −1.11983 + 0.813605i −0.984183 0.177152i \(-0.943312\pi\)
−0.135648 + 0.990757i \(0.543312\pi\)
\(510\) 0.215744 + 0.663993i 0.00955333 + 0.0294021i
\(511\) −11.3929 8.27742i −0.503992 0.366171i
\(512\) −12.4581 38.3421i −0.550575 1.69450i
\(513\) 3.02246 + 9.30218i 0.133445 + 0.410701i
\(514\) 13.0002 + 40.0105i 0.573414 + 1.76479i
\(515\) −0.524947 + 0.381396i −0.0231319 + 0.0168063i
\(516\) −2.90828 + 8.95076i −0.128030 + 0.394035i
\(517\) 16.4602 0.723921
\(518\) −13.6732 9.93418i −0.600767 0.436483i
\(519\) −8.91056 6.47390i −0.391130 0.284173i
\(520\) 0.838137 0.0367547
\(521\) −4.32774 13.3194i −0.189602 0.583534i 0.810395 0.585883i \(-0.199252\pi\)
−0.999997 + 0.00234900i \(0.999252\pi\)
\(522\) 4.41105 13.5758i 0.193067 0.594198i
\(523\) −40.9589 −1.79101 −0.895504 0.445054i \(-0.853185\pi\)
−0.895504 + 0.445054i \(0.853185\pi\)
\(524\) −16.1165 + 11.7093i −0.704051 + 0.511523i
\(525\) −3.55054 + 2.57962i −0.154958 + 0.112584i
\(526\) 48.8279 35.4755i 2.12900 1.54681i
\(527\) −24.9191 −1.08549
\(528\) 4.88822 15.0444i 0.212733 0.654724i
\(529\) 23.2678 1.01165
\(530\) 1.27754 + 0.928186i 0.0554927 + 0.0403178i
\(531\) −17.7317 −0.769490
\(532\) 2.99973 + 9.23222i 0.130055 + 0.400268i
\(533\) −3.59783 11.0730i −0.155839 0.479624i
\(534\) −16.7755 −0.725947
\(535\) 0.420030 + 0.305170i 0.0181595 + 0.0131936i
\(536\) −18.2674 −0.789033
\(537\) 0.704721 2.16891i 0.0304110 0.0935954i
\(538\) −29.9287 −1.29032
\(539\) −21.9887 + 15.9757i −0.947121 + 0.688124i
\(540\) −0.654504 + 0.475525i −0.0281653 + 0.0204633i
\(541\) −1.80270 + 1.30974i −0.0775041 + 0.0563100i −0.625863 0.779933i \(-0.715253\pi\)
0.548359 + 0.836243i \(0.315253\pi\)
\(542\) −46.4650 −1.99584
\(543\) −1.50916 + 4.64472i −0.0647643 + 0.199324i
\(544\) −0.620650 1.91016i −0.0266102 0.0818976i
\(545\) −0.115685 −0.00495541
\(546\) 6.37297 + 4.63024i 0.272738 + 0.198156i
\(547\) −15.5044 11.2646i −0.662920 0.481640i 0.204728 0.978819i \(-0.434369\pi\)
−0.867648 + 0.497179i \(0.834369\pi\)
\(548\) 31.3455 1.33901
\(549\) 4.14549 12.7585i 0.176925 0.544520i
\(550\) −46.1495 + 33.5296i −1.96782 + 1.42971i
\(551\) −1.72923 5.32202i −0.0736676 0.226726i
\(552\) 8.55011 + 26.3145i 0.363917 + 1.12002i
\(553\) 0.154289 + 0.474854i 0.00656105 + 0.0201928i
\(554\) 2.05791 + 1.49516i 0.0874321 + 0.0635231i
\(555\) −0.0746232 0.229667i −0.00316758 0.00974880i
\(556\) 44.4627 32.3041i 1.88564 1.37000i
\(557\) 8.43538 25.9614i 0.357419 1.10002i −0.597175 0.802111i \(-0.703710\pi\)
0.954594 0.297911i \(-0.0962897\pi\)
\(558\) −5.84047 17.9751i −0.247247 0.760947i
\(559\) −8.45198 6.14072i −0.357481 0.259725i
\(560\) −0.166730 + 0.121137i −0.00704564 + 0.00511896i
\(561\) −8.86387 + 27.2802i −0.374233 + 1.15177i
\(562\) −21.8730 15.8916i −0.922655 0.670348i
\(563\) −7.78656 + 5.65727i −0.328165 + 0.238425i −0.739651 0.672990i \(-0.765010\pi\)
0.411487 + 0.911416i \(0.365010\pi\)
\(564\) −9.42879 6.85042i −0.397024 0.288455i
\(565\) 0.0291143 0.0896045i 0.00122485 0.00376969i
\(566\) 0.0156804 0.0482594i 0.000659098 0.00202850i
\(567\) 3.68708 0.154843
\(568\) −22.0875 35.6395i −0.926771 1.49540i
\(569\) −2.48976 −0.104376 −0.0521881 0.998637i \(-0.516620\pi\)
−0.0521881 + 0.998637i \(0.516620\pi\)
\(570\) −0.0641480 + 0.197427i −0.00268686 + 0.00826931i
\(571\) −12.2982 + 37.8501i −0.514666 + 1.58398i 0.269224 + 0.963078i \(0.413233\pi\)
−0.783889 + 0.620900i \(0.786767\pi\)
