Properties

Label 84.2.b.a.55.2
Level $84$
Weight $2$
Character 84.55
Analytic conductor $0.671$
Analytic rank $0$
Dimension $4$
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] = [84,2,Mod(55,84)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(84, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("84.55");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 84.b (of order \(2\), degree \(1\), 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: \(0.670743376979\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.0.2312.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 2x + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 55.2
Root \(1.28078 - 0.599676i\) of defining polynomial
Character \(\chi\) \(=\) 84.55
Dual form 84.2.b.a.55.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.28078 + 0.599676i) q^{2} -1.00000 q^{3} +(1.28078 - 1.53610i) q^{4} +3.33513i q^{5} +(1.28078 - 0.599676i) q^{6} +(-1.56155 + 2.13578i) q^{7} +(-0.719224 + 2.73546i) q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+(-1.28078 + 0.599676i) q^{2} -1.00000 q^{3} +(1.28078 - 1.53610i) q^{4} +3.33513i q^{5} +(1.28078 - 0.599676i) q^{6} +(-1.56155 + 2.13578i) q^{7} +(-0.719224 + 2.73546i) q^{8} +1.00000 q^{9} +(-2.00000 - 4.27156i) q^{10} +0.936426i q^{11} +(-1.28078 + 1.53610i) q^{12} +1.87285i q^{13} +(0.719224 - 3.67188i) q^{14} -3.33513i q^{15} +(-0.719224 - 3.93481i) q^{16} -5.20798i q^{17} +(-1.28078 + 0.599676i) q^{18} +7.12311 q^{19} +(5.12311 + 4.27156i) q^{20} +(1.56155 - 2.13578i) q^{21} +(-0.561553 - 1.19935i) q^{22} -0.936426i q^{23} +(0.719224 - 2.73546i) q^{24} -6.12311 q^{25} +(-1.12311 - 2.39871i) q^{26} -1.00000 q^{27} +(1.28078 + 5.13416i) q^{28} -2.00000 q^{29} +(2.00000 + 4.27156i) q^{30} +(3.28078 + 4.60831i) q^{32} -0.936426i q^{33} +(3.12311 + 6.67026i) q^{34} +(-7.12311 - 5.20798i) q^{35} +(1.28078 - 1.53610i) q^{36} +1.12311 q^{37} +(-9.12311 + 4.27156i) q^{38} -1.87285i q^{39} +(-9.12311 - 2.39871i) q^{40} -1.46228i q^{41} +(-0.719224 + 3.67188i) q^{42} +9.06897i q^{43} +(1.43845 + 1.19935i) q^{44} +3.33513i q^{45} +(0.561553 + 1.19935i) q^{46} +6.24621 q^{47} +(0.719224 + 3.93481i) q^{48} +(-2.12311 - 6.67026i) q^{49} +(7.84233 - 3.67188i) q^{50} +5.20798i q^{51} +(2.87689 + 2.39871i) q^{52} +12.2462 q^{53} +(1.28078 - 0.599676i) q^{54} -3.12311 q^{55} +(-4.71922 - 5.80766i) q^{56} -7.12311 q^{57} +(2.56155 - 1.19935i) q^{58} +4.00000 q^{59} +(-5.12311 - 4.27156i) q^{60} +4.79741i q^{61} +(-1.56155 + 2.13578i) q^{63} +(-6.96543 - 3.93481i) q^{64} -6.24621 q^{65} +(0.561553 + 1.19935i) q^{66} -10.9418i q^{67} +(-8.00000 - 6.67026i) q^{68} +0.936426i q^{69} +(12.2462 + 2.39871i) q^{70} -3.86098i q^{71} +(-0.719224 + 2.73546i) q^{72} +6.67026i q^{73} +(-1.43845 + 0.673500i) q^{74} +6.12311 q^{75} +(9.12311 - 10.9418i) q^{76} +(-2.00000 - 1.46228i) q^{77} +(1.12311 + 2.39871i) q^{78} -2.39871i q^{79} +(13.1231 - 2.39871i) q^{80} +1.00000 q^{81} +(0.876894 + 1.87285i) q^{82} -10.2462 q^{83} +(-1.28078 - 5.13416i) q^{84} +17.3693 q^{85} +(-5.43845 - 11.6153i) q^{86} +2.00000 q^{87} +(-2.56155 - 0.673500i) q^{88} +1.46228i q^{89} +(-2.00000 - 4.27156i) q^{90} +(-4.00000 - 2.92456i) q^{91} +(-1.43845 - 1.19935i) q^{92} +(-8.00000 + 3.74571i) q^{94} +23.7565i q^{95} +(-3.28078 - 4.60831i) q^{96} -10.4160i q^{97} +(6.71922 + 7.26994i) q^{98} +0.936426i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - q^{2} - 4 q^{3} + q^{4} + q^{6} + 2 q^{7} - 7 q^{8} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - q^{2} - 4 q^{3} + q^{4} + q^{6} + 2 q^{7} - 7 q^{8} + 4 q^{9} - 8 q^{10} - q^{12} + 7 q^{14} - 7 q^{16} - q^{18} + 12 q^{19} + 4 q^{20} - 2 q^{21} + 6 q^{22} + 7 q^{24} - 8 q^{25} + 12 q^{26} - 4 q^{27} + q^{28} - 8 q^{29} + 8 q^{30} + 9 q^{32} - 4 q^{34} - 12 q^{35} + q^{36} - 12 q^{37} - 20 q^{38} - 20 q^{40} - 7 q^{42} + 14 q^{44} - 6 q^{46} - 8 q^{47} + 7 q^{48} + 8 q^{49} + 19 q^{50} + 28 q^{52} + 16 q^{53} + q^{54} + 4 q^{55} - 23 q^{56} - 12 q^{57} + 2 q^{58} + 16 q^{59} - 4 q^{60} + 2 q^{63} + q^{64} + 8 q^{65} - 6 q^{66} - 32 q^{68} + 16 q^{70} - 7 q^{72} - 14 q^{74} + 8 q^{75} + 20 q^{76} - 8 q^{77} - 12 q^{78} + 36 q^{80} + 4 q^{81} + 20 q^{82} - 8 q^{83} - q^{84} + 20 q^{85} - 30 q^{86} + 8 q^{87} - 2 q^{88} - 8 q^{90} - 16 q^{91} - 14 q^{92} - 32 q^{94} - 9 q^{96} + 31 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/84\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(43\) \(73\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.28078 + 0.599676i −0.905646 + 0.424035i
\(3\) −1.00000 −0.577350
\(4\) 1.28078 1.53610i 0.640388 0.768051i
\(5\) 3.33513i 1.49152i 0.666217 + 0.745758i \(0.267913\pi\)
−0.666217 + 0.745758i \(0.732087\pi\)
\(6\) 1.28078 0.599676i 0.522875 0.244817i
\(7\) −1.56155 + 2.13578i −0.590211 + 0.807249i
\(8\) −0.719224 + 2.73546i −0.254284 + 0.967130i
\(9\) 1.00000 0.333333
\(10\) −2.00000 4.27156i −0.632456 1.35079i
\(11\) 0.936426i 0.282343i 0.989985 + 0.141172i \(0.0450869\pi\)
−0.989985 + 0.141172i \(0.954913\pi\)
\(12\) −1.28078 + 1.53610i −0.369728 + 0.443435i
\(13\) 1.87285i 0.519436i 0.965685 + 0.259718i \(0.0836296\pi\)
−0.965685 + 0.259718i \(0.916370\pi\)
\(14\) 0.719224 3.67188i 0.192221 0.981352i
\(15\) 3.33513i 0.861127i
\(16\) −0.719224 3.93481i −0.179806 0.983702i
\(17\) 5.20798i 1.26312i −0.775326 0.631561i \(-0.782415\pi\)
0.775326 0.631561i \(-0.217585\pi\)
\(18\) −1.28078 + 0.599676i −0.301882 + 0.141345i
\(19\) 7.12311 1.63415 0.817076 0.576530i \(-0.195593\pi\)
0.817076 + 0.576530i \(0.195593\pi\)
\(20\) 5.12311 + 4.27156i 1.14556 + 0.955149i
\(21\) 1.56155 2.13578i 0.340759 0.466065i
\(22\) −0.561553 1.19935i −0.119723 0.255703i
\(23\) 0.936426i 0.195258i −0.995223 0.0976292i \(-0.968874\pi\)
0.995223 0.0976292i \(-0.0311259\pi\)
\(24\) 0.719224 2.73546i 0.146811 0.558373i
\(25\) −6.12311 −1.22462
\(26\) −1.12311 2.39871i −0.220259 0.470425i
\(27\) −1.00000 −0.192450
\(28\) 1.28078 + 5.13416i 0.242044 + 0.970265i
\(29\) −2.00000 −0.371391 −0.185695 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) 2.00000 + 4.27156i 0.365148 + 0.779876i
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 3.28078 + 4.60831i 0.579965 + 0.814642i
\(33\) 0.936426i 0.163011i
\(34\) 3.12311 + 6.67026i 0.535608 + 1.14394i
\(35\) −7.12311 5.20798i −1.20402 0.880310i
\(36\) 1.28078 1.53610i 0.213463 0.256017i
\(37\) 1.12311 0.184637 0.0923187 0.995730i \(-0.470572\pi\)
0.0923187 + 0.995730i \(0.470572\pi\)
\(38\) −9.12311 + 4.27156i −1.47996 + 0.692938i
\(39\) 1.87285i 0.299896i
\(40\) −9.12311 2.39871i −1.44249 0.379269i
\(41\) 1.46228i 0.228370i −0.993460 0.114185i \(-0.963574\pi\)
0.993460 0.114185i \(-0.0364256\pi\)
\(42\) −0.719224 + 3.67188i −0.110979 + 0.566584i
\(43\) 9.06897i 1.38300i 0.722374 + 0.691502i \(0.243051\pi\)
−0.722374 + 0.691502i \(0.756949\pi\)
\(44\) 1.43845 + 1.19935i 0.216854 + 0.180809i
\(45\) 3.33513i 0.497172i
\(46\) 0.561553 + 1.19935i 0.0827964 + 0.176835i
\(47\) 6.24621 0.911104 0.455552 0.890209i \(-0.349442\pi\)
