Properties

Label 76.3.g.b.11.1
Level $76$
Weight $3$
Character 76.11
Analytic conductor $2.071$
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] = [76,3,Mod(7,76)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(76, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 2]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("76.7");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 76.g (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.07085000914\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-10})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 10x^{2} + 100 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 11.1
Root \(-2.73861 - 1.58114i\) of defining polynomial
Character \(\chi\) \(=\) 76.11
Dual form 76.3.g.b.7.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.00000 q^{2} +(-4.23861 - 2.44716i) q^{3} +4.00000 q^{4} +(1.73861 - 3.01137i) q^{5} +(-8.47723 - 4.89433i) q^{6} -10.0905i q^{7} +8.00000 q^{8} +(7.47723 + 12.9509i) q^{9} +O(q^{10})\) \(q+2.00000 q^{2} +(-4.23861 - 2.44716i) q^{3} +4.00000 q^{4} +(1.73861 - 3.01137i) q^{5} +(-8.47723 - 4.89433i) q^{6} -10.0905i q^{7} +8.00000 q^{8} +(7.47723 + 12.9509i) q^{9} +(3.47723 - 6.02273i) q^{10} +17.5434i q^{11} +(-16.9545 - 9.78866i) q^{12} +(-3.00000 - 5.19615i) q^{13} -20.1810i q^{14} +(-14.7386 + 8.50934i) q^{15} +16.0000 q^{16} +(-2.52277 + 4.36957i) q^{17} +(14.9545 + 25.9019i) q^{18} +(2.28416 + 18.8622i) q^{19} +(6.95445 - 12.0455i) q^{20} +(-24.6931 + 42.7696i) q^{21} +35.0869i q^{22} +(27.6475 - 15.9623i) q^{23} +(-33.9089 - 19.5773i) q^{24} +(6.45445 + 11.1794i) q^{25} +(-6.00000 - 10.3923i) q^{26} -29.1430i q^{27} -40.3619i q^{28} +(-3.73861 - 6.47547i) q^{29} +(-29.4772 + 17.0187i) q^{30} -4.81544i q^{31} +32.0000 q^{32} +(42.9317 - 74.3598i) q^{33} +(-5.04555 + 8.73915i) q^{34} +(-30.3861 - 17.5434i) q^{35} +(29.9089 + 51.8037i) q^{36} -51.3861 q^{37} +(4.56832 + 37.7244i) q^{38} +29.3660i q^{39} +(13.9089 - 24.0909i) q^{40} +(17.4545 - 30.2320i) q^{41} +(-49.3861 + 85.5393i) q^{42} +(9.38613 + 5.41908i) q^{43} +70.1738i q^{44} +52.0000 q^{45} +(55.2950 - 31.9246i) q^{46} +(-19.1703 + 11.0680i) q^{47} +(-67.8178 - 39.1546i) q^{48} -52.8178 q^{49} +(12.9089 + 22.3589i) q^{50} +(21.3861 - 12.3473i) q^{51} +(-12.0000 - 20.7846i) q^{52} +(20.0455 + 34.7199i) q^{53} -58.2861i q^{54} +(52.8297 + 30.5012i) q^{55} -80.7238i q^{56} +(36.4772 - 85.5393i) q^{57} +(-7.47723 - 12.9509i) q^{58} +(-16.7614 - 9.67719i) q^{59} +(-58.9545 + 34.0374i) q^{60} +(-8.26139 - 14.3091i) q^{61} -9.63087i q^{62} +(130.681 - 75.4488i) q^{63} +64.0000 q^{64} -20.8634 q^{65} +(85.8634 - 148.720i) q^{66} +(-83.0109 + 47.9263i) q^{67} +(-10.0911 + 17.4783i) q^{68} -156.249 q^{69} +(-60.7723 - 35.0869i) q^{70} +(12.6594 + 7.30892i) q^{71} +(59.8178 + 103.607i) q^{72} +(-17.4545 + 30.2320i) q^{73} -102.772 q^{74} -63.1804i q^{75} +(9.13665 + 75.4488i) q^{76} +177.022 q^{77} +58.7319i q^{78} +(-68.0911 - 39.3124i) q^{79} +(27.8178 - 48.1819i) q^{80} +(-4.02277 + 6.96765i) q^{81} +(34.9089 - 60.4640i) q^{82} +92.9922i q^{83} +(-98.7723 + 171.079i) q^{84} +(8.77226 + 15.1940i) q^{85} +(18.7723 + 10.8382i) q^{86} +36.5960i q^{87} +140.348i q^{88} +(56.2495 + 97.4270i) q^{89} +104.000 q^{90} +(-52.4317 + 30.2714i) q^{91} +(110.590 - 63.8492i) q^{92} +(-11.7842 + 20.4108i) q^{93} +(-38.3406 + 22.1359i) q^{94} +(60.7723 + 25.9156i) q^{95} +(-135.636 - 78.3093i) q^{96} +(-63.9772 + 110.812i) q^{97} -105.636 q^{98} +(-227.204 + 131.176i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 8 q^{2} - 6 q^{3} + 16 q^{4} - 4 q^{5} - 12 q^{6} + 32 q^{8} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 8 q^{2} - 6 q^{3} + 16 q^{4} - 4 q^{5} - 12 q^{6} + 32 q^{8} + 8 q^{9} - 8 q^{10} - 24 q^{12} - 12 q^{13} - 48 q^{15} + 64 q^{16} - 32 q^{17} + 16 q^{18} + 42 q^{19} - 16 q^{20} - 44 q^{21} + 12 q^{23} - 48 q^{24} - 18 q^{25} - 24 q^{26} - 4 q^{29} - 96 q^{30} + 128 q^{32} + 106 q^{33} - 64 q^{34} - 12 q^{35} + 32 q^{36} - 96 q^{37} + 84 q^{38} - 32 q^{40} + 26 q^{41} - 88 q^{42} - 72 q^{43} + 208 q^{45} + 24 q^{46} - 96 q^{48} - 36 q^{49} - 36 q^{50} - 24 q^{51} - 48 q^{52} + 124 q^{53} + 288 q^{55} + 124 q^{57} - 8 q^{58} - 78 q^{59} - 192 q^{60} - 44 q^{61} + 216 q^{63} + 256 q^{64} + 48 q^{65} + 212 q^{66} - 102 q^{67} - 128 q^{68} - 384 q^{69} - 24 q^{70} + 204 q^{71} + 64 q^{72} - 26 q^{73} - 192 q^{74} + 168 q^{76} + 248 q^{77} - 360 q^{79} - 64 q^{80} - 38 q^{81} + 52 q^{82} - 176 q^{84} - 184 q^{85} - 144 q^{86} - 16 q^{89} + 416 q^{90} - 144 q^{91} + 48 q^{92} - 80 q^{93} + 24 q^{95} - 192 q^{96} - 234 q^{97} - 72 q^{98} - 624 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 1.00000