\(572\) 55.3468 + 40.2118i 2.31417 + 1.68134i
\(573\) 2.35354 1.70995i 0.0983205 0.0714340i
\(574\) 6.79771 + 4.93883i 0.283731 + 0.206143i
\(575\) 10.5053 32.3319i 0.438100 1.34833i
\(576\) −14.4712 + 10.5139i −0.602965 + 0.438080i
\(577\) 9.96039 + 7.23664i 0.414656 + 0.301265i 0.775484 0.631367i \(-0.217506\pi\)
−0.360828 + 0.932632i \(0.617506\pi\)
\(578\) 30.3176 + 93.3080i 1.26105 + 3.88110i
\(579\) 3.57181 10.9929i 0.148440 0.456850i
\(580\) 0.374459 0.272060i 0.0155485 0.0112967i
\(581\) −2.90248 8.93292i −0.120415 0.370600i
\(582\) −11.8541 8.61248i −0.491367 0.356999i
\(583\) 20.0485 + 61.7030i 0.830325 + 2.55548i
\(584\) 20.1584 + 62.0413i 0.834162 + 2.56729i
\(585\) −0.121366 0.373527i −0.00501787 0.0154434i
\(586\) 48.6143 35.3203i 2.00824 1.45907i
\(587\) 2.51331 7.73517i 0.103735 0.319265i −0.885696 0.464265i \(-0.846318\pi\)
0.989432 + 0.145001i \(0.0463184\pi\)
\(588\) 19.2444 0.793625
\(589\) −5.99423 4.35506i −0.246988 0.179447i
\(590\) −0.696172 0.505799i −0.0286609 0.0208234i
\(591\) −14.5340 −0.597849
\(592\) 8.24308 + 25.3696i 0.338788 + 1.04268i
\(593\) 8.78999 27.0528i 0.360962 1.11093i −0.591510 0.806298i \(-0.701468\pi\)
0.952471 0.304628i \(-0.0985322\pi\)
\(594\) −49.7463 −2.04111
\(595\) 0.302334 0.219658i 0.0123945 0.00900512i
\(596\) 23.7811 17.2780i 0.974112 0.707734i
\(597\) 0.538083 0.390940i 0.0220223 0.0160001i
\(598\) −61.0201 −2.49530
\(599\) 8.15920 25.1114i 0.333376 1.02603i −0.634140 0.773218i \(-0.718646\pi\)
0.967516 0.252808i \(-0.0813541\pi\)
\(600\) 20.3299 0.829964
\(601\) 23.1430 + 16.8143i 0.944021 + 0.685871i 0.949385 0.314114i \(-0.101708\pi\)
−0.00536437 + 0.999986i \(0.501708\pi\)
\(602\) 7.53959 0.307291
\(603\) 2.64521 + 8.14112i 0.107721 + 0.331532i
\(604\) −7.44558 22.9151i −0.302956 0.932404i
\(605\) 0.489283 0.0198922
\(606\) −2.77672 2.01740i −0.112796 0.0819514i
\(607\) −36.4871 −1.48097 −0.740483 0.672075i \(-0.765403\pi\)
−0.740483 + 0.672075i \(0.765403\pi\)
\(608\) 0.184540 0.567955i 0.00748408 0.0230336i
\(609\) 2.18967 0.0887300
\(610\) 0.526696 0.382667i 0.0213253 0.0154937i
\(611\) 10.4665 7.60439i 0.423431 0.307641i
\(612\) −57.3342 + 41.6557i −2.31760 + 1.68383i
\(613\) −16.7551 −0.676733 −0.338367 0.941014i \(-0.609874\pi\)
−0.338367 + 0.941014i \(0.609874\pi\)
\(614\) 6.59833 20.3076i 0.266287 0.819547i
\(615\) 0.0370993 + 0.114180i 0.00149599 + 0.00460417i
\(616\) −24.8511 −1.00128
\(617\) 9.16332 + 6.65754i 0.368901 + 0.268022i 0.756755 0.653698i \(-0.226784\pi\)
−0.387854 + 0.921721i \(0.626784\pi\)
\(618\) 22.8551 + 16.6052i 0.919368 + 0.667960i
\(619\) 35.4878 1.42638 0.713188 0.700973i \(-0.247251\pi\)
0.713188 + 0.700973i \(0.247251\pi\)
\(620\) 0.189380 0.582851i 0.00760568 0.0234079i
\(621\) 23.9847 17.4259i 0.962472 0.699276i
\(622\) 14.8393 + 45.6707i 0.595003 + 1.83123i
\(623\) 2.77479 + 8.53992i 0.111170 + 0.342145i
\(624\) −3.84203 11.8245i −0.153804 0.473360i
\(625\) −20.1996 14.6759i −0.807986 0.587036i
\(626\) 16.9755 + 52.2451i 0.678476 + 2.08814i
\(627\) −6.89988 + 5.01306i −0.275555 + 0.200202i
\(628\) 19.8274 61.0224i 0.791198 2.43506i
\(629\) −14.9473 46.0030i −0.595987 1.83426i
\(630\) 0.229308 + 0.166602i 0.00913586 + 0.00663759i
\(631\) 23.0308 16.7329i 0.916843 0.666125i −0.0258931 0.999665i \(-0.508243\pi\)
0.942736 + 0.333539i \(0.108243\pi\)
\(632\) 0.714718 2.19968i 0.0284299 0.0874984i
\(633\) −1.92505 1.39863i −0.0765139 0.0555906i