0.455552 + 0.890209i \(0.349442\pi\)
\(48\) 0.719224 + 3.93481i 0.103811 + 0.567941i
\(49\) −2.12311 6.67026i −0.303301 0.952895i
\(50\) 7.84233 3.67188i 1.10907 0.519283i
\(51\) 5.20798i 0.729264i
\(52\) 2.87689 + 2.39871i 0.398953 + 0.332641i
\(53\) 12.2462 1.68215 0.841073 0.540921i \(-0.181924\pi\)
0.841073 + 0.540921i \(0.181924\pi\)
\(54\) 1.28078 0.599676i 0.174292 0.0816056i
\(55\) −3.12311 −0.421119
\(56\) −4.71922 5.80766i −0.630633 0.776081i
\(57\) −7.12311 −0.943478
\(58\) 2.56155 1.19935i 0.336348 0.157483i
\(59\) 4.00000 0.520756 0.260378 0.965507i \(-0.416153\pi\)
0.260378 + 0.965507i \(0.416153\pi\)
\(60\) −5.12311 4.27156i −0.661390 0.551456i
\(61\) 4.79741i 0.614246i 0.951670 + 0.307123i \(0.0993662\pi\)
−0.951670 + 0.307123i \(0.900634\pi\)
\(62\) 0 0
\(63\) −1.56155 + 2.13578i −0.196737 + 0.269083i
\(64\) −6.96543 3.93481i −0.870679 0.491851i
\(65\) −6.24621 −0.774747
\(66\) 0.561553 + 1.19935i 0.0691224 + 0.147630i
\(67\) 10.9418i 1.33676i −0.743822 0.668378i \(-0.766989\pi\)
0.743822 0.668378i \(-0.233011\pi\)
\(68\) −8.00000 6.67026i −0.970143 0.808888i
\(69\) 0.936426i 0.112732i
\(70\) 12.2462 + 2.39871i 1.46370 + 0.286700i
\(71\) 3.86098i 0.458215i −0.973401 0.229107i \(-0.926419\pi\)
0.973401 0.229107i \(-0.0735807\pi\)
\(72\) −0.719224 + 2.73546i −0.0847613 + 0.322377i
\(73\) 6.67026i 0.780695i 0.920668 + 0.390348i \(0.127645\pi\)
−0.920668 + 0.390348i \(0.872355\pi\)
\(74\) −1.43845 + 0.673500i −0.167216 + 0.0782928i
\(75\) 6.12311 0.707035
\(76\) 9.12311 10.9418i 1.04649 1.25511i
\(77\) −2.00000 1.46228i −0.227921 0.166642i
\(78\) 1.12311 + 2.39871i 0.127167 + 0.271600i
\(79\) 2.39871i 0.269875i −0.990854 0.134938i \(-0.956917\pi\)
0.990854 0.134938i \(-0.0430834\pi\)
\(80\) 13.1231 2.39871i 1.46721 0.268183i
\(81\) 1.00000 0.111111
\(82\) 0.876894 + 1.87285i 0.0968368 + 0.206822i
\(83\) −10.2462 −1.12467 −0.562334 0.826910i \(-0.690096\pi\)
−0.562334 + 0.826910i \(0.690096\pi\)
\(84\) −1.28078 5.13416i −0.139744 0.560183i
\(85\) 17.3693 1.88397
\(86\) −5.43845 11.6153i −0.586443 1.25251i
\(87\) 2.00000 0.214423
\(88\) −2.56155 0.673500i −0.273062 0.0717953i
\(89\) 1.46228i 0.155001i 0.996992 + 0.0775006i \(0.0246940\pi\)
−0.996992 + 0.0775006i \(0.975306\pi\)
\(90\) −2.00000 4.27156i −0.210819 0.450262i
\(91\) −4.00000 2.92456i −0.419314 0.306577i
\(92\) −1.43845 1.19935i −0.149968 0.125041i
\(93\) 0 0
\(94\) −8.00000 + 3.74571i −0.825137 + 0.386340i
\(95\) 23.7565i 2.43737i
\(96\) −3.28078 4.60831i −0.334843 0.470334i
\(97\) 10.4160i 1.05758i −0.848752 0.528791i \(-0.822646\pi\)
0.848752 0.528791i \(-0.177354\pi\)
\(98\) 6.71922 + 7.26994i 0.678744 + 0.734375i
\(99\) 0.936426i 0.0941144i
\(100\) −7.84233 + 9.40572i −0.784233 + 0.940572i
\(101\) 13.7511i 1.36829i 0.729348 + 0.684143i \(0.239824\pi\)
−0.729348 + 0.684143i \(0.760176\pi\)
\(102\) −3.12311 6.67026i −0.309234 0.660455i
\(103\) −8.00000 −0.788263 −0.394132 0.919054i \(-0.628955\pi\)
−0.394132 + 0.919054i \(0.628955\pi\)
\(104\) −5.12311 1.34700i −0.502362 0.132084i
\(105\) 7.12311 + 5.20798i 0.695144 + 0.508247i
\(106\) −15.6847 + 7.34376i −1.52343 + 0.713289i
\(107\) 9.47954i 0.916422i −0.888843 0.458211i \(-0.848490\pi\)
0.888843 0.458211i \(-0.151510\pi\)
\(108\) −1.28078 + 1.53610i −0.123243 + 0.147812i
\(109\) −8.24621 −0.789844 −0.394922 0.918715i \(-0.629228\pi\)
−0.394922 + 0.918715i \(0.629228\pi\)
\(110\) 4.00000 1.87285i 0.381385 0.178570i
\(111\) −1.12311 −0.106600
\(112\) 9.52699 + 4.60831i 0.900216 + 0.435444i
\(113\) −4.24621 −0.399450 −0.199725 0.979852i \(-0.564005\pi\)
−0.199725 + 0.979852i \(0.564005\pi\)
\(114\) 9.12311 4.27156i 0.854457 0.400068i
\(115\) 3.12311 0.291231
\(116\) −2.56155 + 3.07221i −0.237834 + 0.285247i
\(117\) 1.87285i 0.173145i
\(118\) −5.12311 + 2.39871i −0.471620 + 0.220819i
\(119\) 11.1231 + 8.13254i 1.01965 + 0.745509i
\(120\) 9.12311 + 2.39871i 0.832822 + 0.218971i
\(121\) 10.1231 0.920282
\(122\) −2.87689 6.14441i −0.260462 0.556289i
\(123\) 1.46228i 0.131849i
\(124\) 0 0
\(125\) 3.74571i 0.335026i
\(126\) 0.719224 3.67188i 0.0640735 0.327117i
\(127\) 9.89012i 0.877606i −0.898583 0.438803i \(-0.855403\pi\)
0.898583 0.438803i \(-0.144597\pi\)
\(128\) 11.2808 + 0.862603i 0.997089 + 0.0762440i
\(129\) 9.06897i 0.798478i
\(130\) 8.00000 3.74571i 0.701646 0.328520i
\(131\) 5.75379 0.502711 0.251355 0.967895i \(-0.419124\pi\)
0.251355 + 0.967895i \(0.419124\pi\)
\(132\) −1.43845 1.19935i −0.125201 0.104390i
\(133\) −11.1231 + 15.2134i −0.964496 + 1.31917i
\(134\) 6.56155 + 14.0140i 0.566832 + 1.21063i
\(135\) 3.33513i 0.287042i
\(136\) 14.2462 + 3.74571i 1.22160 + 0.321192i
\(137\) 0.246211 0.0210352 0.0105176 0.999945i \(-0.496652\pi\)
0.0105176 + 0.999945i \(0.496652\pi\)
\(138\) −0.561553 1.19935i −0.0478025 0.102096i
\(139\) −12.0000 −1.01783 −0.508913 0.860818i \(-0.669953\pi\)
−0.508913 + 0.860818i \(0.669953\pi\)
\(140\) −17.1231 + 4.27156i −1.44717 + 0.361013i
\(141\) −6.24621 −0.526026
\(142\) 2.31534 + 4.94506i 0.194299 + 0.414980i
\(143\) −1.75379 −0.146659
\(144\) −0.719224 3.93481i −0.0599353 0.327901i
\(145\) 6.67026i 0.553935i
\(146\) −4.00000 8.54312i −0.331042 0.707033i
\(147\) 2.12311 + 6.67026i 0.175111 + 0.550154i
\(148\) 1.43845 1.72521i 0.118240 0.141811i
\(149\) −10.0000 −0.819232 −0.409616 0.912258i \(-0.634337\pi\)
−0.409616 + 0.912258i \(0.634337\pi\)
\(150\) −7.84233 + 3.67188i −0.640323 + 0.299808i
\(151\) 9.06897i 0.738022i −0.929425 0.369011i \(-0.879696\pi\)
0.929425 0.369011i \(-0.120304\pi\)
\(152\) −5.12311 + 19.4849i −0.415539 + 1.58044i
\(153\) 5.20798i 0.421041i
\(154\) 3.43845 + 0.673500i 0.277078 + 0.0542722i
\(155\) 0 0
\(156\) −2.87689 2.39871i −0.230336 0.192050i
\(157\) 21.8836i 1.74650i −0.487268 0.873252i \(-0.662007\pi\)
0.487268 0.873252i \(-0.337993\pi\)
\(158\) 1.43845 + 3.07221i 0.114437 + 0.244412i
\(159\) −12.2462 −0.971188
\(160\) −15.3693 + 10.9418i −1.21505 + 0.865027i
\(161\) 2.00000 + 1.46228i 0.157622 + 0.115244i
\(162\) −1.28078 + 0.599676i −0.100627 + 0.0471150i
\(163\) 15.7392i 1.23279i 0.787436 + 0.616396i \(0.211408\pi\)
−0.787436 + 0.616396i \(0.788592\pi\)
\(164\) −2.24621 1.87285i −0.175400 0.146245i
\(165\) 3.12311 0.243133
\(166\) 13.1231 6.14441i 1.01855 0.476899i
\(167\) 14.2462 1.10240 0.551202 0.834372i \(-0.314169\pi\)
0.551202 + 0.834372i \(0.314169\pi\)
\(168\) 4.71922 + 5.80766i 0.364096 + 0.448071i
\(169\) 9.49242 0.730186
\(170\) −22.2462 + 10.4160i −1.70621 + 0.798868i
\(171\) 7.12311 0.544718
\(172\) 13.9309 + 11.6153i 1.06222 + 0.885660i
\(173\) 16.6757i 1.26783i −0.773404 0.633913i \(-0.781448\pi\)
0.773404 0.633913i \(-0.218552\pi\)
\(174\) −2.56155 + 1.19935i −0.194191 + 0.0909227i
\(175\) 9.56155 13.0776i 0.722785 0.988574i
\(176\) 3.68466 0.673500i 0.277742 0.0507670i
\(177\) −4.00000 −0.300658
\(178\) −0.876894 1.87285i −0.0657260 0.140376i
\(179\) 16.1498i 1.20709i −0.797328 0.603547i \(-0.793754\pi\)
0.797328 0.603547i \(-0.206246\pi\)
\(180\) 5.12311 + 4.27156i 0.381854 + 0.318383i