\(3\) −4.23861 2.44716i −1.41287 0.815721i −0.417213 0.908809i \(-0.636993\pi\)
−0.995658 + 0.0930873i \(0.970326\pi\)
\(4\) 4.00000 1.00000
\(5\) 1.73861 3.01137i 0.347723 0.602273i −0.638122 0.769935i \(-0.720288\pi\)
0.985845 + 0.167662i \(0.0536218\pi\)
\(6\) −8.47723 4.89433i −1.41287 0.815721i
\(7\) 10.0905i 1.44150i −0.693197 0.720749i \(-0.743798\pi\)
0.693197 0.720749i \(-0.256202\pi\)
\(8\) 8.00000 1.00000
\(9\) 7.47723 + 12.9509i 0.830803 + 1.43899i
\(10\) 3.47723 6.02273i 0.347723 0.602273i
\(11\) 17.5434i 1.59486i 0.603413 + 0.797429i \(0.293807\pi\)
−0.603413 + 0.797429i \(0.706193\pi\)
\(12\) −16.9545 9.78866i −1.41287 0.815721i
\(13\) −3.00000 5.19615i −0.230769 0.399704i 0.727265 0.686356i \(-0.240791\pi\)
−0.958035 + 0.286652i \(0.907458\pi\)
\(14\) 20.1810i 1.44150i
\(15\) −14.7386 + 8.50934i −0.982574 + 0.567289i
\(16\) 16.0000 1.00000
\(17\) −2.52277 + 4.36957i −0.148398 + 0.257034i −0.930636 0.365947i \(-0.880745\pi\)
0.782237 + 0.622981i \(0.214078\pi\)
\(18\) 14.9545 + 25.9019i 0.830803 + 1.43899i
\(19\) 2.28416 + 18.8622i 0.120219 + 0.992747i
\(20\) 6.95445 12.0455i 0.347723 0.602273i
\(21\) −24.6931 + 42.7696i −1.17586 + 2.03665i
\(22\) 35.0869i 1.59486i
\(23\) 27.6475 15.9623i 1.20207 0.694013i 0.241052 0.970512i \(-0.422508\pi\)
0.961014 + 0.276499i \(0.0891743\pi\)
\(24\) −33.9089 19.5773i −1.41287 0.815721i
\(25\) 6.45445 + 11.1794i 0.258178 + 0.447177i
\(26\) −6.00000 10.3923i −0.230769 0.399704i
\(27\) 29.1430i 1.07937i
\(28\) 40.3619i 1.44150i
\(29\) −3.73861 6.47547i −0.128918 0.223292i 0.794340 0.607474i \(-0.207817\pi\)
−0.923258 + 0.384182i \(0.874484\pi\)
\(30\) −29.4772 + 17.0187i −0.982574 + 0.567289i
\(31\) 4.81544i 0.155337i −0.996979 0.0776683i \(-0.975252\pi\)
0.996979 0.0776683i \(-0.0247475\pi\)
\(32\) 32.0000 1.00000
\(33\) 42.9317 74.3598i 1.30096 2.25333i
\(34\) −5.04555 + 8.73915i −0.148398 + 0.257034i
\(35\) −30.3861 17.5434i −0.868175 0.501241i
\(36\) 29.9089 + 51.8037i 0.830803 + 1.43899i
\(37\) −51.3861 −1.38881 −0.694407 0.719582i \(-0.744333\pi\)
−0.694407 + 0.719582i \(0.744333\pi\)
\(38\) 4.56832 + 37.7244i 0.120219 + 0.992747i
\(39\) 29.3660i 0.752974i
\(40\) 13.9089 24.0909i 0.347723 0.602273i
\(41\) 17.4545 30.2320i 0.425718 0.737366i −0.570769 0.821111i \(-0.693355\pi\)
0.996487 + 0.0837450i \(0.0266881\pi\)
\(42\) −49.3861 + 85.5393i −1.17586 + 2.03665i
\(43\) 9.38613 + 5.41908i 0.218282 + 0.126025i 0.605155 0.796108i \(-0.293111\pi\)
−0.386872 + 0.922133i \(0.626445\pi\)
\(44\) 70.1738i 1.59486i
\(45\) 52.0000 1.15556
\(46\) 55.2950 31.9246i 1.20207 0.694013i
\(47\) −19.1703 + 11.0680i −0.407879 + 0.235489i −0.689878 0.723926i \(-0.742336\pi\)
0.281999 + 0.959415i \(0.409002\pi\)
\(48\) −67.8178 39.1546i −1.41287 0.815721i
\(49\) −52.8178 −1.07791
\(50\) 12.9089 + 22.3589i 0.258178 + 0.447177i
\(51\) 21.3861 12.3473i 0.419336 0.242104i
\(52\) −12.0000 20.7846i −0.230769 0.399704i
\(53\) 20.0455 + 34.7199i 0.378218 + 0.655093i 0.990803 0.135312i \(-0.0432037\pi\)
−0.612585 + 0.790405i \(0.709870\pi\)
\(54\) 58.2861i 1.07937i
\(55\) 52.8297 + 30.5012i 0.960540 + 0.554568i
\(56\) 80.7238i 1.44150i
\(57\) 36.4772 85.5393i 0.639951 1.50069i
\(58\) −7.47723 12.9509i −0.128918 0.223292i
\(59\) −16.7614 9.67719i −0.284091 0.164020i 0.351183 0.936307i \(-0.385780\pi\)
−0.635274 + 0.772287i \(0.719113\pi\)
\(60\) −58.9545 + 34.0374i −0.982574 + 0.567289i
\(61\) −8.26139 14.3091i −0.135433 0.234576i 0.790330 0.612681i \(-0.209909\pi\)
−0.925763 + 0.378105i \(0.876576\pi\)
\(62\) 9.63087i 0.155337i
\(63\) 130.681 75.4488i 2.07430 1.19760i
\(64\) 64.0000 1.00000
\(65\) −20.8634 −0.320975
\(66\) 85.8634 148.720i 1.30096 2.25333i
\(67\) −83.0109 + 47.9263i −1.23897 + 0.715319i −0.968883 0.247518i \(-0.920385\pi\)
−0.270085 + 0.962837i \(0.587052\pi\)