\(634\) −0.0456876 + 0.0331940i −0.00181449 + 0.00131830i
\(635\) −0.0929190 0.0675096i −0.00368738 0.00267904i
\(636\) 14.1953 43.6886i 0.562880 1.73237i
\(637\) −6.60137 + 20.3169i −0.261556 + 0.804986i
\(638\) 28.4611 1.12679
\(639\) −12.6848 + 15.0043i −0.501804 + 0.593563i
\(640\) −0.892601 −0.0352832
\(641\) 7.79176 23.9806i 0.307756 0.947175i −0.670878 0.741567i \(-0.734083\pi\)
0.978634 0.205608i \(-0.0659172\pi\)
\(642\) 6.98511 21.4980i 0.275680 0.848457i
\(643\) 5.09407 + 3.70106i 0.200891 + 0.145956i 0.683683 0.729779i \(-0.260377\pi\)
−0.482792 + 0.875735i \(0.660377\pi\)
\(644\) 23.8043 17.2948i 0.938021 0.681512i
\(645\) 0.0871532 + 0.0633205i 0.00343165 + 0.00249324i
\(646\) −12.8490 + 39.5453i −0.505539 + 1.55589i
\(647\) 10.6643 7.74806i 0.419256 0.304607i −0.358082 0.933690i \(-0.616569\pi\)
0.777338 + 0.629083i \(0.216569\pi\)
\(648\) −13.8178 10.0392i −0.542815 0.394378i
\(649\) −10.9251 33.6240i −0.428847 1.31986i
\(650\) −13.8548 + 42.6408i −0.543431 + 1.67251i
\(651\) 2.34554 1.70413i 0.0919288 0.0667902i
\(652\) 23.3446 + 71.8474i 0.914246 + 2.81376i
\(653\) −10.7278 7.79418i −0.419810 0.305010i 0.357751 0.933817i \(-0.383544\pi\)
−0.777561 + 0.628807i \(0.783544\pi\)
\(654\) 1.55643 + 4.79019i 0.0608611 + 0.187311i
\(655\) 0.0704639 + 0.216866i 0.00275325 + 0.00847364i
\(656\) −4.09808 12.6126i −0.160003 0.492440i
\(657\) 24.7305 17.9677i 0.964828 0.700989i
\(658\) −2.88519 + 8.87972i −0.112477 + 0.346167i
\(659\) −17.7262 −0.690514 −0.345257 0.938508i \(-0.612208\pi\)
−0.345257 + 0.938508i \(0.612208\pi\)
\(660\) −0.570713 0.414647i −0.0222150 0.0161401i
\(661\) −19.8499 14.4218i −0.772072 0.560943i 0.130517 0.991446i \(-0.458336\pi\)
−0.902589 + 0.430503i \(0.858336\pi\)
\(662\) −25.8345 −1.00409
\(663\) 6.96679 + 21.4416i 0.270568 + 0.832722i
\(664\) −13.4452 + 41.3801i −0.521776 + 1.60586i
\(665\) 0.111115 0.00430885
\(666\) 29.6804 21.5641i 1.15009 0.835591i
\(667\) −13.7223 + 9.96980i −0.531328 + 0.386032i
\(668\) −70.3268 + 51.0954i −2.72102 + 1.97694i
\(669\) 18.6234 0.720021
\(670\) −0.128372 + 0.395087i −0.00495942 + 0.0152635i
\(671\) 26.7477 1.03258
\(672\) 0.189049 + 0.137352i 0.00729272 + 0.00529847i
\(673\) 32.8103 1.26475 0.632373 0.774664i \(-0.282081\pi\)
0.632373 + 0.774664i \(0.282081\pi\)
\(674\) 1.50145 + 4.62097i 0.0578335 + 0.177993i
\(675\) −6.73138 20.7171i −0.259091 0.797400i
\(676\) 1.42062 0.0546390
\(677\) 25.6589 + 18.6423i 0.986150 + 0.716480i 0.959075 0.283153i \(-0.0913806\pi\)
0.0270755 + 0.999633i \(0.491381\pi\)
\(678\) −4.10196 −0.157535
\(679\) −2.42362 + 7.45912i −0.0930098 + 0.286255i
\(680\) −1.73112 −0.0663855
\(681\) −12.0143 + 8.72888i −0.460388 + 0.334491i
\(682\) 30.4871 22.1501i 1.16741 0.848173i
\(683\) −17.5821 + 12.7741i −0.672761 + 0.488789i −0.870948 0.491375i \(-0.836495\pi\)
0.198188 + 0.980164i \(0.436495\pi\)
\(684\) −21.0717 −0.805695
\(685\) 0.110874 0.341235i 0.00423627 0.0130379i
\(686\) −10.4685 32.2189i −0.399691 1.23012i
\(687\) 12.7421 0.486140
\(688\) −9.62718 6.99455i −0.367033 0.266665i
\(689\) 41.2541 + 29.9728i 1.57165 + 1.14187i
\(690\) 0.629214 0.0239538
\(691\) −8.76590 + 26.9787i −0.333471 + 1.02632i 0.634000 + 0.773333i \(0.281412\pi\)
−0.967471 + 0.252984i \(0.918588\pi\)
\(692\) 43.8947 31.8914i 1.66863 1.21233i
\(693\) 3.59856 + 11.0752i 0.136698 + 0.420713i
\(694\) −4.71211 14.5024i −0.178869 0.550503i
\(695\) −0.194399 0.598298i −0.00737396 0.0226947i