\(181\) 1.87285i 0.139208i −0.997575 0.0696040i \(-0.977826\pi\)
0.997575 0.0696040i \(-0.0221736\pi\)
\(182\) 6.87689 + 1.34700i 0.509749 + 0.0998463i
\(183\) 4.79741i 0.354635i
\(184\) 2.56155 + 0.673500i 0.188840 + 0.0496511i
\(185\) 3.74571i 0.275390i
\(186\) 0 0
\(187\) 4.87689 0.356634
\(188\) 8.00000 9.59482i 0.583460 0.699774i
\(189\) 1.56155 2.13578i 0.113586 0.155355i
\(190\) −14.2462 30.4268i −1.03353 2.20739i
\(191\) 2.80928i 0.203272i 0.994822 + 0.101636i \(0.0324078\pi\)
−0.994822 + 0.101636i \(0.967592\pi\)
\(192\) 6.96543 + 3.93481i 0.502687 + 0.283970i
\(193\) −15.3693 −1.10631 −0.553154 0.833079i \(-0.686576\pi\)
−0.553154 + 0.833079i \(0.686576\pi\)
\(194\) 6.24621 + 13.3405i 0.448452 + 0.957794i
\(195\) 6.24621 0.447300
\(196\) −12.9654 5.28181i −0.926102 0.377272i
\(197\) −16.2462 −1.15749 −0.578747 0.815507i \(-0.696458\pi\)
−0.578747 + 0.815507i \(0.696458\pi\)
\(198\) −0.561553 1.19935i −0.0399078 0.0852343i
\(199\) −3.12311 −0.221391 −0.110696 0.993854i \(-0.535308\pi\)
−0.110696 + 0.993854i \(0.535308\pi\)
\(200\) 4.40388 16.7495i 0.311401 1.18437i
\(201\) 10.9418i 0.771777i
\(202\) −8.24621 17.6121i −0.580201 1.23918i
\(203\) 3.12311 4.27156i 0.219199 0.299805i
\(204\) 8.00000 + 6.67026i 0.560112 + 0.467012i
\(205\) 4.87689 0.340617
\(206\) 10.2462 4.79741i 0.713887 0.334251i
\(207\) 0.936426i 0.0650861i
\(208\) 7.36932 1.34700i 0.510970 0.0933976i
\(209\) 6.67026i 0.461392i
\(210\) −12.2462 2.39871i −0.845069 0.165526i
\(211\) 12.8147i 0.882199i 0.897458 + 0.441099i \(0.145411\pi\)
−0.897458 + 0.441099i \(0.854589\pi\)
\(212\) 15.6847 18.8114i 1.07723 1.29197i
\(213\) 3.86098i 0.264550i
\(214\) 5.68466 + 12.1412i 0.388595 + 0.829954i
\(215\) −30.2462 −2.06277
\(216\) 0.719224 2.73546i 0.0489370 0.186124i
\(217\) 0 0
\(218\) 10.5616 4.94506i 0.715319 0.334922i
\(219\) 6.67026i 0.450735i
\(220\) −4.00000 + 4.79741i −0.269680 + 0.323441i
\(221\) 9.75379 0.656111
\(222\) 1.43845 0.673500i 0.0965423 0.0452024i
\(223\) 27.1231 1.81630 0.908149 0.418648i \(-0.137496\pi\)
0.908149 + 0.418648i \(0.137496\pi\)
\(224\) −14.9654 0.189103i −0.999920 0.0126350i
\(225\) −6.12311 −0.408207
\(226\) 5.43845 2.54635i 0.361760 0.169381i
\(227\) −16.4924 −1.09464 −0.547320 0.836923i \(-0.684352\pi\)
−0.547320 + 0.836923i \(0.684352\pi\)
\(228\) −9.12311 + 10.9418i −0.604192 + 0.724640i
\(229\) 5.61856i 0.371285i 0.982617 + 0.185642i \(0.0594366\pi\)
−0.982617 + 0.185642i \(0.940563\pi\)
\(230\) −4.00000 + 1.87285i −0.263752 + 0.123492i
\(231\) 2.00000 + 1.46228i 0.131590 + 0.0962109i
\(232\) 1.43845 5.47091i 0.0944387 0.359183i
\(233\) 22.4924 1.47353 0.736764 0.676150i \(-0.236353\pi\)
0.736764 + 0.676150i \(0.236353\pi\)
\(234\) −1.12311 2.39871i −0.0734197 0.156808i
\(235\) 20.8319i 1.35893i
\(236\) 5.12311 6.14441i 0.333486 0.399967i
\(237\) 2.39871i 0.155813i
\(238\) −19.1231 3.74571i −1.23957 0.242798i
\(239\) 16.1498i 1.04464i 0.852748 + 0.522322i \(0.174934\pi\)
−0.852748 + 0.522322i \(0.825066\pi\)
\(240\) −13.1231 + 2.39871i −0.847093 + 0.154836i
\(241\) 23.7565i 1.53029i 0.643858 + 0.765145i \(0.277333\pi\)
−0.643858 + 0.765145i \(0.722667\pi\)
\(242\) −12.9654 + 6.07059i −0.833450 + 0.390232i
\(243\) −1.00000 −0.0641500
\(244\) 7.36932 + 6.14441i 0.471772 + 0.393356i
\(245\) 22.2462 7.08084i 1.42126 0.452378i
\(246\) −0.876894 1.87285i −0.0559087 0.119409i
\(247\) 13.3405i 0.848837i
\(248\) 0 0
\(249\) 10.2462 0.649327
\(250\) 2.24621 + 4.79741i 0.142063 + 0.303415i
\(251\) −5.75379 −0.363176 −0.181588 0.983375i \(-0.558124\pi\)
−0.181588 + 0.983375i \(0.558124\pi\)
\(252\) 1.28078 + 5.13416i 0.0806813 + 0.323422i
\(253\) 0.876894 0.0551299
\(254\) 5.93087 + 12.6670i 0.372136 + 0.794800i
\(255\) −17.3693 −1.08771
\(256\) −14.9654 + 5.66001i −0.935340 + 0.353751i
\(257\) 2.28343i 0.142436i 0.997461 + 0.0712181i \(0.0226886\pi\)
−0.997461 + 0.0712181i \(0.977311\pi\)
\(258\) 5.43845 + 11.6153i 0.338583 + 0.723138i
\(259\) −1.75379 + 2.39871i −0.108975 + 0.149048i
\(260\) −8.00000 + 9.59482i −0.496139 + 0.595046i
\(261\) −2.00000 −0.123797
\(262\) −7.36932 + 3.45041i −0.455278 + 0.213167i
\(263\) 24.6929i 1.52263i −0.648382 0.761315i \(-0.724554\pi\)
0.648382 0.761315i \(-0.275446\pi\)
\(264\) 2.56155 + 0.673500i 0.157653 + 0.0414511i
\(265\) 40.8427i 2.50895i
\(266\) 5.12311 26.1552i 0.314118 1.60368i
\(267\) 1.46228i 0.0894900i
\(268\) −16.8078 14.0140i −1.02670 0.856043i
\(269\) 10.8265i 0.660106i −0.943962 0.330053i \(-0.892933\pi\)
0.943962 0.330053i \(-0.107067\pi\)
\(270\) 2.00000 + 4.27156i 0.121716 + 0.259959i
\(271\) −28.4924 −1.73079 −0.865396 0.501089i \(-0.832933\pi\)
−0.865396 + 0.501089i \(0.832933\pi\)
\(272\) −20.4924 + 3.74571i −1.24254 + 0.227117i
\(273\) 4.00000 + 2.92456i 0.242091 + 0.177002i
\(274\) −0.315342 + 0.147647i −0.0190505 + 0.00891969i
\(275\) 5.73384i 0.345763i
\(276\) 1.43845 + 1.19935i 0.0865843 + 0.0721926i
\(277\) −5.12311 −0.307818 −0.153909 0.988085i \(-0.549186\pi\)
−0.153909 + 0.988085i \(0.549186\pi\)
\(278\) 15.3693 7.19612i 0.921790 0.431594i
\(279\) 0 0
\(280\) 19.3693 15.7392i 1.15754 0.940599i
\(281\) 16.2462 0.969168 0.484584 0.874745i \(-0.338971\pi\)
0.484584 + 0.874745i \(0.338971\pi\)
\(282\) 8.00000 3.74571i 0.476393 0.223054i
\(283\) 8.87689 0.527677 0.263838 0.964567i \(-0.415011\pi\)
0.263838 + 0.964567i \(0.415011\pi\)
\(284\) −5.93087 4.94506i −0.351932 0.293435i
\(285\) 23.7565i 1.40721i
\(286\) 2.24621 1.05171i 0.132821 0.0621887i
\(287\) 3.12311 + 2.28343i 0.184351 + 0.134786i
\(288\) 3.28078 + 4.60831i 0.193322 + 0.271547i
\(289\) −10.1231 −0.595477
\(290\) 4.00000 + 8.54312i 0.234888 + 0.501669i
\(291\) 10.4160i 0.610595i
\(292\) 10.2462 + 8.54312i 0.599614 + 0.499948i
\(293\) 13.7511i 0.803348i 0.915783 + 0.401674i \(0.131571\pi\)
−0.915783 + 0.401674i \(0.868429\pi\)
\(294\) −6.71922 7.26994i −0.391873 0.423992i
\(295\) 13.3405i 0.776716i
\(296\) −0.807764 + 3.07221i −0.0469503 + 0.178568i
\(297\) 0.936426i 0.0543370i
\(298\) 12.8078 5.99676i 0.741934 0.347383i
\(299\) 1.75379 0.101424
\(300\) 7.84233 9.40572i 0.452777 0.543039i
\(301\) −19.3693 14.1617i −1.11643 0.816265i
\(302\) 5.43845 + 11.6153i 0.312947 + 0.668387i
\(303\) 13.7511i 0.789980i
\(304\) −5.12311 28.0281i −0.293830 1.60752i
\(305\) −16.0000 −0.916157
\(306\) 3.12311 + 6.67026i 0.178536 + 0.381314i
\(307\) 19.6155 1.11952 0.559759 0.828656i \(-0.310894\pi\)
0.559759 + 0.828656i \(0.310894\pi\)
\(308\) −4.80776 + 1.19935i −0.273948 + 0.0683395i
\(309\) 8.00000 0.455104
\(310\) 0 0
\(311\) 8.00000 0.453638 0.226819 0.973937i \(-0.427167\pi\)
0.226819 + 0.973937i \(0.427167\pi\)
\(312\) 5.12311 + 1.34700i 0.290039 + 0.0762589i
\(313\) 22.9354i 1.29638i −0.761478 0.648191i \(-0.775526\pi\)
0.761478 0.648191i \(-0.224474\pi\)
\(314\) 13.1231 + 28.0281i 0.740580 + 1.58171i
\(315\) −7.12311 5.20798i −0.401342 0.293437i
\(316\) −3.68466 3.07221i −0.207278 0.172825i
\(317\) −14.4924 −0.813976 −0.406988 0.913434i \(-0.633421\pi\)