\(68\) −10.0911 + 17.4783i −0.148398 + 0.257034i
\(69\) −156.249 −2.26449
\(70\) −60.7723 35.0869i −0.868175 0.501241i
\(71\) 12.6594 + 7.30892i 0.178302 + 0.102943i 0.586495 0.809953i \(-0.300508\pi\)
−0.408193 + 0.912896i \(0.633841\pi\)
\(72\) 59.8178 + 103.607i 0.830803 + 1.43899i
\(73\) −17.4545 + 30.2320i −0.239102 + 0.414137i −0.960457 0.278429i \(-0.910186\pi\)
0.721355 + 0.692566i \(0.243520\pi\)
\(74\) −102.772 −1.38881
\(75\) 63.1804i 0.842405i
\(76\) 9.13665 + 75.4488i 0.120219 + 0.992747i
\(77\) 177.022 2.29898
\(78\) 58.7319i 0.752974i
\(79\) −68.0911 39.3124i −0.861913 0.497625i 0.00273968 0.999996i \(-0.499128\pi\)
−0.864652 + 0.502371i \(0.832461\pi\)
\(80\) 27.8178 48.1819i 0.347723 0.602273i
\(81\) −4.02277 + 6.96765i −0.0496639 + 0.0860204i
\(82\) 34.9089 60.4640i 0.425718 0.737366i
\(83\) 92.9922i 1.12039i 0.828361 + 0.560194i \(0.189274\pi\)
−0.828361 + 0.560194i \(0.810726\pi\)
\(84\) −98.7723 + 171.079i −1.17586 + 2.03665i
\(85\) 8.77226 + 15.1940i 0.103203 + 0.178753i
\(86\) 18.7723 + 10.8382i 0.218282 + 0.126025i
\(87\) 36.5960i 0.420644i
\(88\) 140.348i 1.59486i
\(89\) 56.2495 + 97.4270i 0.632017 + 1.09468i 0.987139 + 0.159865i \(0.0511059\pi\)
−0.355122 + 0.934820i \(0.615561\pi\)
\(90\) 104.000 1.15556
\(91\) −52.4317 + 30.2714i −0.576172 + 0.332653i
\(92\) 110.590 63.8492i 1.20207 0.694013i
\(93\) −11.7842 + 20.4108i −0.126711 + 0.219471i
\(94\) −38.3406 + 22.1359i −0.407879 + 0.235489i
\(95\) 60.7723 + 25.9156i 0.639708 + 0.272796i
\(96\) −135.636 78.3093i −1.41287 0.815721i
\(97\) −63.9772 + 110.812i −0.659559 + 1.14239i 0.321171 + 0.947021i \(0.395924\pi\)
−0.980730 + 0.195368i \(0.937410\pi\)
\(98\) −105.636 −1.07791
\(99\) −227.204 + 131.176i −2.29499 + 1.32501i
\(100\) 25.8178 + 44.7177i 0.258178 + 0.447177i
\(101\) −80.9425 140.197i −0.801411 1.38809i −0.918687 0.394986i \(-0.870750\pi\)
0.117276 0.993099i \(-0.462584\pi\)
\(102\) 42.7723 24.6946i 0.419336 0.242104i
\(103\) 166.723i 1.61867i −0.587349 0.809334i \(-0.699828\pi\)
0.587349 0.809334i \(-0.300172\pi\)
\(104\) −24.0000 41.5692i −0.230769 0.399704i
\(105\) 85.8634 + 148.720i 0.817746 + 1.41638i
\(106\) 40.0911 + 69.4398i 0.378218 + 0.655093i
\(107\) 181.629i 1.69746i −0.528823 0.848732i \(-0.677367\pi\)
0.528823 0.848732i \(-0.322633\pi\)
\(108\) 116.572i 1.07937i
\(109\) −40.8634 + 70.7774i −0.374893 + 0.649334i −0.990311 0.138867i \(-0.955654\pi\)
0.615418 + 0.788201i \(0.288987\pi\)
\(110\) 105.659 + 61.0025i 0.960540 + 0.554568i
\(111\) 217.806 + 125.750i 1.96222 + 1.13289i
\(112\) 161.448i 1.44150i
\(113\) −27.0911 −0.239744 −0.119872 0.992789i \(-0.538248\pi\)
−0.119872 + 0.992789i \(0.538248\pi\)
\(114\) 72.9545 171.079i 0.639951 1.50069i
\(115\) 111.009i 0.965296i
\(116\) −14.9545 25.9019i −0.128918 0.223292i
\(117\) 44.8634 77.7056i 0.383447 0.664150i
\(118\) −33.5228 19.3544i −0.284091 0.164020i
\(119\) 44.0911 + 25.4560i 0.370513 + 0.213916i
\(120\) −117.909 + 68.0747i −0.982574 + 0.567289i
\(121\) −186.772 −1.54357
\(122\) −16.5228 28.6183i −0.135433 0.234576i
\(123\) −147.965 + 85.4278i −1.20297 + 0.694535i
\(124\) 19.2617i 0.155337i
\(125\) 131.818 1.05454
\(126\) 261.362 150.898i 2.07430 1.19760i
\(127\) −122.204 + 70.5545i −0.962236 + 0.555547i −0.896860 0.442314i \(-0.854158\pi\)
−0.0653753 + 0.997861i \(0.520824\pi\)
\(128\) 128.000 1.00000
\(129\) −26.5228 45.9388i −0.205603 0.356115i
\(130\) −41.7267 −0.320975
\(131\) 117.056 + 67.5826i 0.893560 + 0.515897i 0.875105 0.483932i \(-0.160792\pi\)
0.0184550 + 0.999830i \(0.494125\pi\)
\(132\) 171.727 297.439i 1.30096 2.25333i
\(133\) 190.329 23.0483i 1.43104 0.173295i
\(134\) −166.022 + 95.8527i −1.23897 + 0.715319i
\(135\) −87.7603 50.6685i −0.650077 0.375322i
\(136\) −20.1822 + 34.9566i −0.148398 + 0.257034i
\(137\) 55.5911 + 96.2866i 0.405774 + 0.702822i 0.994411 0.105576i \(-0.0336685\pi\)
−0.588637 + 0.808398i \(0.700335\pi\)
\(138\) −312.499 −2.26449
\(139\) −13.7376 + 7.93139i −0.0988315 + 0.0570604i −0.548601 0.836084i \(-0.684839\pi\)
0.449770 + 0.893145i \(0.351506\pi\)
\(140\) −121.545 70.1738i −0.868175 0.501241i
\(141\) 108.341 0.768373
\(142\) 25.3188 + 14.6178i 0.178302 + 0.102943i
\(143\) 91.1584 52.6303i 0.637471 0.368044i
\(144\) 119.636 + 207.215i 0.830803 + 1.43899i