\(696\) −8.20607 5.96206i −0.311050 0.225991i
\(697\) 7.43111 + 22.8706i 0.281473 + 0.866285i
\(698\) −41.9259 + 30.4609i −1.58692 + 1.15296i
\(699\) 4.45448 13.7095i 0.168484 0.518540i
\(700\) −6.68076 20.5613i −0.252509 0.777143i
\(701\) 0.861950 + 0.626244i 0.0325554 + 0.0236529i 0.603944 0.797027i \(-0.293595\pi\)
−0.571389 + 0.820680i \(0.693595\pi\)
\(702\) −31.6321 + 22.9820i −1.19388 + 0.867401i
\(703\) 4.44432 13.6782i 0.167621 0.515883i
\(704\) −28.8533 20.9631i −1.08745 0.790078i
\(705\) −0.107927 + 0.0784132i −0.00406475 + 0.00295321i
\(706\) −42.4769 30.8613i −1.59864 1.16148i
\(707\) −0.567712 + 1.74724i −0.0213510 + 0.0657117i
\(708\) −7.73547 + 23.8073i −0.290717 + 0.894735i
\(709\) 38.2390 1.43610 0.718049 0.695993i \(-0.245036\pi\)
0.718049 + 0.695993i \(0.245036\pi\)
\(710\) −0.926025 + 0.227257i −0.0347531 + 0.00852879i
\(711\) −1.08381 −0.0406460
\(712\) 12.8537 39.5596i 0.481713 1.48256i
\(713\) −6.93994 + 21.3589i −0.259903 + 0.799898i
\(714\) −13.1630 9.56348i −0.492613 0.357904i
\(715\) 0.633527 0.460284i 0.0236926 0.0172137i
\(716\) 9.08866 + 6.60330i 0.339659 + 0.246777i
\(717\) −6.97027 + 21.4523i −0.260309 + 0.801150i
\(718\) 19.5518 14.2052i 0.729667 0.530134i
\(719\) −22.9466 16.6717i −0.855765 0.621750i 0.0709643 0.997479i \(-0.477392\pi\)
−0.926730 + 0.375729i \(0.877392\pi\)
\(720\) −0.138241 0.425463i −0.00515195 0.0158561i
\(721\) 4.67283 14.3815i 0.174025 0.535595i
\(722\) 27.7342 20.1501i 1.03216 0.749908i
\(723\) −0.914802 2.81547i −0.0340219 0.104709i
\(724\) −19.4634 14.1410i −0.723351 0.525545i
\(725\) 3.85120 + 11.8528i 0.143030 + 0.440201i
\(726\) −6.58281 20.2598i −0.244311 0.751911i
\(727\) −3.99736 12.3026i −0.148254 0.456279i 0.849161 0.528134i \(-0.177108\pi\)
−0.997415 + 0.0718550i \(0.977108\pi\)
\(728\) −15.8020 + 11.4808i −0.585662 + 0.425508i
\(729\) 0.829750 2.55371i 0.0307315 0.0945818i
\(730\) 1.48349 0.0549063
\(731\) 17.4571 + 12.6833i 0.645673 + 0.469109i
\(732\) −15.3217 11.1318i −0.566305 0.411445i
\(733\) 17.0281 0.628945 0.314473 0.949267i \(-0.398172\pi\)
0.314473 + 0.949267i \(0.398172\pi\)
\(734\) −1.42032 4.37130i −0.0524251 0.161348i
\(735\) 0.0680705 0.209499i 0.00251082 0.00772750i
\(736\) −1.81011 −0.0667216
\(737\) −13.8079 + 10.0320i −0.508621 + 0.369534i
\(738\) −14.7558 + 10.7207i −0.543167 + 0.394634i
\(739\) 19.0150 13.8152i 0.699479 0.508201i −0.180284 0.983615i \(-0.557702\pi\)
0.879762 + 0.475414i \(0.157702\pi\)
\(740\) 1.18959 0.0437303
\(741\) −2.07146 + 6.37529i −0.0760969 + 0.234202i
\(742\) −36.8007 −1.35100
\(743\) −36.9203 26.8242i −1.35448 0.984084i −0.998775 0.0494845i \(-0.984242\pi\)
−0.355701 0.934600i \(-0.615758\pi\)
\(744\) −13.4302 −0.492376
\(745\) −0.103975 0.320002i −0.00380935 0.0117240i
\(746\) 8.40078 + 25.8549i 0.307574 + 0.946616i
\(747\) 20.3885 0.745977
\(748\) −114.316 83.0552i −4.17980 3.03680i
\(749\) −12.0994 −0.442101
\(750\) 0.285791 0.879574i 0.0104356 0.0321175i
\(751\) −5.90633 −0.215525 −0.107762 0.994177i \(-0.534369\pi\)
−0.107762 + 0.994177i \(0.534369\pi\)
\(752\) 11.9219 8.66174i 0.434745 0.315861i
\(753\) −19.5229 + 14.1842i −0.711456 + 0.516903i
\(754\) 18.0975 13.1486i 0.659073 0.478845i
\(755\) −0.275796 −0.0100373
\(756\) 5.82609 17.9308i 0.211893 0.652139i
\(757\) −8.15429 25.0963i −0.296373 0.912142i −0.982757 0.184902i \(-0.940803\pi\)
0.686384 0.727239i \(-0.259197\pi\)
\(758\) 75.6259 2.74686