−0.406988 + 0.913434i \(0.633421\pi\)
\(318\) 15.6847 7.34376i 0.879552 0.411818i
\(319\) 1.87285i 0.104860i
\(320\) 13.1231 23.2306i 0.733604 1.29863i
\(321\) 9.47954i 0.529097i
\(322\) −3.43845 0.673500i −0.191617 0.0375327i
\(323\) 37.0970i 2.06413i
\(324\) 1.28078 1.53610i 0.0711542 0.0853390i
\(325\) 11.4677i 0.636112i
\(326\) −9.43845 20.1584i −0.522747 1.11647i
\(327\) 8.24621 0.456017
\(328\) 4.00000 + 1.05171i 0.220863 + 0.0580707i
\(329\) −9.75379 + 13.3405i −0.537744 + 0.735487i
\(330\) −4.00000 + 1.87285i −0.220193 + 0.103097i
\(331\) 17.6121i 0.968048i −0.875055 0.484024i \(-0.839175\pi\)
0.875055 0.484024i \(-0.160825\pi\)
\(332\) −13.1231 + 15.7392i −0.720224 + 0.863803i
\(333\) 1.12311 0.0615458
\(334\) −18.2462 + 8.54312i −0.998388 + 0.467459i
\(335\) 36.4924 1.99379
\(336\) −9.52699 4.60831i −0.519740 0.251404i
\(337\) 8.24621 0.449200 0.224600 0.974451i \(-0.427892\pi\)
0.224600 + 0.974451i \(0.427892\pi\)
\(338\) −12.1577 + 5.69238i −0.661290 + 0.309625i
\(339\) 4.24621 0.230623
\(340\) 22.2462 26.6811i 1.20647 1.44698i
\(341\) 0 0
\(342\) −9.12311 + 4.27156i −0.493321 + 0.230979i
\(343\) 17.5616 + 5.88148i 0.948235 + 0.317570i
\(344\) −24.8078 6.52262i −1.33754 0.351676i
\(345\) −3.12311 −0.168142
\(346\) 10.0000 + 21.3578i 0.537603 + 1.14820i
\(347\) 20.1261i 1.08042i 0.841529 + 0.540212i \(0.181656\pi\)
−0.841529 + 0.540212i \(0.818344\pi\)
\(348\) 2.56155 3.07221i 0.137314 0.164688i
\(349\) 21.8836i 1.17140i −0.810526 0.585702i \(-0.800819\pi\)
0.810526 0.585702i \(-0.199181\pi\)
\(350\) −4.40388 + 22.4833i −0.235397 + 1.20178i
\(351\) 1.87285i 0.0999655i
\(352\) −4.31534 + 3.07221i −0.230008 + 0.163749i
\(353\) 28.9645i 1.54162i −0.637063 0.770812i \(-0.719851\pi\)
0.637063 0.770812i \(-0.280149\pi\)
\(354\) 5.12311 2.39871i 0.272290 0.127490i
\(355\) 12.8769 0.683435
\(356\) 2.24621 + 1.87285i 0.119049 + 0.0992610i
\(357\) −11.1231 8.13254i −0.588697 0.430420i
\(358\) 9.68466 + 20.6843i 0.511850 + 1.09320i
\(359\) 22.8201i 1.20440i 0.798346 + 0.602199i \(0.205708\pi\)
−0.798346 + 0.602199i \(0.794292\pi\)
\(360\) −9.12311 2.39871i −0.480830 0.126423i
\(361\) 31.7386 1.67045
\(362\) 1.12311 + 2.39871i 0.0590291 + 0.126073i
\(363\) −10.1231 −0.531325
\(364\) −9.61553 + 2.39871i −0.503991 + 0.125726i
\(365\) −22.2462 −1.16442
\(366\) 2.87689 + 6.14441i 0.150378 + 0.321174i
\(367\) −33.3693 −1.74186 −0.870932 0.491403i \(-0.836484\pi\)
−0.870932 + 0.491403i \(0.836484\pi\)
\(368\) −3.68466 + 0.673500i −0.192076 + 0.0351086i
\(369\) 1.46228i 0.0761232i
\(370\) −2.24621 4.79741i −0.116775 0.249406i
\(371\) −19.1231 + 26.1552i −0.992822 + 1.35791i
\(372\) 0 0
\(373\) −10.0000 −0.517780 −0.258890 0.965907i \(-0.583357\pi\)
−0.258890 + 0.965907i \(0.583357\pi\)
\(374\) −6.24621 + 2.92456i −0.322984 + 0.151225i
\(375\) 3.74571i 0.193427i
\(376\) −4.49242 + 17.0862i −0.231679 + 0.881155i
\(377\) 3.74571i 0.192914i
\(378\) −0.719224 + 3.67188i −0.0369929 + 0.188861i
\(379\) 25.1035i 1.28948i −0.764402 0.644740i \(-0.776966\pi\)
0.764402 0.644740i \(-0.223034\pi\)
\(380\) 36.4924 + 30.4268i 1.87202 + 1.56086i
\(381\) 9.89012i 0.506686i
\(382\) −1.68466 3.59806i −0.0861946 0.184093i
\(383\) −9.75379 −0.498395 −0.249198 0.968453i \(-0.580167\pi\)
−0.249198 + 0.968453i \(0.580167\pi\)
\(384\) −11.2808 0.862603i −0.575670 0.0440195i
\(385\) 4.87689 6.67026i 0.248550 0.339948i
\(386\) 19.6847 9.21662i 1.00192 0.469113i
\(387\) 9.06897i 0.461002i
\(388\) −16.0000 13.3405i −0.812277 0.677263i
\(389\) −16.2462 −0.823716 −0.411858 0.911248i \(-0.635120\pi\)
−0.411858 + 0.911248i \(0.635120\pi\)
\(390\) −8.00000 + 3.74571i −0.405096 + 0.189671i
\(391\) −4.87689 −0.246635
\(392\) 19.7732 1.01025i 0.998697 0.0510253i
\(393\) −5.75379 −0.290240
\(394\) 20.8078 9.74247i 1.04828 0.490819i
\(395\) 8.00000 0.402524
\(396\) 1.43845 + 1.19935i 0.0722847 + 0.0602697i
\(397\) 18.1379i 0.910317i 0.890410 + 0.455159i \(0.150417\pi\)
−0.890410 + 0.455159i \(0.849583\pi\)
\(398\) 4.00000 1.87285i 0.200502 0.0938776i
\(399\) 11.1231 15.2134i 0.556852 0.761622i
\(400\) 4.40388 + 24.0932i 0.220194 + 1.20466i
\(401\) 8.24621 0.411796 0.205898 0.978573i \(-0.433988\pi\)
0.205898 + 0.978573i \(0.433988\pi\)
\(402\) −6.56155 14.0140i −0.327261 0.698956i
\(403\) 0 0
\(404\) 21.1231 + 17.6121i 1.05091 + 0.876234i
\(405\) 3.33513i 0.165724i
\(406\) −1.43845 + 7.34376i −0.0713889 + 0.364465i
\(407\) 1.05171i 0.0521311i
\(408\) −14.2462 3.74571i −0.705293 0.185440i
\(409\) 0.821147i 0.0406031i −0.999794 0.0203016i \(-0.993537\pi\)
0.999794 0.0203016i \(-0.00646263\pi\)
\(410\) −6.24621 + 2.92456i −0.308478 + 0.144434i
\(411\) −0.246211 −0.0121447
\(412\) −10.2462 + 12.2888i −0.504795 + 0.605427i
\(413\) −6.24621 + 8.54312i −0.307356 + 0.420379i
\(414\) 0.561553 + 1.19935i 0.0275988 + 0.0589450i
\(415\) 34.1725i 1.67746i
\(416\) −8.63068 + 6.14441i −0.423154 + 0.301255i
\(417\) 12.0000 0.587643
\(418\) −4.00000 8.54312i −0.195646 0.417858i
\(419\) −16.4924 −0.805708 −0.402854 0.915264i \(-0.631982\pi\)
−0.402854 + 0.915264i \(0.631982\pi\)
\(420\) 17.1231 4.27156i 0.835522 0.208431i
\(421\) 10.8769 0.530107 0.265054 0.964234i \(-0.414610\pi\)
0.265054 + 0.964234i \(0.414610\pi\)
\(422\) −7.68466 16.4127i −0.374083 0.798959i
\(423\) 6.24621 0.303701
\(424\) −8.80776 + 33.4990i −0.427743 + 1.62685i
\(425\) 31.8890i 1.54685i
\(426\) −2.31534 4.94506i −0.112179 0.239589i
\(427\) −10.2462 7.49141i −0.495849 0.362535i
\(428\) −14.5616 12.1412i −0.703859 0.586866i
\(429\) 1.75379 0.0846737
\(430\) 38.7386 18.1379i 1.86814 0.874689i
\(431\) 4.68213i 0.225530i −0.993622 0.112765i \(-0.964029\pi\)
0.993622 0.112765i \(-0.0359708\pi\)
\(432\) 0.719224 + 3.93481i 0.0346037 + 0.189314i
\(433\) 13.3405i 0.641105i −0.947231 0.320552i \(-0.896131\pi\)
0.947231 0.320552i \(-0.103869\pi\)
\(434\) 0 0
\(435\) 6.67026i 0.319815i
\(436\) −10.5616 + 12.6670i −0.505807 + 0.606641i
\(437\) 6.67026i 0.319082i
\(438\) 4.00000 + 8.54312i 0.191127 + 0.408206i
\(439\) −6.63068 −0.316465 −0.158233 0.987402i \(-0.550580\pi\)
−0.158233 + 0.987402i \(0.550580\pi\)
\(440\) 2.24621 8.54312i 0.107084 0.407277i
\(441\) −2.12311 6.67026i −0.101100 0.317632i
\(442\) −12.4924 + 5.84912i −0.594204 + 0.278214i
\(443\) 18.8438i 0.895296i 0.894210 + 0.447648i \(0.147738\pi\)
−0.894210 + 0.447648i \(0.852262\pi\)
\(444\) −1.43845 + 1.72521i −0.0682657 + 0.0818746i
\(445\) −4.87689 −0.231187
\(446\) −34.7386 + 16.2651i −1.64492 + 0.770174i
\(447\) 10.0000 0.472984
\(448\) 19.2808 8.73222i 0.910931 0.412559i
\(449\) 11.7538 0.554696 0.277348 0.960770i \(-0.410545\pi\)
0.277348 + 0.960770i \(0.410545\pi\)
\(450\) 7.84233 3.67188i 0.369691 0.173094i
\(451\) 1.36932 0.0644786
\(452\) −5.43845 + 6.52262i −0.255803 + 0.306798i
\(453\) 9.06897i 0.426097i
\(454\) 21.1231 9.89012i 0.991356 0.464166i
\(455\) 9.75379 13.3405i 0.457265 0.625414i
\(456\) 5.12311 19.4849i 0.239911 0.912466i
\(457\) 0.246211 0.0115173 0.00575864 0.999983i \(-0.498167\pi\)
0.00575864 + 0.999983i \(0.498167\pi\)