\(145\) −26.0000 −0.179310
\(146\) −34.9089 + 60.4640i −0.239102 + 0.414137i
\(147\) 223.874 + 129.254i 1.52295 + 0.879278i
\(148\) −205.545 −1.38881
\(149\) 19.7842 34.2672i 0.132780 0.229981i −0.791967 0.610563i \(-0.790943\pi\)
0.924747 + 0.380582i \(0.124276\pi\)
\(150\) 126.361i 0.842405i
\(151\) 4.81544i 0.0318903i −0.999873 0.0159452i \(-0.994924\pi\)
0.999873 0.0159452i \(-0.00507571\pi\)
\(152\) 18.2733 + 150.898i 0.120219 + 0.992747i
\(153\) −75.4534 −0.493160
\(154\) 354.043 2.29898
\(155\) −14.5010 8.37218i −0.0935551 0.0540141i
\(156\) 117.464i 0.752974i
\(157\) −29.0455 + 50.3084i −0.185003 + 0.320435i −0.943578 0.331151i \(-0.892563\pi\)
0.758574 + 0.651587i \(0.225896\pi\)
\(158\) −136.182 78.6248i −0.861913 0.497625i
\(159\) 196.219i 1.23408i
\(160\) 55.6356 96.3637i 0.347723 0.602273i
\(161\) −161.067 278.977i −1.00042 1.73277i
\(162\) −8.04555 + 13.9353i −0.0496639 + 0.0860204i
\(163\) 207.884i 1.27536i −0.770301 0.637680i \(-0.779894\pi\)
0.770301 0.637680i \(-0.220106\pi\)
\(164\) 69.8178 120.928i 0.425718 0.737366i
\(165\) −149.283 258.566i −0.904746 1.56707i
\(166\) 185.984i 1.12039i
\(167\) −103.319 + 59.6512i −0.618676 + 0.357193i −0.776353 0.630298i \(-0.782933\pi\)
0.157678 + 0.987491i \(0.449599\pi\)
\(168\) −197.545 + 342.157i −1.17586 + 2.03665i
\(169\) 66.5000 115.181i 0.393491 0.681547i
\(170\) 17.5445 + 30.3880i 0.103203 + 0.178753i
\(171\) −227.204 + 170.619i −1.32868 + 0.997772i
\(172\) 37.5445 + 21.6763i 0.218282 + 0.126025i
\(173\) 48.1366 83.3751i 0.278247 0.481937i −0.692703 0.721223i \(-0.743580\pi\)
0.970949 + 0.239286i \(0.0769135\pi\)
\(174\) 73.1920i 0.420644i
\(175\) 112.806 65.1285i 0.644605 0.372163i
\(176\) 280.695i 1.59486i
\(177\) 47.3634 + 82.0357i 0.267590 + 0.463479i
\(178\) 112.499 + 194.854i 0.632017 + 1.09468i
\(179\) 205.366i 1.14730i −0.819101 0.573649i \(-0.805527\pi\)
0.819101 0.573649i \(-0.194473\pi\)
\(180\) 208.000 1.15556
\(181\) 107.943 + 186.962i 0.596368 + 1.03294i 0.993352 + 0.115114i \(0.0367233\pi\)
−0.396985 + 0.917825i \(0.629943\pi\)
\(182\) −104.863 + 60.5429i −0.576172 + 0.332653i
\(183\) 80.8679i 0.441901i
\(184\) 221.180 127.698i 1.20207 0.694013i
\(185\) −89.3406 + 154.742i −0.482922 + 0.836446i
\(186\) −23.5683 + 40.8215i −0.126711 + 0.219471i
\(187\) −76.6573 44.2581i −0.409932 0.236675i
\(188\) −76.6812 + 44.2719i −0.407879 + 0.235489i
\(189\) −294.067 −1.55591
\(190\) 121.545 + 51.8312i 0.639708 + 0.272796i
\(191\) 182.548i 0.955748i 0.878428 + 0.477874i \(0.158592\pi\)
−0.878428 + 0.477874i \(0.841408\pi\)
\(192\) −271.271 156.619i −1.41287 0.815721i
\(193\) 50.5228 87.5080i 0.261776 0.453409i −0.704938 0.709269i \(-0.749025\pi\)
0.966714 + 0.255860i \(0.0823585\pi\)
\(194\) −127.954 + 221.624i −0.659559 + 1.14239i
\(195\) 88.4317 + 51.0561i 0.453496 + 0.261826i
\(196\) −211.271 −1.07791
\(197\) 10.1584 0.0515654 0.0257827 0.999668i \(-0.491792\pi\)
0.0257827 + 0.999668i \(0.491792\pi\)
\(198\) −454.408 + 262.353i −2.29499 + 1.32501i
\(199\) 158.976 91.7849i 0.798875 0.461231i −0.0442024 0.999023i \(-0.514075\pi\)
0.843078 + 0.537792i \(0.180741\pi\)
\(200\) 51.6356 + 89.4355i 0.258178 + 0.447177i
\(201\) 469.135 2.33400
\(202\) −161.885 280.393i −0.801411 1.38809i
\(203\) −65.3406 + 37.7244i −0.321875 + 0.185834i
\(204\) 85.5445 49.3891i 0.419336 0.242104i
\(205\) −60.6931 105.123i −0.296064 0.512797i
\(206\) 333.445i 1.61867i
\(207\) 413.453 + 238.707i 1.99736 + 1.15318i
\(208\) −48.0000 83.1384i −0.230769 0.399704i
\(209\) −330.908 + 40.0721i −1.58329 + 0.191732i
\(210\) 171.727 + 297.439i 0.817746 + 1.41638i
\(211\) 255.226 + 147.355i 1.20960 + 0.698363i 0.962672 0.270671i \(-0.0872454\pi\)
0.246928 + 0.969034i \(0.420579\pi\)
\(212\) 80.1822 + 138.880i 0.378218 + 0.655093i
\(213\) −35.7723 61.9594i −0.167945 0.290889i
\(214\) 363.257i 1.69746i
\(215\) 32.6377 18.8434i 0.151803 0.0876436i
\(216\) 233.144i 1.07937i
\(217\) −48.5901 −0.223917
\(218\) −81.7267 + 141.555i −0.374893 + 0.649334i
\(219\) 147.965 85.4278i 0.675641 0.390081i
\(220\) 211.319 + 122.005i 0.960540 + 0.554568i
\(221\) 30.2733 0.136983
\(222\) 435.612 + 251.501i 1.96222 + 1.13289i
\(223\) 28.9425 + 16.7100i 0.129787 + 0.0749327i 0.563488 0.826124i \(-0.309459\pi\)