\(759\) 20.9141 + 15.1950i 0.759134 + 0.551543i
\(760\) −0.416417 0.302545i −0.0151050 0.0109745i
\(761\) −3.89929 −0.141349 −0.0706746 0.997499i \(-0.522515\pi\)
−0.0706746 + 0.997499i \(0.522515\pi\)
\(762\) −1.54525 + 4.75578i −0.0559783 + 0.172284i
\(763\) 2.18110 1.58466i 0.0789611 0.0573686i
\(764\) 4.42846 + 13.6294i 0.160216 + 0.493095i
\(765\) 0.250675 + 0.771497i 0.00906316 + 0.0278936i
\(766\) 6.07067 + 18.6836i 0.219342 + 0.675066i
\(767\) −22.4807 16.3332i −0.811731 0.589757i
\(768\) 8.13343 + 25.0321i 0.293490 + 0.903269i
\(769\) −6.48774 + 4.71362i −0.233954 + 0.169977i −0.698585 0.715527i \(-0.746187\pi\)
0.464632 + 0.885504i \(0.346187\pi\)
\(770\) −0.174637 + 0.537478i −0.00629349 + 0.0193694i
\(771\) −4.32880 13.3227i −0.155898 0.479805i
\(772\) 46.0650 + 33.4682i 1.65792 + 1.20455i
\(773\) −12.8995 + 9.37207i −0.463964 + 0.337090i −0.795084 0.606499i \(-0.792573\pi\)
0.331120 + 0.943589i \(0.392573\pi\)
\(774\) −5.05742 + 15.5651i −0.181785 + 0.559477i
\(775\) 13.3499 + 9.69924i 0.479541 + 0.348407i
\(776\) 29.3926 21.3550i 1.05513 0.766598i
\(777\) 4.55291 + 3.30788i 0.163335 + 0.118670i
\(778\) 4.37442 13.4631i 0.156831 0.482675i
\(779\) −2.20951 + 6.80018i −0.0791640 + 0.243642i
\(780\) −0.554459 −0.0198528
\(781\) −36.2677 14.8091i −1.29776 0.529910i
\(782\) 126.034 4.50695
\(783\) −3.35851 + 10.3364i −0.120023 + 0.369394i
\(784\) −7.51925 + 23.1419i −0.268545 + 0.826496i
\(785\) −0.594173 0.431692i −0.0212069 0.0154077i
\(786\) 8.03175 5.83541i 0.286483 0.208142i
\(787\) 5.27755 + 3.83437i 0.188124 + 0.136680i 0.677861 0.735190i \(-0.262907\pi\)
−0.489737 + 0.871870i \(0.662907\pi\)
\(788\) 22.1246 68.0924i 0.788155 2.42569i
\(789\) −16.2587 + 11.8126i −0.578825 + 0.420541i
\(790\) −0.0425519 0.0309158i −0.00151393 0.00109993i
\(791\) 0.678494 + 2.08819i 0.0241245 + 0.0742475i
\(792\) 16.6697 51.3040i 0.592331 1.82301i
\(793\) 17.0080 12.3570i 0.603972 0.438811i
\(794\) 1.13835 + 3.50348i 0.0403985 + 0.124334i
\(795\) −0.425394 0.309067i −0.0150872 0.0109615i
\(796\) 1.01247 + 3.11606i 0.0358860 + 0.110446i
\(797\) 3.30088 + 10.1591i 0.116923 + 0.359853i 0.992343 0.123510i \(-0.0394152\pi\)
−0.875420 + 0.483363i \(0.839415\pi\)
\(798\) −1.49494 4.60094i −0.0529202 0.162872i
\(799\) −21.6180 + 15.7064i −0.764791 + 0.555653i
\(800\) −0.410992 + 1.26490i −0.0145308 + 0.0447211i
\(801\) −19.4915 −0.688700
\(802\) −38.2097 27.7609i −1.34923 0.980273i
\(803\) 49.3089 + 35.8250i 1.74007 + 1.26424i
\(804\) 12.0846 0.426191
\(805\) −0.104076 0.320314i −0.00366821 0.0112896i
\(806\) 9.15271 28.1691i 0.322390 0.992215i
\(807\) 9.96566 0.350808
\(808\) 6.88497 5.00223i 0.242212 0.175978i
\(809\) 2.03654 1.47963i 0.0716009 0.0520211i −0.551409 0.834235i \(-0.685910\pi\)
0.623010 + 0.782214i \(0.285910\pi\)
\(810\) −0.314230 + 0.228302i −0.0110409 + 0.00802170i
\(811\) 7.42334 0.260669 0.130334 0.991470i \(-0.458395\pi\)
0.130334 + 0.991470i \(0.458395\pi\)
\(812\) −3.33326 + 10.2587i −0.116974 + 0.360010i
\(813\) 15.4719 0.542624
\(814\) 59.1783 + 42.9955i 2.07420 + 1.50699i
\(815\) 0.864723 0.0302899
\(816\) 7.93548 + 24.4229i 0.277797 + 0.854973i
\(817\) 1.98262 + 6.10187i 0.0693631 + 0.213478i
\(818\) −61.8765 −2.16346
\(819\) 7.40479 + 5.37990i 0.258744 + 0.187989i
\(820\) −0.591412 −0.0206530
\(821\) 5.20610 16.0227i 0.181694 0.559197i −0.818182 0.574960i \(-0.805018\pi\)
0.999876 + 0.0157630i \(0.00501773\pi\)
\(822\) −15.6212 −0.544853