\(458\) −3.36932 7.19612i −0.157438 0.336252i
\(459\) 5.20798i 0.243088i
\(460\) 4.00000 4.79741i 0.186501 0.223680i
\(461\) 6.25969i 0.291543i −0.989318 0.145771i \(-0.953434\pi\)
0.989318 0.145771i \(-0.0465664\pi\)
\(462\) −3.43845 0.673500i −0.159971 0.0313341i
\(463\) 39.2652i 1.82481i 0.409292 + 0.912404i \(0.365776\pi\)
−0.409292 + 0.912404i \(0.634224\pi\)
\(464\) 1.43845 + 7.86962i 0.0667782 + 0.365338i
\(465\) 0 0
\(466\) −28.8078 + 13.4882i −1.33449 + 0.624828i
\(467\) 34.2462 1.58473 0.792363 0.610050i \(-0.208851\pi\)
0.792363 + 0.610050i \(0.208851\pi\)
\(468\) 2.87689 + 2.39871i 0.132984 + 0.110880i
\(469\) 23.3693 + 17.0862i 1.07909 + 0.788969i
\(470\) −12.4924 26.6811i −0.576232 1.23071i
\(471\) 21.8836i 1.00835i
\(472\) −2.87689 + 10.9418i −0.132420 + 0.503638i
\(473\) −8.49242 −0.390482
\(474\) −1.43845 3.07221i −0.0660701 0.141111i
\(475\) −43.6155 −2.00122
\(476\) 26.7386 6.67026i 1.22556 0.305731i
\(477\) 12.2462 0.560715
\(478\) −9.68466 20.6843i −0.442966 0.946077i
\(479\) 12.4924 0.570793 0.285397 0.958409i \(-0.407875\pi\)
0.285397 + 0.958409i \(0.407875\pi\)
\(480\) 15.3693 10.9418i 0.701510 0.499424i
\(481\) 2.10341i 0.0959073i
\(482\) −14.2462 30.4268i −0.648897 1.38590i
\(483\) −2.00000 1.46228i −0.0910032 0.0665360i
\(484\) 12.9654 15.5501i 0.589338 0.706824i
\(485\) 34.7386 1.57740
\(486\) 1.28078 0.599676i 0.0580972 0.0272019i
\(487\) 1.57756i 0.0714860i −0.999361 0.0357430i \(-0.988620\pi\)
0.999361 0.0357430i \(-0.0113798\pi\)
\(488\) −13.1231 3.45041i −0.594055 0.156193i
\(489\) 15.7392i 0.711753i
\(490\) −24.2462 + 22.4095i −1.09533 + 1.01236i
\(491\) 11.3524i 0.512326i 0.966634 + 0.256163i \(0.0824585\pi\)
−0.966634 + 0.256163i \(0.917542\pi\)
\(492\) 2.24621 + 1.87285i 0.101267 + 0.0844347i
\(493\) 10.4160i 0.469112i
\(494\) −8.00000 17.0862i −0.359937 0.768746i
\(495\) −3.12311 −0.140373
\(496\) 0 0
\(497\) 8.24621 + 6.02913i 0.369893 + 0.270444i
\(498\) −13.1231 + 6.14441i −0.588060 + 0.275338i
\(499\) 13.8664i 0.620744i −0.950615 0.310372i \(-0.899546\pi\)
0.950615 0.310372i \(-0.100454\pi\)
\(500\) −5.75379 4.79741i −0.257317 0.214547i
\(501\) −14.2462 −0.636474
\(502\) 7.36932 3.45041i 0.328909 0.153999i
\(503\) −26.7386 −1.19222 −0.596108 0.802904i \(-0.703287\pi\)
−0.596108 + 0.802904i \(0.703287\pi\)
\(504\) −4.71922 5.80766i −0.210211 0.258694i
\(505\) −45.8617 −2.04082
\(506\) −1.12311 + 0.525853i −0.0499281 + 0.0233770i
\(507\) −9.49242 −0.421573
\(508\) −15.1922 12.6670i −0.674046 0.562008i
\(509\) 3.33513i 0.147827i −0.997265 0.0739136i \(-0.976451\pi\)
0.997265 0.0739136i \(-0.0235489\pi\)
\(510\) 22.2462 10.4160i 0.985079 0.461227i
\(511\) −14.2462 10.4160i −0.630215 0.460775i
\(512\) 15.7732 16.2236i 0.697083 0.716990i
\(513\) −7.12311 −0.314493
\(514\) −1.36932 2.92456i −0.0603980 0.128997i
\(515\) 26.6811i 1.17571i
\(516\) −13.9309 11.6153i −0.613272 0.511336i
\(517\) 5.84912i 0.257244i
\(518\) 0.807764 4.12391i 0.0354911 0.181194i
\(519\) 16.6757i 0.731980i
\(520\) 4.49242 17.0862i 0.197006 0.749281i
\(521\) 29.7856i 1.30493i 0.757818 + 0.652466i \(0.226266\pi\)
−0.757818 + 0.652466i \(0.773734\pi\)
\(522\) 2.56155 1.19935i 0.112116 0.0524942i
\(523\) 32.4924 1.42079 0.710397 0.703801i \(-0.248515\pi\)
0.710397 + 0.703801i \(0.248515\pi\)
\(524\) 7.36932 8.83841i 0.321930 0.386108i
\(525\) −9.56155 + 13.0776i −0.417300 + 0.570753i
\(526\) 14.8078 + 31.6261i 0.645649 + 1.37896i
\(527\) 0 0
\(528\) −3.68466 + 0.673500i −0.160354 + 0.0293103i
\(529\) 22.1231 0.961874
\(530\) −24.4924 52.3104i −1.06388 2.27222i
\(531\) 4.00000 0.173585
\(532\) 9.12311 + 36.5712i 0.395537 + 1.58556i
\(533\) 2.73863 0.118623
\(534\) 0.876894 + 1.87285i 0.0379469 + 0.0810463i
\(535\) 31.6155 1.36686
\(536\) 29.9309 + 7.86962i 1.29282 + 0.339916i
\(537\) 16.1498i 0.696916i
\(538\) 6.49242 + 13.8664i 0.279908 + 0.597822i
\(539\) 6.24621 1.98813i 0.269043 0.0856349i
\(540\) −5.12311 4.27156i −0.220463 0.183819i
\(541\) 2.87689 0.123687 0.0618437 0.998086i \(-0.480302\pi\)
0.0618437 + 0.998086i \(0.480302\pi\)
\(542\) 36.4924 17.0862i 1.56748 0.733917i
\(543\) 1.87285i 0.0803718i
\(544\) 24.0000 17.0862i 1.02899 0.732566i
\(545\) 27.5022i 1.17806i
\(546\) −6.87689 1.34700i −0.294304 0.0576463i
\(547\) 16.7909i 0.717929i −0.933351 0.358964i \(-0.883130\pi\)
0.933351 0.358964i \(-0.116870\pi\)
\(548\) 0.315342 0.378206i 0.0134707 0.0161562i
\(549\) 4.79741i 0.204749i
\(550\) 3.43845 + 7.34376i 0.146616 + 0.313139i
\(551\) −14.2462 −0.606909
\(552\) −2.56155 0.673500i −0.109027 0.0286661i
\(553\) 5.12311 + 3.74571i 0.217857 + 0.159284i
\(554\) 6.56155 3.07221i 0.278774 0.130526i
\(555\) 3.74571i 0.158996i
\(556\) −15.3693 + 18.4332i −0.651804 + 0.781743i
\(557\) 14.0000 0.593199 0.296600 0.955002i \(-0.404147\pi\)
0.296600 + 0.955002i \(0.404147\pi\)
\(558\) 0 0
\(559\) −16.9848 −0.718382
\(560\) −15.3693 + 31.7738i −0.649472 + 1.34269i
\(561\) −4.87689 −0.205903
\(562\) −20.8078 + 9.74247i −0.877723 + 0.410961i
\(563\) 2.24621 0.0946665 0.0473333 0.998879i \(-0.484928\pi\)
0.0473333 + 0.998879i \(0.484928\pi\)
\(564\) −8.00000 + 9.59482i −0.336861 + 0.404015i
\(565\) 14.1617i 0.595786i
\(566\) −11.3693 + 5.32326i −0.477888 + 0.223753i
\(567\) −1.56155 + 2.13578i −0.0655791 + 0.0896943i
\(568\) 10.5616 + 2.77691i 0.443153 + 0.116517i
\(569\) −30.9848 −1.29895 −0.649476 0.760382i \(-0.725012\pi\)
−0.649476 + 0.760382i \(0.725012\pi\)
\(570\) 14.2462 + 30.4268i 0.596708 + 1.27444i
\(571\) 8.83841i 0.369876i −0.982750 0.184938i \(-0.940792\pi\)
0.982750 0.184938i \(-0.0592084\pi\)
\(572\) −2.24621 + 2.69400i −0.0939188 + 0.112642i
\(573\) 2.80928i 0.117359i
\(574\) −5.36932 1.05171i −0.224111 0.0438973i
\(575\) 5.73384i 0.239118i
\(576\) −6.96543 3.93481i −0.290226 0.163950i
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) 12.9654 6.07059i 0.539291 0.252503i
\(579\) 15.3693 0.638727
\(580\) −10.2462 8.54312i −0.425451 0.354734i
\(581\) 16.0000 21.8836i 0.663792 0.907887i
\(582\) −6.24621 13.3405i −0.258914 0.552983i
\(583\) 11.4677i 0.474943i
\(584\) −18.2462 4.79741i −0.755034 0.198518i
\(585\) −6.24621 −0.258249
\(586\) −8.24621 17.6121i −0.340648 0.727549i
\(587\) −21.7538 −0.897875 −0.448937 0.893563i \(-0.648197\pi\)
−0.448937 + 0.893563i \(0.648197\pi\)
\(588\) 12.9654 + 5.28181i 0.534686 + 0.217818i
\(589\) 0 0
\(590\) −8.00000 17.0862i −0.329355 0.703429i
\(591\) 16.2462 0.668280
\(592\) −0.807764 4.41921i −0.0331989 0.181628i
\(593\) 26.0399i 1.06933i −0.845064 0.534666i \(-0.820438\pi\)
0.845064 0.534666i \(-0.179562\pi\)
\(594\) 0.561553 + 1.19935i 0.0230408 + 0.0492100i
\(595\) −27.1231 + 37.0970i −1.11194 + 1.52083i
\(596\) −12.8078 + 15.3610i −0.524626 + 0.629212i
\(597\) 3.12311 0.127820
\(598\) −2.24621 + 1.05171i −0.0918544 + 0.0430074i
\(599\) 17.2015i 0.702835i −0.936219 0.351417i \(-0.885700\pi\)
0.936219 0.351417i \(-0.114300\pi\)
\(600\) −4.40388 + 16.7495i −0.179788 + 0.683795i
\(601\) 17.0862i 0.696962i −0.937316 0.348481i \(-0.886698\pi\)