−0.433701 + 0.901057i \(0.642792\pi\)
\(224\) 322.895i 1.44150i
\(225\) −96.5228 + 167.182i −0.428990 + 0.743033i
\(226\) −54.1822 −0.239744
\(227\) 27.1743i 0.119711i −0.998207 0.0598553i \(-0.980936\pi\)
0.998207 0.0598553i \(-0.0190639\pi\)
\(228\) 145.909 342.157i 0.639951 1.50069i
\(229\) −251.818 −1.09964 −0.549821 0.835283i \(-0.685304\pi\)
−0.549821 + 0.835283i \(0.685304\pi\)
\(230\) 222.018i 0.965296i
\(231\) −750.327 433.201i −3.24817 1.87533i
\(232\) −29.9089 51.8037i −0.128918 0.223292i
\(233\) 82.2723 142.500i 0.353100 0.611587i −0.633691 0.773586i \(-0.718461\pi\)
0.986791 + 0.161999i \(0.0517943\pi\)
\(234\) 89.7267 155.411i 0.383447 0.664150i
\(235\) 76.9717i 0.327539i
\(236\) −67.0455 38.7088i −0.284091 0.164020i
\(237\) 192.408 + 333.260i 0.811848 + 1.40616i
\(238\) 88.1822 + 50.9120i 0.370513 + 0.213916i
\(239\) 119.247i 0.498943i 0.968382 + 0.249471i \(0.0802569\pi\)
−0.968382 + 0.249471i \(0.919743\pi\)
\(240\) −235.818 + 136.149i −0.982574 + 0.567289i
\(241\) 33.1139 + 57.3549i 0.137402 + 0.237987i 0.926512 0.376264i \(-0.122791\pi\)
−0.789110 + 0.614251i \(0.789458\pi\)
\(242\) −373.545 −1.54357
\(243\) −193.046 + 111.455i −0.794426 + 0.458662i
\(244\) −33.0455 57.2366i −0.135433 0.234576i
\(245\) −91.8297 + 159.054i −0.374815 + 0.649199i
\(246\) −295.931 + 170.856i −1.20297 + 0.694535i
\(247\) 91.1584 68.4555i 0.369062 0.277148i
\(248\) 38.5235i 0.155337i
\(249\) 227.567 394.158i 0.913925 1.58296i
\(250\) 263.636 1.05454
\(251\) −161.124 + 93.0248i −0.641927 + 0.370617i −0.785356 0.619044i \(-0.787520\pi\)
0.143429 + 0.989661i \(0.454187\pi\)
\(252\) 522.725 301.795i 2.07430 1.19760i
\(253\) 280.034 + 485.032i 1.10685 + 1.91712i
\(254\) −244.408 + 141.109i −0.962236 + 0.555547i
\(255\) 85.8686i 0.336740i
\(256\) 256.000 1.00000
\(257\) −151.862 263.033i −0.590904 1.02348i −0.994111 0.108367i \(-0.965438\pi\)
0.403207 0.915109i \(-0.367895\pi\)
\(258\) −53.0455 91.8776i −0.205603 0.356115i
\(259\) 518.511i 2.00197i
\(260\) −83.4534 −0.320975
\(261\) 55.9089 96.8371i 0.214210 0.371023i
\(262\) 234.113 + 135.165i 0.893560 + 0.515897i
\(263\) 75.2376 + 43.4384i 0.286074 + 0.165165i 0.636170 0.771549i \(-0.280518\pi\)
−0.350096 + 0.936714i \(0.613851\pi\)
\(264\) 343.453 594.879i 1.30096 2.25333i
\(265\) 139.406 0.526060
\(266\) 380.657 46.0966i 1.43104 0.173295i
\(267\) 550.607i 2.06220i
\(268\) −332.043 + 191.705i −1.23897 + 0.715319i
\(269\) −97.6356 + 169.110i −0.362958 + 0.628661i −0.988446 0.151572i \(-0.951566\pi\)
0.625489 + 0.780233i \(0.284900\pi\)
\(270\) −175.521 101.337i −0.650077 0.375322i
\(271\) −304.010 175.520i −1.12181 0.647676i −0.179946 0.983677i \(-0.557592\pi\)
−0.941862 + 0.336001i \(0.890926\pi\)
\(272\) −40.3644 + 69.9132i −0.148398 + 0.257034i
\(273\) 296.317 1.08541
\(274\) 111.182 + 192.573i 0.405774 + 0.702822i
\(275\) −196.126 + 113.233i −0.713185 + 0.411757i
\(276\) −624.998 −2.26449
\(277\) −115.430 −0.416713 −0.208357 0.978053i \(-0.566811\pi\)
−0.208357 + 0.978053i \(0.566811\pi\)
\(278\) −27.4752 + 15.8628i −0.0988315 + 0.0570604i
\(279\) 62.3644 36.0061i 0.223528 0.129054i
\(280\) −243.089 140.348i −0.868175 0.501241i
\(281\) 11.9990 + 20.7828i 0.0427009 + 0.0739602i 0.886586 0.462564i \(-0.153070\pi\)
−0.843885 + 0.536524i \(0.819737\pi\)
\(282\) 216.681 0.768373
\(283\) −125.237 72.3053i −0.442532 0.255496i 0.262139 0.965030i \(-0.415572\pi\)
−0.704671 + 0.709534i \(0.748905\pi\)
\(284\) 50.6377 + 29.2357i 0.178302 + 0.102943i
\(285\) −194.170 258.566i −0.681299 0.907249i
\(286\) 182.317 105.261i 0.637471 0.368044i
\(287\) −305.055 176.124i −1.06291 0.613672i
\(288\) 239.271 + 414.430i 0.830803 + 1.43899i
\(289\) 131.771 + 228.234i 0.455956 + 0.789739i
\(290\) −52.0000 −0.179310
\(291\) 542.349 313.126i 1.86374 1.07603i
\(292\) −69.8178 + 120.928i −0.239102 + 0.414137i
\(293\) 215.794 0.736498 0.368249 0.929727i \(-0.379957\pi\)
0.368249 + 0.929727i \(0.379957\pi\)
\(294\) 447.748 + 258.508i 1.52295 + 0.879278i
\(295\) −58.2831 + 33.6498i −0.197570 + 0.114067i
\(296\) −411.089 −1.38881
\(297\) 511.269 1.72144
\(298\) 39.5683 68.5343i 0.132780 0.229981i
\(299\) −165.885 95.7738i −0.554800 0.320314i
\(300\) 252.722i 0.842405i
\(301\) 54.6812 94.7105i 0.181665 0.314653i