\(823\) 4.63854 3.37010i 0.161689 0.117474i −0.503998 0.863705i \(-0.668138\pi\)
0.665688 + 0.746230i \(0.268138\pi\)
\(824\) −56.6701 + 41.1732i −1.97420 + 1.43434i
\(825\) 15.3669 11.1647i 0.535005 0.388704i
\(826\) 20.0539 0.697765
\(827\) −4.31284 + 13.2736i −0.149972 + 0.461567i −0.997617 0.0689976i \(-0.978020\pi\)
0.847645 + 0.530564i \(0.178020\pi\)
\(828\) 19.7369 + 60.7439i 0.685905 + 2.11100i
\(829\) −52.5333 −1.82456 −0.912278 0.409571i \(-0.865678\pi\)
−0.912278 + 0.409571i \(0.865678\pi\)
\(830\) 0.800483 + 0.581585i 0.0277852 + 0.0201871i
\(831\) −0.685241 0.497857i −0.0237708 0.0172705i
\(832\) −28.0316 −0.971819
\(833\) 13.6347 41.9634i 0.472416 1.45395i
\(834\) −22.1583 + 16.0990i −0.767280 + 0.557461i
\(835\) 0.307481 + 0.946328i 0.0106408 + 0.0327490i
\(836\) −12.9830 39.9574i −0.449025 1.38196i
\(837\) 4.44685 + 13.6860i 0.153706 + 0.473057i
\(838\) 37.1837 + 27.0155i 1.28449 + 0.933236i
\(839\) −4.48967 13.8178i −0.155001 0.477043i 0.843160 0.537662i \(-0.180693\pi\)
−0.998161 + 0.0606191i \(0.980693\pi\)
\(840\) 0.162944 0.118386i 0.00562209 0.00408469i
\(841\) −7.04000 + 21.6669i −0.242759 + 0.747134i
\(842\) 17.3515 + 53.4023i 0.597971 + 1.84036i
\(843\) 7.28326 + 5.29159i 0.250849 + 0.182252i
\(844\) 9.48307 6.88986i 0.326421 0.237159i
\(845\) 0.00502494 0.0154652i 0.000172863 0.000532018i
\(846\) −16.3964 11.9127i −0.563721 0.409567i
\(847\) −9.22483 + 6.70223i −0.316969 + 0.230291i
\(848\) 46.9902 + 34.1404i 1.61365 + 1.17239i
\(849\) −0.00522127 + 0.0160694i −0.000179194 + 0.000551501i
\(850\) 28.6164 88.0721i 0.981533 3.02085i
\(851\) −43.5934 −1.49436
\(852\) 14.6117 + 23.5768i 0.500589 + 0.807730i
\(853\) −45.7488 −1.56641 −0.783204 0.621765i \(-0.786416\pi\)
−0.783204 + 0.621765i \(0.786416\pi\)
\(854\) −4.68840 + 14.4294i −0.160434 + 0.493765i
\(855\) −0.0745339 + 0.229392i −0.00254900 + 0.00784503i
\(856\) 45.3439 + 32.9443i 1.54982 + 1.12601i
\(857\) −23.3744 + 16.9825i −0.798453 + 0.580110i −0.910460 0.413597i \(-0.864272\pi\)
0.112007 + 0.993707i \(0.464272\pi\)
\(858\) −27.5825 20.0398i −0.941650 0.684149i
\(859\) 4.75705 14.6407i 0.162309 0.499535i −0.836519 0.547938i \(-0.815413\pi\)
0.998828 + 0.0484029i \(0.0154132\pi\)
\(860\) −0.429329 + 0.311926i −0.0146400 + 0.0106366i
\(861\) −2.26350 1.64453i −0.0771399 0.0560454i
\(862\) 4.68832 + 14.4292i 0.159685 + 0.491460i
\(863\) −2.59354 + 7.98209i −0.0882851 + 0.271714i −0.985446 0.169991i \(-0.945626\pi\)
0.897161 + 0.441705i \(0.145626\pi\)
\(864\) −0.938339 + 0.681743i −0.0319229 + 0.0231934i
\(865\) −0.191915 0.590654i −0.00652531 0.0200828i
\(866\) −31.5768 22.9419i −1.07302 0.779597i
\(867\) −10.0952 31.0697i −0.342850 1.05518i
\(868\) 4.41341 + 13.5831i 0.149801 + 0.461040i
\(869\) −0.667770 2.05519i −0.0226526 0.0697174i
\(870\) −0.186614 + 0.135583i −0.00632681 + 0.00459670i
\(871\) −4.14535 + 12.7581i −0.140460 + 0.432291i
\(872\) −12.4887 −0.422920
\(873\) −13.7733 10.0069i −0.466155 0.338682i
\(874\) 30.3170 + 22.0266i 1.02549 + 0.745062i
\(875\) −0.495038 −0.0167353
\(876\) −13.3356 41.0427i −0.450567 1.38670i
\(877\) −2.86602 + 8.82069i −0.0967785 + 0.297853i −0.987713 0.156278i \(-0.950050\pi\)
0.890935 + 0.454132i \(0.150050\pi\)
\(878\) 26.7561 0.902975
\(879\) −16.1876 + 11.7610i −0.545993 + 0.396687i
\(880\) 0.721615 0.524284i 0.0243256 0.0176736i
\(881\) 2.90353 2.10954i 0.0978223 0.0710721i −0.537799 0.843073i \(-0.680744\pi\)