0.937316 0.348481i \(-0.113302\pi\)
\(602\) 33.3002 + 6.52262i 1.35721 + 0.265842i
\(603\) 10.9418i 0.445585i
\(604\) −13.9309 11.6153i −0.566839 0.472621i
\(605\) 33.7619i 1.37262i
\(606\) 8.24621 + 17.6121i 0.334979 + 0.715442i
\(607\) 7.61553 0.309105 0.154552 0.987985i \(-0.450606\pi\)
0.154552 + 0.987985i \(0.450606\pi\)
\(608\) 23.3693 + 32.8255i 0.947751 + 1.33125i
\(609\) −3.12311 + 4.27156i −0.126555 + 0.173092i
\(610\) 20.4924 9.59482i 0.829714 0.388483i
\(611\) 11.6982i 0.473260i
\(612\) −8.00000 6.67026i −0.323381 0.269629i
\(613\) 8.73863 0.352950 0.176475 0.984305i \(-0.443531\pi\)
0.176475 + 0.984305i \(0.443531\pi\)
\(614\) −25.1231 + 11.7630i −1.01389 + 0.474715i
\(615\) −4.87689 −0.196655
\(616\) 5.43845 4.41921i 0.219121 0.178055i
\(617\) 32.2462 1.29818 0.649092 0.760710i \(-0.275149\pi\)
0.649092 + 0.760710i \(0.275149\pi\)
\(618\) −10.2462 + 4.79741i −0.412163 + 0.192980i
\(619\) 20.0000 0.803868 0.401934 0.915669i \(-0.368338\pi\)
0.401934 + 0.915669i \(0.368338\pi\)
\(620\) 0 0
\(621\) 0.936426i 0.0375775i
\(622\) −10.2462 + 4.79741i −0.410836 + 0.192359i
\(623\) −3.12311 2.28343i −0.125125 0.0914835i
\(624\) −7.36932 + 1.34700i −0.295009 + 0.0539232i
\(625\) −18.1231 −0.724924
\(626\) 13.7538 + 29.3751i 0.549712 + 1.17406i
\(627\) 6.67026i 0.266385i
\(628\) −33.6155 28.0281i −1.34141 1.11844i
\(629\) 5.84912i 0.233220i
\(630\) 12.2462 + 2.39871i 0.487901 + 0.0955667i
\(631\) 40.3169i 1.60499i −0.596659 0.802495i \(-0.703506\pi\)
0.596659 0.802495i \(-0.296494\pi\)
\(632\) 6.56155 + 1.72521i 0.261005 + 0.0686250i
\(633\) 12.8147i 0.509338i
\(634\) 18.5616 8.69076i 0.737173 0.345154i
\(635\) 32.9848 1.30896
\(636\) −15.6847 + 18.8114i −0.621937 + 0.745922i
\(637\) 12.4924 3.97626i 0.494968 0.157545i
\(638\) 1.12311 + 2.39871i 0.0444642 + 0.0949657i
\(639\) 3.86098i 0.152738i
\(640\) −2.87689 + 37.6229i −0.113719 + 1.48717i
\(641\) −42.4924 −1.67835 −0.839175 0.543862i \(-0.816962\pi\)
−0.839175 + 0.543862i \(0.816962\pi\)
\(642\) −5.68466 12.1412i −0.224356 0.479174i
\(643\) −11.6155 −0.458072 −0.229036 0.973418i \(-0.573557\pi\)
−0.229036 + 0.973418i \(0.573557\pi\)
\(644\) 4.80776 1.19935i 0.189452 0.0472611i
\(645\) 30.2462 1.19094
\(646\) 22.2462 + 47.5130i 0.875265 + 1.86937i
\(647\) −32.9848 −1.29677 −0.648384 0.761313i \(-0.724555\pi\)
−0.648384 + 0.761313i \(0.724555\pi\)
\(648\) −0.719224 + 2.73546i −0.0282538 + 0.107459i
\(649\) 3.74571i 0.147032i
\(650\) 6.87689 + 14.6875i 0.269734 + 0.576092i
\(651\) 0 0
\(652\) 24.1771 + 20.1584i 0.946848 + 0.789465i
\(653\) 16.7386 0.655033 0.327517 0.944845i \(-0.393788\pi\)
0.327517 + 0.944845i \(0.393788\pi\)
\(654\) −10.5616 + 4.94506i −0.412989 + 0.193367i
\(655\) 19.1896i 0.749801i
\(656\) −5.75379 + 1.05171i −0.224648 + 0.0410622i
\(657\) 6.67026i 0.260232i
\(658\) 4.49242 22.9354i 0.175133 0.894113i
\(659\) 26.7963i 1.04384i 0.852995 + 0.521919i \(0.174783\pi\)
−0.852995 + 0.521919i \(0.825217\pi\)
\(660\) 4.00000 4.79741i 0.155700 0.186739i
\(661\) 8.54312i 0.332289i 0.986101 + 0.166144i \(0.0531318\pi\)
−0.986101 + 0.166144i \(0.946868\pi\)
\(662\) 10.5616 + 22.5571i 0.410486 + 0.876708i
\(663\) −9.75379 −0.378806
\(664\) 7.36932 28.0281i 0.285985 1.08770i
\(665\) −50.7386 37.0970i −1.96756 1.43856i
\(666\) −1.43845 + 0.673500i −0.0557387 + 0.0260976i
\(667\) 1.87285i 0.0725171i
\(668\) 18.2462 21.8836i 0.705967 0.846704i
\(669\) −27.1231 −1.04864
\(670\) −46.7386 + 21.8836i −1.80567 + 0.845439i
\(671\) −4.49242 −0.173428
\(672\) 14.9654 + 0.189103i 0.577304 + 0.00729480i
\(673\) −27.8617 −1.07399 −0.536996 0.843585i \(-0.680441\pi\)
−0.536996 + 0.843585i \(0.680441\pi\)
\(674\) −10.5616 + 4.94506i −0.406816 + 0.190477i
\(675\) 6.12311 0.235678
\(676\) 12.1577 14.5813i 0.467603 0.560821i
\(677\) 9.18425i 0.352979i 0.984302 + 0.176490i \(0.0564742\pi\)
−0.984302 + 0.176490i \(0.943526\pi\)
\(678\) −5.43845 + 2.54635i −0.208862 + 0.0977921i
\(679\) 22.2462 + 16.2651i 0.853731 + 0.624197i
\(680\) −12.4924 + 47.5130i −0.479063 + 1.82204i
\(681\) 16.4924 0.631991
\(682\) 0 0
\(683\) 32.1843i 1.23150i 0.787942 + 0.615750i \(0.211147\pi\)
−0.787942 + 0.615750i \(0.788853\pi\)
\(684\) 9.12311 10.9418i 0.348831 0.418371i
\(685\) 0.821147i 0.0313744i
\(686\) −26.0194 + 2.99838i −0.993426 + 0.114479i
\(687\) 5.61856i 0.214361i
\(688\) 35.6847 6.52262i 1.36046 0.248672i
\(689\) 22.9354i 0.873767i
\(690\) 4.00000 1.87285i 0.152277 0.0712983i
\(691\) 12.0000 0.456502 0.228251 0.973602i \(-0.426699\pi\)
0.228251 + 0.973602i \(0.426699\pi\)
\(692\) −25.6155 21.3578i −0.973756 0.811901i
\(693\) −2.00000 1.46228i −0.0759737 0.0555474i
\(694\) −12.0691 25.7770i −0.458138 0.978481i
\(695\) 40.0216i 1.51811i
\(696\) −1.43845 + 5.47091i −0.0545242 + 0.207374i
\(697\) −7.61553 −0.288459
\(698\) 13.1231 + 28.0281i 0.496717 + 1.06088i
\(699\) −22.4924 −0.850742
\(700\) −7.84233 31.4370i −0.296412 1.18821i
\(701\) −34.0000 −1.28416 −0.642081 0.766637i \(-0.721929\pi\)
−0.642081 + 0.766637i \(0.721929\pi\)
\(702\) 1.12311 + 2.39871i 0.0423889 + 0.0905333i
\(703\) 8.00000 0.301726
\(704\) 3.68466 6.52262i 0.138871 0.245830i
\(705\) 20.8319i 0.784576i
\(706\) 17.3693 + 37.0970i 0.653703 + 1.39616i
\(707\) −29.3693 21.4731i −1.10455 0.807578i
\(708\) −5.12311 + 6.14441i −0.192538 + 0.230921i
\(709\) 6.00000 0.225335 0.112667 0.993633i \(-0.464061\pi\)
0.112667 + 0.993633i \(0.464061\pi\)
\(710\) −16.4924 + 7.72197i −0.618950 + 0.289800i
\(711\) 2.39871i 0.0899585i
\(712\) −4.00000 1.05171i −0.149906 0.0394143i
\(713\) 0 0
\(714\) 19.1231 + 3.74571i 0.715664 + 0.140180i
\(715\) 5.84912i 0.218745i
\(716\) −24.8078 20.6843i −0.927110 0.773008i
\(717\) 16.1498i 0.603126i
\(718\) −13.6847 29.2274i −0.510707 1.09076i
\(719\) 28.4924 1.06259 0.531294 0.847187i \(-0.321706\pi\)
0.531294 + 0.847187i \(0.321706\pi\)
\(720\) 13.1231 2.39871i 0.489069 0.0893945i
\(721\) 12.4924 17.0862i 0.465242 0.636325i
\(722\) −40.6501 + 19.0329i −1.51284 + 0.708332i
\(723\) 23.7565i 0.883514i
\(724\) −2.87689 2.39871i −0.106919 0.0891472i
\(725\) 12.2462 0.454813
\(726\) 12.9654 6.07059i 0.481192 0.225301i
\(727\) 32.9848 1.22334 0.611670 0.791113i \(-0.290498\pi\)
0.611670 + 0.791113i \(0.290498\pi\)
\(728\) 10.8769 8.83841i 0.403125 0.327573i
\(729\) 1.00000 0.0370370
\(730\) 28.4924 13.3405i 1.05455 0.493755i
\(731\) 47.2311 1.74690
\(732\) −7.36932 6.14441i −0.272378 0.227104i
\(733\) 36.0453i 1.33136i 0.746235 + 0.665682i \(0.231859\pi\)
−0.746235 + 0.665682i \(0.768141\pi\)
\(734\) 42.7386 20.0108i 1.57751 0.738612i
\(735\) −22.2462 + 7.08084i −0.820564 + 0.261181i
\(736\) 4.31534 3.07221i 0.159066 0.113243i
\(737\) 10.2462 0.377424
\(738\) 0.876894 + 1.87285i 0.0322789 + 0.0689407i
\(739\) 36.5712i 1.34529i 0.739964 + 0.672646i \(0.234842\pi\)
−0.739964 + 0.672646i \(0.765158\pi\)
\(740\) 5.75379 + 4.79741i 0.211513 + 0.176356i
\(741\) 13.3405i 0.490077i
\(742\) 8.80776 44.9666i 0.323343 1.65078i
\(743\) 35.1089i 1.28802i −0.765017 0.644010i \(-0.777269\pi\)