\(302\) 9.63087i 0.0318903i
\(303\) 792.319i 2.61491i
\(304\) 36.5466 + 301.795i 0.120219 + 0.992747i
\(305\) −57.4534 −0.188372
\(306\) −150.907 −0.493160
\(307\) 77.7831 + 44.9081i 0.253365 + 0.146280i 0.621304 0.783569i \(-0.286603\pi\)
−0.367939 + 0.929850i \(0.619936\pi\)
\(308\) 708.087 2.29898
\(309\) −407.998 + 706.673i −1.32038 + 2.28697i
\(310\) −29.0021 16.7444i −0.0935551 0.0540141i
\(311\) 345.134i 1.10976i 0.831932 + 0.554878i \(0.187235\pi\)
−0.831932 + 0.554878i \(0.812765\pi\)
\(312\) 234.928i 0.752974i
\(313\) −261.361 452.691i −0.835020 1.44630i −0.894014 0.448039i \(-0.852123\pi\)
0.0589940 0.998258i \(-0.481211\pi\)
\(314\) −58.0911 + 100.617i −0.185003 + 0.320435i
\(315\) 524.705i 1.66573i
\(316\) −272.364 157.250i −0.861913 0.497625i
\(317\) −1.54659 2.67877i −0.00487882 0.00845037i 0.863576 0.504219i \(-0.168220\pi\)
−0.868455 + 0.495769i \(0.834886\pi\)
\(318\) 392.438i 1.23408i
\(319\) 113.602 65.5881i 0.356119 0.205605i
\(320\) 111.271 192.727i 0.347723 0.602273i
\(321\) −444.475 + 769.854i −1.38466 + 2.39830i
\(322\) −322.135 557.953i −1.00042 1.73277i
\(323\) −88.1822 37.6043i −0.273010 0.116422i
\(324\) −16.0911 + 27.8706i −0.0496639 + 0.0860204i
\(325\) 38.7267 67.0766i 0.119159 0.206390i
\(326\) 415.767i 1.27536i
\(327\) 346.408 199.999i 1.05935 0.611617i
\(328\) 139.636 241.856i 0.425718 0.737366i
\(329\) 111.681 + 193.437i 0.339456 + 0.587956i
\(330\) −298.566 517.132i −0.904746 1.56707i
\(331\) 103.542i 0.312817i −0.987692 0.156408i \(-0.950008\pi\)
0.987692 0.156408i \(-0.0499916\pi\)
\(332\) 371.969i 1.12039i
\(333\) −384.226 665.498i −1.15383 1.99849i
\(334\) −206.638 + 119.302i −0.618676 + 0.357193i
\(335\) 333.301i 0.994930i
\(336\) −395.089 + 684.314i −1.17586 + 2.03665i
\(337\) 248.203 429.900i 0.736507 1.27567i −0.217552 0.976049i \(-0.569807\pi\)
0.954059 0.299619i \(-0.0968595\pi\)
\(338\) 133.000 230.363i 0.393491 0.681547i
\(339\) 114.829 + 66.2964i 0.338728 + 0.195564i
\(340\) 35.0890 + 60.7760i 0.103203 + 0.178753i
\(341\) 84.4793 0.247740
\(342\) −454.408 + 341.238i −1.32868 + 0.997772i
\(343\) 38.5235i 0.112313i
\(344\) 75.0890 + 43.3527i 0.218282 + 0.126025i
\(345\) −271.657 + 470.524i −0.787413 + 1.36384i
\(346\) 96.2733 166.750i 0.278247 0.481937i
\(347\) 484.351 + 279.640i 1.39583 + 0.805880i 0.993952 0.109815i \(-0.0350258\pi\)
0.401873 + 0.915695i \(0.368359\pi\)
\(348\) 146.384i 0.420644i
\(349\) −507.271 −1.45350 −0.726750 0.686902i \(-0.758970\pi\)
−0.726750 + 0.686902i \(0.758970\pi\)
\(350\) 225.612 130.257i 0.644605 0.372163i
\(351\) −151.432 + 87.4291i −0.431429 + 0.249086i
\(352\) 561.390i 1.59486i
\(353\) −95.7723 −0.271310 −0.135655 0.990756i \(-0.543314\pi\)
−0.135655 + 0.990756i \(0.543314\pi\)
\(354\) 94.7267 + 164.071i 0.267590 + 0.463479i
\(355\) 44.0197 25.4148i 0.123999 0.0715909i
\(356\) 224.998 + 389.708i 0.632017 + 1.09468i
\(357\) −124.590 215.796i −0.348992 0.604471i
\(358\) 410.733i 1.14730i
\(359\) −185.715 107.222i −0.517311 0.298670i 0.218523 0.975832i \(-0.429876\pi\)
−0.735834 + 0.677162i \(0.763210\pi\)
\(360\) 416.000 1.15556
\(361\) −350.565 + 86.1686i −0.971095 + 0.238694i
\(362\) 215.885 + 373.924i 0.596368 + 1.03294i
\(363\) 791.655 + 457.062i 2.18087 + 1.25913i
\(364\) −209.727 + 121.086i −0.576172 + 0.332653i
\(365\) 60.6931 + 105.123i 0.166282 + 0.288010i
\(366\) 161.736i 0.441901i
\(367\) −332.602 + 192.028i −0.906272 + 0.523237i −0.879230 0.476398i \(-0.841942\pi\)
−0.0270425 + 0.999634i \(0.508609\pi\)
\(368\) 442.360 255.397i 1.20207 0.694013i
\(369\) 522.043 1.41475
\(370\) −178.681 + 309.485i −0.482922 + 0.836446i
\(371\) 350.341 202.269i 0.944314 0.545200i
\(372\) −47.1366 + 81.6431i −0.126711 + 0.219471i
\(373\) 258.091 0.691933 0.345967 0.938247i \(-0.387551\pi\)
0.345967 + 0.938247i \(0.387551\pi\)
\(374\) −153.315 88.5163i −0.409932 0.236675i
\(375\) −558.725 322.580i −1.48993 0.860213i
\(376\) −153.362 + 88.5438i −0.407879 + 0.235489i
\(377\) −22.4317 + 38.8528i −0.0595005 + 0.103058i
\(378\) −588.135 −1.55591
\(379\) 118.568i 0.312845i 0.987690 + 0.156423i \(0.0499962\pi\)
−0.987690 + 0.156423i \(0.950004\pi\)
\(380\) 243.089 + 103.662i 0.639708 + 0.272796i
\(381\) 690.634 1.81269
\(382\) 365.096i 0.955748i