0.635621 + 0.772001i \(0.280744\pi\)
\(882\) 33.4655 1.12684
\(883\) −14.3137 + 44.0529i −0.481693 + 1.48250i 0.355022 + 0.934858i \(0.384474\pi\)
−0.836714 + 0.547640i \(0.815526\pi\)
\(884\) −111.060 −3.73535
\(885\) 0.231811 + 0.168421i 0.00779225 + 0.00566140i
\(886\) 18.4206 0.618853
\(887\) 3.07456 + 9.46251i 0.103234 + 0.317720i 0.989312 0.145816i \(-0.0465806\pi\)
−0.886078 + 0.463536i \(0.846581\pi\)
\(888\) −8.05587 24.7934i −0.270337 0.832013i
\(889\) 2.67662 0.0897710
\(890\) −0.765266 0.555998i −0.0256518 0.0186371i
\(891\) −15.9578 −0.534608
\(892\) −28.3496 + 87.2512i −0.949216 + 2.92139i
\(893\) −7.94514 −0.265874
\(894\) −11.8515 + 8.61060i −0.396373 + 0.287982i
\(895\) 0.104033 0.0755846i 0.00347745 0.00252651i
\(896\) 16.8289 12.2269i 0.562213 0.408472i
\(897\) 20.3185 0.678414
\(898\) −9.98523 + 30.7314i −0.333211 + 1.02552i
\(899\) −2.54416 7.83012i −0.0848525 0.261149i
\(900\) 46.9291 1.56430
\(901\) −85.2079 61.9072i −2.83869 2.06243i
\(902\) −29.4208 21.3754i −0.979604 0.711724i
\(903\) −2.51053 −0.0835453
\(904\) 3.14300 9.67316i 0.104535 0.321725i
\(905\) −0.222787 + 0.161864i −0.00740570 + 0.00538056i
\(906\) 3.71056 + 11.4199i 0.123275 + 0.379401i
\(907\) −5.17980 15.9418i −0.171992 0.529338i 0.827491 0.561479i \(-0.189767\pi\)
−0.999483 + 0.0321409i \(0.989767\pi\)
\(908\) −22.6063 69.5750i −0.750216 2.30893i
\(909\) −3.22628 2.34403i −0.107009 0.0777466i
\(910\) 0.137261 + 0.422445i 0.00455015 + 0.0140039i
\(911\) 25.0425 18.1945i 0.829696 0.602810i −0.0897771 0.995962i \(-0.528615\pi\)
0.919473 + 0.393152i \(0.128615\pi\)
\(912\) −2.35948 + 7.26174i −0.0781302 + 0.240460i
\(913\) 12.5620 + 38.6620i 0.415743 + 1.27953i
\(914\) 32.0953 + 23.3186i 1.06162 + 0.771312i
\(915\) −0.175379 + 0.127420i −0.00579786 + 0.00421239i
\(916\) −19.3968 + 59.6971i −0.640887 + 1.97245i
\(917\) −4.29915 3.12351i −0.141970 0.103147i
\(918\) 65.3342 47.4681i 2.15635 1.56668i
\(919\) 28.5867 + 20.7694i 0.942987 + 0.685120i 0.949138 0.314861i \(-0.101958\pi\)
−0.00615103 + 0.999981i \(0.501958\pi\)
\(920\) −0.482115 + 1.48380i −0.0158949 + 0.0489194i
\(921\) −2.19711 + 6.76201i −0.0723973 + 0.222816i
\(922\) 17.4428 0.574448
\(923\) −29.9031 + 7.33854i −0.984271 + 0.241551i
\(924\) 16.4399 0.540834
\(925\) −9.89802 + 30.4630i −0.325445 + 1.00162i
\(926\) −5.66408 + 17.4322i −0.186133 + 0.572859i
\(927\) 26.5555 + 19.2937i 0.872197 + 0.633688i
\(928\) 0.536848 0.390043i 0.0176229 0.0128038i
\(929\) 21.9212 + 15.9267i 0.719210 + 0.522537i 0.886132 0.463433i \(-0.153383\pi\)
−0.166921 + 0.985970i \(0.553383\pi\)
\(930\) −0.0943788 + 0.290468i −0.00309480 + 0.00952482i
\(931\) 10.6137 7.71128i 0.347849 0.252727i
\(932\) 57.4486 + 41.7388i 1.88179 + 1.36720i
\(933\) −4.94120 15.2074i −0.161768 0.497869i
\(934\) −13.3432 + 41.0660i −0.436601 + 1.34372i
\(935\) −1.30851 + 0.950691i −0.0427930 + 0.0310909i
\(936\) −13.1020 40.3237i −0.428251 1.31802i
\(937\) 35.7948 + 26.0064i 1.16936 + 0.849593i 0.990933 0.134359i \(-0.0428975\pi\)
0.178432 + 0.983952i \(0.442897\pi\)
\(938\) −2.99164 9.20731i −0.0976804 0.300629i
\(939\) −5.65249 17.3966i −0.184462 0.567716i
\(940\) −0.203077 0.625006i −0.00662363 0.0203854i
\(941\) −9.78443 + 7.10880i −0.318963 + 0.231740i −0.735733 0.677272i \(-0.763162\pi\)
0.416770 + 0.909012i \(0.363162\pi\)
\(942\) −9.88111 + 30.4109i −0.321944 + 0.990841i
\(943\) 21.6726 0.705758
\(944\) −25.6065 18.6042i −0.833421 0.605515i