0.765017 0.644010i \(-0.222731\pi\)
\(744\) 0 0
\(745\) 33.3513i 1.22190i
\(746\) 12.8078 5.99676i 0.468926 0.219557i
\(747\) −10.2462 −0.374889
\(748\) 6.24621 7.49141i 0.228384 0.273913i
\(749\) 20.2462 + 14.8028i 0.739780 + 0.540883i
\(750\) −2.24621 4.79741i −0.0820200 0.175177i
\(751\) 28.8492i 1.05272i 0.850261 + 0.526361i \(0.176444\pi\)
−0.850261 + 0.526361i \(0.823556\pi\)
\(752\) −4.49242 24.5776i −0.163822 0.896254i
\(753\) 5.75379 0.209680
\(754\) 2.24621 + 4.79741i 0.0818022 + 0.174711i
\(755\) 30.2462 1.10077
\(756\) −1.28078 5.13416i −0.0465814 0.186728i
\(757\) −34.9848 −1.27155 −0.635773 0.771876i \(-0.719319\pi\)
−0.635773 + 0.771876i \(0.719319\pi\)
\(758\) 15.0540 + 32.1520i 0.546785 + 1.16781i
\(759\) −0.876894 −0.0318292
\(760\) −64.9848 17.0862i −2.35725 0.619783i
\(761\) 29.7856i 1.07973i −0.841752 0.539864i \(-0.818476\pi\)
0.841752 0.539864i \(-0.181524\pi\)
\(762\) −5.93087 12.6670i −0.214853 0.458878i
\(763\) 12.8769 17.6121i 0.466175 0.637600i
\(764\) 4.31534 + 3.59806i 0.156124 + 0.130173i
\(765\) 17.3693 0.627989
\(766\) 12.4924 5.84912i 0.451370 0.211337i
\(767\) 7.49141i 0.270499i
\(768\) 14.9654 5.66001i 0.540019 0.204238i
\(769\) 32.5302i 1.17307i −0.809925 0.586534i \(-0.800492\pi\)
0.809925 0.586534i \(-0.199508\pi\)
\(770\) −2.24621 + 11.4677i −0.0809478 + 0.413266i
\(771\) 2.28343i 0.0822356i
\(772\) −19.6847 + 23.6089i −0.708466 + 0.849701i
\(773\) 3.33513i 0.119956i 0.998200 + 0.0599782i \(0.0191031\pi\)
−0.998200 + 0.0599782i \(0.980897\pi\)
\(774\) −5.43845 11.6153i −0.195481 0.417504i
\(775\) 0 0
\(776\) 28.4924 + 7.49141i 1.02282 + 0.268926i
\(777\) 1.75379 2.39871i 0.0629168 0.0860531i
\(778\) 20.8078 9.74247i 0.745994 0.349284i
\(779\) 10.4160i 0.373191i
\(780\) 8.00000 9.59482i 0.286446 0.343550i
\(781\) 3.61553 0.129374
\(782\) 6.24621 2.92456i 0.223364 0.104582i
\(783\) 2.00000 0.0714742
\(784\) −24.7192 + 13.1514i −0.882829 + 0.469694i
\(785\) 72.9848 2.60494
\(786\) 7.36932 3.45041i 0.262855 0.123072i
\(787\) −44.9848 −1.60354 −0.801768 0.597635i \(-0.796107\pi\)
−0.801768 + 0.597635i \(0.796107\pi\)
\(788\) −20.8078 + 24.9559i −0.741246 + 0.889015i
\(789\) 24.6929i 0.879091i
\(790\) −10.2462 + 4.79741i −0.364544 + 0.170684i
\(791\) 6.63068 9.06897i 0.235760 0.322455i
\(792\) −2.56155 0.673500i −0.0910208 0.0239318i
\(793\) −8.98485 −0.319061
\(794\) −10.8769 23.2306i −0.386007 0.824425i
\(795\) 40.8427i 1.44854i
\(796\) −4.00000 + 4.79741i −0.141776 + 0.170040i
\(797\) 39.6110i 1.40309i 0.712623 + 0.701547i \(0.247507\pi\)
−0.712623 + 0.701547i \(0.752493\pi\)
\(798\) −5.12311 + 26.1552i −0.181356 + 0.925884i
\(799\) 32.5302i 1.15083i
\(800\) −20.0885 28.2172i −0.710237 0.997627i
\(801\) 1.46228i 0.0516671i
\(802\) −10.5616 + 4.94506i −0.372941 + 0.174616i
\(803\) −6.24621 −0.220424
\(804\) 16.8078 + 14.0140i 0.592764 + 0.494237i
\(805\) −4.87689 + 6.67026i −0.171888 + 0.235096i
\(806\) 0 0
\(807\) 10.8265i 0.381112i
\(808\) −37.6155 9.89012i −1.32331 0.347933i
\(809\) 22.4924 0.790791 0.395396 0.918511i \(-0.370607\pi\)
0.395396 + 0.918511i \(0.370607\pi\)
\(810\) −2.00000 4.27156i −0.0702728 0.150087i
\(811\) 0.492423 0.0172913 0.00864565 0.999963i \(-0.497248\pi\)
0.00864565 + 0.999963i \(0.497248\pi\)
\(812\) −2.56155 10.2683i −0.0898929 0.360347i
\(813\) 28.4924 0.999273
\(814\) −0.630683 1.34700i −0.0221054 0.0472123i
\(815\) −52.4924 −1.83873
\(816\) 20.4924 3.74571i 0.717378 0.131126i
\(817\) 64.5992i 2.26004i
\(818\) 0.492423 + 1.05171i 0.0172171 + 0.0367720i
\(819\) −4.00000 2.92456i −0.139771 0.102192i
\(820\) 6.24621 7.49141i 0.218127 0.261611i
\(821\) −57.2311 −1.99738 −0.998689 0.0511922i \(-0.983698\pi\)
−0.998689 + 0.0511922i \(0.983698\pi\)
\(822\) 0.315342 0.147647i 0.0109988 0.00514978i
\(823\) 13.0452i 0.454728i 0.973810 + 0.227364i \(0.0730108\pi\)
−0.973810 + 0.227364i \(0.926989\pi\)
\(824\) 5.75379 21.8836i 0.200443 0.762353i
\(825\) 5.73384i 0.199627i
\(826\) 2.87689 14.6875i 0.100100 0.511044i
\(827\) 55.9408i 1.94525i 0.232373 + 0.972627i \(0.425351\pi\)
−0.232373 + 0.972627i \(0.574649\pi\)
\(828\) −1.43845 1.19935i −0.0499895 0.0416804i
\(829\) 21.0625i 0.731531i 0.930707 + 0.365765i \(0.119193\pi\)
−0.930707 + 0.365765i \(0.880807\pi\)
\(830\) 20.4924 + 43.7673i 0.711302 + 1.51918i
\(831\) 5.12311 0.177719
\(832\) 7.36932 13.0452i 0.255485 0.452262i
\(833\) −34.7386 + 11.0571i −1.20362 + 0.383106i
\(834\) −15.3693 + 7.19612i −0.532196 + 0.249181i
\(835\) 47.5130i 1.64426i
\(836\) 10.2462 + 8.54312i 0.354373 + 0.295470i
\(837\) 0 0
\(838\) 21.1231 9.89012i 0.729686 0.341648i
\(839\) −42.7386 −1.47550 −0.737751 0.675073i \(-0.764112\pi\)
−0.737751 + 0.675073i \(0.764112\pi\)
\(840\) −19.3693 + 15.7392i −0.668305 + 0.543055i
\(841\) −25.0000 −0.862069
\(842\) −13.9309 + 6.52262i −0.480089 + 0.224784i
\(843\) −16.2462 −0.559549
\(844\) 19.6847 + 16.4127i 0.677574 + 0.564950i
\(845\) 31.6585i 1.08908i
\(846\) −8.00000 + 3.74571i −0.275046 + 0.128780i
\(847\) −15.8078 + 21.6207i −0.543161 + 0.742897i
\(848\) −8.80776 48.1865i −0.302460 1.65473i
\(849\) −8.87689 −0.304654
\(850\) −19.1231 40.8427i −0.655917 1.40089i
\(851\) 1.05171i 0.0360520i
\(852\) 5.93087 + 4.94506i 0.203188 + 0.169415i
\(853\) 50.2070i 1.71905i 0.511090 + 0.859527i \(0.329242\pi\)
−0.511090 + 0.859527i \(0.670758\pi\)
\(854\) 17.6155 + 3.45041i 0.602791 + 0.118071i
\(855\) 23.7565i 0.812455i
\(856\) 25.9309 + 6.81791i 0.886299 + 0.233031i
\(857\) 56.4667i 1.92887i −0.264329 0.964433i \(-0.585150\pi\)
0.264329 0.964433i \(-0.414850\pi\)
\(858\) −2.24621 + 1.05171i −0.0766844 + 0.0359046i
\(859\) −25.8617 −0.882391 −0.441196 0.897411i \(-0.645445\pi\)
−0.441196 + 0.897411i \(0.645445\pi\)
\(860\) −38.7386 + 46.4613i −1.32098 + 1.58432i
\(861\) −3.12311 2.28343i −0.106435 0.0778190i
\(862\) 2.80776 + 5.99676i 0.0956328 + 0.204251i
\(863\) 8.65840i 0.294735i 0.989082 + 0.147368i \(0.0470800\pi\)
−0.989082 + 0.147368i \(0.952920\pi\)
\(864\) −3.28078 4.60831i −0.111614 0.156778i
\(865\) 55.6155 1.89098
\(866\) 8.00000 + 17.0862i 0.271851 + 0.580614i
\(867\) 10.1231 0.343799
\(868\) 0 0
\(869\) 2.24621 0.0761975
\(870\) −4.00000 8.54312i −0.135613 0.289639i
\(871\) 20.4924 0.694359
\(872\) 5.93087 22.5571i 0.200845 0.763881i
\(873\) 10.4160i 0.352527i
\(874\) 4.00000 + 8.54312i 0.135302 + 0.288975i
\(875\) 8.00000 + 5.84912i 0.270449 + 0.197736i
\(876\) −10.2462 8.54312i −0.346187 0.288645i
\(877\) 36.2462 1.22395 0.611974 0.790878i \(-0.290376\pi\)
0.611974 + 0.790878i \(0.290376\pi\)
\(878\) 8.49242 3.97626i 0.286605 0.134192i
\(879\) 13.7511i 0.463813i
\(880\) 2.24621 + 12.2888i 0.0757198 + 0.414256i
\(881\) 46.8719i 1.57915i 0.613652 + 0.789577i \(0.289700\pi\)
−0.613652 + 0.789577i \(0.710300\pi\)
\(882\) 6.71922 + 7.26994i 0.226248 + 0.244792i
\(883\) 18.6638i 0.628087i 0.949409 + 0.314043i \(0.101684\pi\)
−0.949409 + 0.314043i \(0.898316\pi\)
\(884\) 12.4924 14.9828i 0.420166 0.503927i
\(885\) 13.3405i 0.448437i
\(886\) −11.3002 24.1347i −0.379637 0.810821i