\(383\) 534.077 + 308.350i 1.39446 + 0.805090i 0.993805 0.111140i \(-0.0354502\pi\)
0.400652 + 0.916230i \(0.368783\pi\)
\(384\) −542.542 313.237i −1.41287 0.815721i
\(385\) 307.772 533.077i 0.799408 1.38462i
\(386\) 101.046 175.016i 0.261776 0.453409i
\(387\) 162.079i 0.418808i
\(388\) −255.909 + 443.247i −0.659559 + 1.14239i
\(389\) −210.954 365.384i −0.542299 0.939290i −0.998772 0.0495524i \(-0.984221\pi\)
0.456472 0.889738i \(-0.349113\pi\)
\(390\) 176.863 + 102.112i 0.453496 + 0.261826i
\(391\) 161.077i 0.411962i
\(392\) −422.542 −1.07791
\(393\) −330.771 572.913i −0.841657 1.45779i
\(394\) 20.3168 0.0515654
\(395\) −236.768 + 136.698i −0.599413 + 0.346071i
\(396\) −908.816 + 524.705i −2.29499 + 1.32501i
\(397\) 264.533 458.184i 0.666329 1.15412i −0.312594 0.949887i \(-0.601198\pi\)
0.978923 0.204229i \(-0.0654687\pi\)
\(398\) 317.952 183.570i 0.798875 0.461231i
\(399\) −863.132 368.073i −2.16324 0.922488i
\(400\) 103.271 + 178.871i 0.258178 + 0.447177i
\(401\) −0.955488 + 1.65495i −0.00238276 + 0.00412707i −0.867214 0.497935i \(-0.834092\pi\)
0.864832 + 0.502062i \(0.167425\pi\)
\(402\) 938.269 2.33400
\(403\) −25.0217 + 14.4463i −0.0620887 + 0.0358469i
\(404\) −323.770 560.786i −0.801411 1.38809i
\(405\) 13.9881 + 24.2281i 0.0345385 + 0.0598224i
\(406\) −130.681 + 75.4488i −0.321875 + 0.185834i
\(407\) 901.489i 2.21496i
\(408\) 171.089 98.7783i 0.419336 0.242104i
\(409\) 142.932 + 247.565i 0.349466 + 0.605293i 0.986155 0.165828i \(-0.0530296\pi\)
−0.636689 + 0.771121i \(0.719696\pi\)
\(410\) −121.386 210.247i −0.296064 0.512797i
\(411\) 544.162i 1.32400i
\(412\) 666.891i 1.61867i
\(413\) −97.6475 + 169.130i −0.236435 + 0.409517i
\(414\) 826.907 + 477.415i 1.99736 + 1.15318i
\(415\) 280.034 + 161.677i 0.674780 + 0.389584i
\(416\) −96.0000 166.277i −0.230769 0.399704i
\(417\) 77.6377 0.186181
\(418\) −661.816 + 80.1441i −1.58329 + 0.191732i
\(419\) 833.373i 1.98896i −0.104936 0.994479i \(-0.533464\pi\)
0.104936 0.994479i \(-0.466536\pi\)
\(420\) 343.453 + 594.879i 0.817746 + 1.41638i
\(421\) 404.964 701.419i 0.961910 1.66608i 0.244214 0.969721i \(-0.421470\pi\)
0.717696 0.696356i \(-0.245197\pi\)
\(422\) 510.451 + 294.709i 1.20960 + 0.698363i
\(423\) −286.681 165.515i −0.677733 0.391289i
\(424\) 160.364 + 277.759i 0.378218 + 0.655093i
\(425\) −65.1325 −0.153253
\(426\) −71.5445 123.919i −0.167945 0.290889i
\(427\) −144.386 + 83.3614i −0.338141 + 0.195226i
\(428\) 726.515i 1.69746i
\(429\) −515.180 −1.20089
\(430\) 65.2754 37.6868i 0.151803 0.0876436i
\(431\) 222.564 128.497i 0.516390 0.298138i −0.219066 0.975710i \(-0.570301\pi\)
0.735456 + 0.677572i \(0.236968\pi\)
\(432\) 466.289i 1.07937i
\(433\) 121.137 + 209.815i 0.279761 + 0.484561i 0.971325 0.237754i \(-0.0764113\pi\)
−0.691564 + 0.722315i \(0.743078\pi\)
\(434\) −97.1801 −0.223917
\(435\) 110.204 + 63.6263i 0.253342 + 0.146267i
\(436\) −163.453 + 283.110i −0.374893 + 0.649334i
\(437\) 364.236 + 485.032i 0.833491 + 1.10991i
\(438\) 295.931 170.856i 0.675641 0.390081i
\(439\) −251.216 145.040i −0.572246 0.330386i 0.185800 0.982588i \(-0.440512\pi\)
−0.758046 + 0.652201i \(0.773846\pi\)
\(440\) 422.638 + 244.010i 0.960540 + 0.554568i
\(441\) −394.931 684.040i −0.895534 1.55111i
\(442\) 60.5466 0.136983
\(443\) 187.649 108.339i 0.423586 0.244557i −0.273024 0.962007i \(-0.588024\pi\)
0.696610 + 0.717450i \(0.254691\pi\)
\(444\) 871.224 + 503.001i 1.96222 + 1.13289i
\(445\) 391.184 0.879066
\(446\) 57.8851 + 33.4200i 0.129787 + 0.0749327i
\(447\) −167.715 + 96.8302i −0.375201 + 0.216622i
\(448\) 645.791i 1.44150i
\(449\) −315.820 −0.703385 −0.351693 0.936116i \(-0.614394\pi\)
−0.351693 + 0.936116i \(0.614394\pi\)
\(450\) −193.046 + 334.365i −0.428990 + 0.743033i
\(451\) 530.373 + 306.211i 1.17599 + 0.678960i
\(452\) −108.364 −0.239744
\(453\) −11.7842 + 20.4108i −0.0260136 + 0.0450569i
\(454\) 54.3486i 0.119711i
\(455\) 210.521i 0.462684i
\(456\) 291.818 684.314i 0.639951 1.50069i
\(457\) −642.996 −1.40699 −0.703497 0.710699i \(-0.748379\pi\)
−0.703497 + 0.710699i \(0.748379\pi\)
\(458\) −503.636 −1.09964
\(459\) 127.343 + 73.5213i 0.277435 + 0.160177i
\(460\) 444.036i 0.965296i
\(461\) 109.907 190.364i 0.238410 0.412938i −0.721848 0.692051i \(-0.756707\pi\)