\(945\) −0.174592 0.126849i −0.00567948 0.00412638i
\(946\) −32.6317 −1.06095
\(947\) −0.144306 0.444127i −0.00468931 0.0144322i 0.948684 0.316224i \(-0.102415\pi\)
−0.953374 + 0.301792i \(0.902415\pi\)
\(948\) −0.472813 + 1.45517i −0.0153562 + 0.0472617i
\(949\) 47.9045 1.55505
\(950\) 22.2758 16.1843i 0.722721 0.525088i
\(951\) 0.0152131 0.0110529i 0.000493317 0.000358416i
\(952\) 32.6382 23.7130i 1.05781 0.768543i
\(953\) −47.2896 −1.53186 −0.765931 0.642923i \(-0.777721\pi\)
−0.765931 + 0.642923i \(0.777721\pi\)
\(954\) 24.6852 75.9734i 0.799214 2.45973i
\(955\) 0.164038 0.00530813
\(956\) −89.8942 65.3120i −2.90739 2.11234i
\(957\) −9.47699 −0.306348
\(958\) −19.6201 60.3845i −0.633898 1.95094i
\(959\) 2.58386 + 7.95231i 0.0834373 + 0.256794i
\(960\) 0.289049 0.00932903
\(961\) 16.2604 + 11.8139i 0.524529 + 0.381093i
\(962\) 57.4929 1.85365
\(963\) 8.11604 24.9786i 0.261536 0.804924i
\(964\) 14.5832 0.469692
\(965\) 0.527283 0.383093i 0.0169738 0.0123322i
\(966\) −11.8630 + 8.61900i −0.381687 + 0.277312i
\(967\) 8.17108 5.93664i 0.262764 0.190909i −0.448601 0.893732i \(-0.648077\pi\)
0.711365 + 0.702823i \(0.248077\pi\)
\(968\) 52.8201 1.69770
\(969\) 4.27847 13.1678i 0.137444 0.423010i
\(970\) −0.255312 0.785770i −0.00819757 0.0252295i
\(971\) 37.9632 1.21830 0.609148 0.793057i \(-0.291512\pi\)
0.609148 + 0.793057i \(0.291512\pi\)
\(972\) 51.7389 + 37.5905i 1.65953 + 1.20572i
\(973\) 11.8607 + 8.61727i 0.380235 + 0.276257i
\(974\) −59.3868 −1.90287
\(975\) 4.61338 14.1985i 0.147746 0.454717i
\(976\) 19.3729 14.0752i 0.620110 0.450536i
\(977\) −5.96992 18.3735i −0.190995 0.587821i −1.00000 1.98463e-5i \(-0.999994\pi\)
0.809005 0.587801i \(-0.200006\pi\)
\(978\) −11.6340 35.8056i −0.372013 1.14494i
\(979\) −12.0094 36.9611i −0.383822 1.18128i
\(980\) 0.877893 + 0.637826i 0.0280432 + 0.0203746i
\(981\) 1.80842 + 5.56574i 0.0577384 + 0.177701i
\(982\) 21.4918 15.6147i 0.685830 0.498285i
\(983\) −3.98686 + 12.2703i −0.127161 + 0.391362i −0.994289 0.106724i \(-0.965964\pi\)
0.867127 + 0.498086i \(0.165964\pi\)
\(984\) 4.00501 + 12.3262i 0.127675 + 0.392944i
\(985\) −0.663014 0.481708i −0.0211254 0.0153485i
\(986\) −37.3794 + 27.1577i −1.19040 + 0.864878i
\(987\) 0.960712 2.95677i 0.0305798 0.0941149i
\(988\) −26.7152 19.4097i −0.849923 0.617505i
\(989\) 15.7330 11.4307i 0.500281 0.363475i
\(990\) −0.992456 0.721061i −0.0315423 0.0229168i
\(991\) 15.9502 49.0895i 0.506673 1.55938i −0.291265 0.956642i \(-0.594076\pi\)
0.797939 0.602738i \(-0.205924\pi\)
\(992\) 0.271507 0.835614i 0.00862037 0.0265308i
\(993\) 8.60236 0.272988
\(994\) 14.3461 16.9694i 0.455030 0.538236i
\(995\) 0.0375035 0.00118894
\(996\) 8.89452 27.3745i 0.281834 0.867395i
\(997\) −2.93531 + 9.03394i −0.0929621 + 0.286108i −0.986717 0.162447i \(-0.948061\pi\)
0.893755 + 0.448555i \(0.148061\pi\)
\(998\) −66.6281 48.4081i −2.10907 1.53233i
\(999\) −22.5982 + 16.4186i −0.714977 + 0.519461i
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 71.2.c.a.57.5 yes 20
3.2 odd 2 639.2.f.c.199.1 20
71.5 even 5 inner 71.2.c.a.5.5 20
71.17 odd 10 5041.2.a.j.1.9 10
71.54 even 5 5041.2.a.i.1.9 10
213.5 odd 10 639.2.f.c.289.1 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
71.2.c.a.5.5 20 71.5 even 5 inner
71.2.c.a.57.5 yes 20 1.1 even 1 trivial
639.2.f.c.199.1 20 3.2 odd 2
639.2.f.c.289.1 20 213.5 odd 10
5041.2.a.i.1.9 10 71.54 even 5
5041.2.a.j.1.9 10 71.17 odd 10