\(887\) −26.7386 −0.897795 −0.448898 0.893583i \(-0.648183\pi\)
−0.448898 + 0.893583i \(0.648183\pi\)
\(888\) 0.807764 3.07221i 0.0271068 0.103096i
\(889\) 21.1231 + 15.4439i 0.708446 + 0.517973i
\(890\) 6.24621 2.92456i 0.209373 0.0980314i
\(891\) 0.936426i 0.0313715i
\(892\) 34.7386 41.6639i 1.16314 1.39501i
\(893\) 44.4924 1.48888
\(894\) −12.8078 + 5.99676i −0.428356 + 0.200562i
\(895\) 53.8617 1.80040
\(896\) −19.4579 + 22.7462i −0.650041 + 0.759899i
\(897\) −1.75379 −0.0585573
\(898\) −15.0540 + 7.04847i −0.502358 + 0.235210i
\(899\) 0 0
\(900\) −7.84233 + 9.40572i −0.261411 + 0.313524i
\(901\) 63.7781i 2.12476i
\(902\) −1.75379 + 0.821147i −0.0583948 + 0.0273412i
\(903\) 19.3693 + 14.1617i 0.644571 + 0.471271i
\(904\) 3.05398 11.6153i 0.101574 0.386320i
\(905\) 6.24621 0.207631
\(906\) −5.43845 11.6153i −0.180680 0.385893i
\(907\) 38.4440i 1.27651i −0.769824 0.638256i \(-0.779656\pi\)
0.769824 0.638256i \(-0.220344\pi\)
\(908\) −21.1231 + 25.3341i −0.700995 + 0.840740i
\(909\) 13.7511i 0.456095i
\(910\) −4.49242 + 22.9354i −0.148922 + 0.760299i
\(911\) 5.73384i 0.189971i 0.995479 + 0.0949853i \(0.0302804\pi\)
−0.995479 + 0.0949853i \(0.969720\pi\)
\(912\) 5.12311 + 28.0281i 0.169643 + 0.928102i
\(913\) 9.59482i 0.317542i
\(914\) −0.315342 + 0.147647i −0.0104306 + 0.00488373i
\(915\) 16.0000 0.528944
\(916\) 8.63068 + 7.19612i 0.285166 + 0.237766i
\(917\) −8.98485 + 12.2888i −0.296706 + 0.405813i
\(918\) −3.12311 6.67026i −0.103078 0.220152i
\(919\) 9.06897i 0.299158i −0.988750 0.149579i \(-0.952208\pi\)
0.988750 0.149579i \(-0.0477918\pi\)
\(920\) −2.24621 + 8.54312i −0.0740554 + 0.281658i
\(921\) −19.6155 −0.646354
\(922\) 3.75379 + 8.01726i 0.123624 + 0.264035i
\(923\) 7.23106 0.238013
\(924\) 4.80776 1.19935i 0.158164 0.0394558i
\(925\) −6.87689 −0.226111
\(926\) −23.5464 50.2899i −0.773783 1.65263i
\(927\) −8.00000 −0.262754
\(928\) −6.56155 9.21662i −0.215394 0.302550i
\(929\) 3.56569i 0.116987i −0.998288 0.0584933i \(-0.981370\pi\)
0.998288 0.0584933i \(-0.0186296\pi\)
\(930\) 0 0
\(931\) −15.1231 47.5130i −0.495640 1.55718i
\(932\) 28.8078 34.5507i 0.943630 1.13174i
\(933\) −8.00000 −0.261908
\(934\) −43.8617 + 20.5366i −1.43520 + 0.671980i
\(935\) 16.2651i 0.531925i
\(936\) −5.12311 1.34700i −0.167454 0.0440281i
\(937\) 28.7845i 0.940348i 0.882574 + 0.470174i \(0.155809\pi\)
−0.882574 + 0.470174i \(0.844191\pi\)
\(938\) −40.1771 7.86962i −1.31183 0.256952i
\(939\) 22.9354i 0.748467i
\(940\) 32.0000 + 26.6811i 1.04372 + 0.870240i
\(941\) 53.7727i 1.75294i −0.481457 0.876470i \(-0.659892\pi\)
0.481457 0.876470i \(-0.340108\pi\)
\(942\) −13.1231 28.0281i −0.427574 0.913203i
\(943\) −1.36932 −0.0445911
\(944\) −2.87689 15.7392i −0.0936349 0.512268i
\(945\) 7.12311 + 5.20798i 0.231715 + 0.169416i
\(946\) 10.8769 5.09271i 0.353638 0.165578i
\(947\) 48.6800i 1.58189i −0.611889 0.790943i \(-0.709590\pi\)
0.611889 0.790943i \(-0.290410\pi\)
\(948\) 3.68466 + 3.07221i 0.119672 + 0.0997806i
\(949\) −12.4924 −0.405521
\(950\) 55.8617 26.1552i 1.81239 0.848587i
\(951\) 14.4924 0.469949
\(952\) −30.2462 + 24.5776i −0.980285 + 0.796566i
\(953\) −21.2311 −0.687741 −0.343871 0.939017i \(-0.611738\pi\)
−0.343871 + 0.939017i \(0.611738\pi\)
\(954\) −15.6847 + 7.34376i −0.507810 + 0.237763i
\(955\) −9.36932 −0.303184
\(956\) 24.8078 + 20.6843i 0.802340 + 0.668978i
\(957\) 1.87285i 0.0605407i
\(958\) −16.0000 + 7.49141i −0.516937 + 0.242037i
\(959\) −0.384472 + 0.525853i −0.0124152 + 0.0169807i
\(960\) −13.1231 + 23.2306i −0.423546 + 0.749766i
\(961\) −31.0000 −1.00000
\(962\) −1.26137 2.69400i −0.0406681 0.0868580i
\(963\) 9.47954i 0.305474i
\(964\) 36.4924 + 30.4268i 1.17534 + 0.979980i
\(965\) 51.2587i 1.65008i
\(966\) 3.43845 + 0.673500i 0.110630 + 0.0216695i
\(967\) 8.83841i 0.284224i 0.989851 + 0.142112i \(0.0453893\pi\)
−0.989851 + 0.142112i \(0.954611\pi\)
\(968\) −7.28078 + 27.6913i −0.234013 + 0.890032i
\(969\) 37.0970i 1.19173i
\(970\) −44.4924 + 20.8319i −1.42857 + 0.668873i
\(971\) −12.0000 −0.385098 −0.192549 0.981287i \(-0.561675\pi\)
−0.192549 + 0.981287i \(0.561675\pi\)
\(972\) −1.28078 + 1.53610i −0.0410809 + 0.0492705i
\(973\) 18.7386 25.6294i 0.600733 0.821639i
\(974\) 0.946025 + 2.02050i 0.0303126 + 0.0647410i
\(975\) 11.4677i 0.367260i
\(976\) 18.8769 3.45041i 0.604235 0.110445i
\(977\) −11.2614 −0.360283 −0.180142 0.983641i \(-0.557656\pi\)
−0.180142 + 0.983641i \(0.557656\pi\)
\(978\) 9.43845 + 20.1584i 0.301808 + 0.644596i
\(979\) −1.36932 −0.0437636
\(980\) 17.6155 43.2414i 0.562707 1.38130i
\(981\) −8.24621 −0.263281
\(982\) −6.80776 14.5399i −0.217244 0.463986i
\(983\) 5.26137 0.167812 0.0839058 0.996474i \(-0.473261\pi\)
0.0839058 + 0.996474i \(0.473261\pi\)
\(984\) −4.00000 1.05171i −0.127515 0.0335272i
\(985\) 54.1833i 1.72642i
\(986\) −6.24621 13.3405i −0.198920 0.424849i
\(987\) 9.75379 13.3405i 0.310467 0.424634i
\(988\) 20.4924 + 17.0862i 0.651951 + 0.543586i
\(989\) 8.49242 0.270043
\(990\) 4.00000 1.87285i 0.127128 0.0595232i
\(991\) 0.525853i 0.0167043i 0.999965 + 0.00835213i \(0.00265860\pi\)
−0.999965 + 0.00835213i \(0.997341\pi\)
\(992\) 0 0
\(993\) 17.6121i 0.558903i
\(994\) −14.1771 2.77691i −0.449670 0.0880783i
\(995\) 10.4160i 0.330208i
\(996\) 13.1231 15.7392i 0.415822 0.498717i
\(997\) 19.7802i 0.626446i −0.949680 0.313223i \(-0.898591\pi\)
0.949680 0.313223i \(-0.101409\pi\)
\(998\) 8.31534 + 17.7597i 0.263218 + 0.562175i
\(999\) −1.12311 −0.0355335
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 84.2.b.a.55.2 yes 4
3.2 odd 2 252.2.b.e.55.3 4
4.3 odd 2 84.2.b.b.55.1 yes 4
7.2 even 3 588.2.o.c.31.4 8
7.3 odd 6 588.2.o.a.19.2 8
7.4 even 3 588.2.o.c.19.2 8
7.5 odd 6 588.2.o.a.31.4 8
7.6 odd 2 84.2.b.b.55.2 yes 4
8.3 odd 2 1344.2.b.e.895.1 4
8.5 even 2 1344.2.b.f.895.1 4
12.11 even 2 252.2.b.d.55.4 4
21.20 even 2 252.2.b.d.55.3 4
24.5 odd 2 4032.2.b.n.3583.4 4
24.11 even 2 4032.2.b.j.3583.4 4
28.3 even 6 588.2.o.c.19.4 8
28.11 odd 6 588.2.o.a.19.4 8
28.19 even 6 588.2.o.c.31.2 8
28.23 odd 6 588.2.o.a.31.2 8
28.27 even 2 inner 84.2.b.a.55.1 4
56.13 odd 2 1344.2.b.e.895.4 4
56.27 even 2 1344.2.b.f.895.4 4
84.83 odd 2 252.2.b.e.55.4 4
168.83 odd 2 4032.2.b.n.3583.1 4
168.125 even 2 4032.2.b.j.3583.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
84.2.b.a.55.1 4 28.27 even 2 inner
84.2.b.a.55.2 yes 4 1.1 even 1 trivial
84.2.b.b.55.1 yes 4 4.3 odd 2
84.2.b.b.55.2 yes 4 7.6 odd 2
252.2.b.d.55.3 4 21.20 even 2
252.2.b.d.55.4 4 12.11 even 2
252.2.b.e.55.3 4 3.2 odd 2
252.2.b.e.55.4 4 84.83 odd 2
588.2.o.a.19.2 8 7.3 odd 6
588.2.o.a.19.4 8 28.11 odd 6
588.2.o.a.31.2 8 28.23 odd 6
588.2.o.a.31.4 8 7.5 odd 6
588.2.o.c.19.2 8 7.4 even 3
588.2.o.c.19.4 8 28.3 even 6
588.2.o.c.31.2 8 28.19 even 6
588.2.o.c.31.4 8 7.2 even 3
1344.2.b.e.895.1 4 8.3 odd 2
1344.2.b.e.895.4 4 56.13 odd 2
1344.2.b.f.895.1 4 8.5 even 2
1344.2.b.f.895.4 4 56.27 even 2
4032.2.b.j.3583.1 4 168.125 even 2
4032.2.b.j.3583.4 4 24.11 even 2
4032.2.b.n.3583.1 4 168.83 odd 2
4032.2.b.n.3583.4 4 24.5 odd 2