0.960258 + 0.279114i \(0.0900406\pi\)
\(462\) −1500.65 866.403i −3.24817 1.87533i
\(463\) 66.7372i 0.144141i 0.997400 + 0.0720704i \(0.0229606\pi\)
−0.997400 + 0.0720704i \(0.977039\pi\)
\(464\) −59.8178 103.607i −0.128918 0.223292i
\(465\) 40.9762 + 70.9728i 0.0881208 + 0.152630i
\(466\) 164.545 284.999i 0.353100 0.611587i
\(467\) 171.878i 0.368046i 0.982922 + 0.184023i \(0.0589121\pi\)
−0.982922 + 0.184023i \(0.941088\pi\)
\(468\) 179.453 310.822i 0.383447 0.664150i
\(469\) 483.600 + 837.620i 1.03113 + 1.78597i
\(470\) 153.943i 0.327539i
\(471\) 246.226 142.158i 0.522772 0.301823i
\(472\) −134.091 77.4175i −0.284091 0.164020i
\(473\) −95.0694 + 164.665i −0.200992 + 0.348129i
\(474\) 384.816 + 666.520i 0.811848 + 1.40616i
\(475\) −196.126 + 147.281i −0.412896 + 0.310065i
\(476\) 176.364 + 101.824i 0.370513 + 0.213916i
\(477\) −299.770 + 519.217i −0.628449 + 1.08851i
\(478\) 238.495i 0.498943i
\(479\) −19.8178 + 11.4418i −0.0413733 + 0.0238869i −0.520544 0.853835i \(-0.674271\pi\)
0.479171 + 0.877722i \(0.340937\pi\)
\(480\) −471.636 + 272.299i −0.982574 + 0.567289i
\(481\) 154.158 + 267.010i 0.320496 + 0.555115i
\(482\) 66.2277 + 114.710i 0.137402 + 0.237987i
\(483\) 1576.63i 3.26425i
\(484\) −747.089 −1.54357
\(485\) 222.463 + 385.318i 0.458687 + 0.794469i
\(486\) −386.091 + 222.910i −0.794426 + 0.458662i
\(487\) 146.082i 0.299963i −0.988689 0.149982i \(-0.952079\pi\)
0.988689 0.149982i \(-0.0479215\pi\)
\(488\) −66.0911 114.473i −0.135433 0.234576i
\(489\) −508.726 + 881.139i −1.04034 + 1.80192i
\(490\) −183.659 + 318.107i −0.374815 + 0.649199i
\(491\) −412.931 238.406i −0.840999 0.485551i 0.0166045 0.999862i \(-0.494714\pi\)
−0.857604 + 0.514311i \(0.828048\pi\)
\(492\) −591.861 + 341.711i −1.20297 + 0.694535i
\(493\) 37.7267 0.0765248
\(494\) 182.317 136.911i 0.369062 0.277148i
\(495\) 912.259i 1.84295i
\(496\) 77.0470i 0.155337i
\(497\) 73.7505 127.740i 0.148391 0.257021i
\(498\) 455.135 788.316i 0.913925 1.58296i
\(499\) 501.621 + 289.611i 1.00525 + 0.580382i 0.909798 0.415052i \(-0.136236\pi\)
0.0954538 + 0.995434i \(0.469570\pi\)
\(500\) 527.271 1.05454
\(501\) 583.905 1.16548
\(502\) −322.247 + 186.050i −0.641927 + 0.370617i
\(503\) −181.830 + 104.979i −0.361490 + 0.208707i −0.669734 0.742601i \(-0.733592\pi\)
0.308244 + 0.951307i \(0.400259\pi\)
\(504\) 1045.45 603.590i 2.07430 1.19760i
\(505\) −562.911 −1.11468
\(506\) 560.067 + 970.065i 1.10685 + 1.91712i
\(507\) −563.736 + 325.473i −1.11190 + 0.641958i
\(508\) −488.816 + 282.218i −0.962236 + 0.555547i
\(509\) 70.9545 + 122.897i 0.139400 + 0.241447i 0.927270 0.374394i \(-0.122149\pi\)
−0.787870 + 0.615842i \(0.788816\pi\)
\(510\) 171.737i 0.336740i
\(511\) 305.055 + 176.124i 0.596977 + 0.344665i
\(512\) 512.000 1.00000
\(513\) 549.702 66.5674i 1.07154 0.129761i
\(514\) −303.725 526.066i −0.590904 1.02348i
\(515\) −502.063 289.866i −0.974880 0.562847i
\(516\) −106.091 183.755i −0.205603 0.356115i
\(517\) −194.170 336.313i −0.375571 0.650508i
\(518\) 1037.02i 2.00197i
\(519\) −408.065 + 235.597i −0.786253 + 0.453943i
\(520\) −166.907 −0.320975
\(521\) −162.683 −0.312252 −0.156126 0.987737i \(-0.549901\pi\)
−0.156126 + 0.987737i \(0.549901\pi\)
\(522\) 111.818 193.674i 0.214210 0.371023i
\(523\) 531.564 306.899i 1.01638 0.586804i 0.103323 0.994648i \(-0.467052\pi\)
0.913052 + 0.407843i \(0.133719\pi\)
\(524\) 468.226 + 270.330i 0.893560 + 0.515897i
\(525\) −637.521 −1.21433
\(526\) 150.475 + 86.8769i 0.286074 + 0.165165i
\(527\) 21.0414 + 12.1483i 0.0399268 + 0.0230517i
\(528\) 686.907 1189.76i 1.30096 2.25333i
\(529\) 245.090 424.508i 0.463308 0.802473i
\(530\) 278.812 0.526060
\(531\) 289.434i 0.545074i
\(532\) 761.315 92.1932i 1.43104 0.173295i
\(533\) −209.453 −0.392971
\(534\) 1101.21i 2.06220i
\(535\) −546.950 315.782i −1.02234 0.590247i
\(536\) −664.087 + 383.411i −1.23897 + 0.715319i
\(537\) −502.565 + 870.468i −0.935876 + 1.62098i
\(538\) −195.271 + 338.220i −0.362958 + 0.628661i
\(539\) 926.606i 1.71912i
\(540\) −351.041 202.674i −0.650077 0.375322i
\(541\) −125.818 217.923i −0.232565 0.402815i 0.725997 0.687698i \(-0.241379\pi\)
−0.958562 + 0.284883i \(0.908045\pi\)
\(542\) −608.020 351.040i −1.12181 0.647676i
\(543\) 1056.61i 1.94588i
\(544\) −80.7288 + 139.826i −0.148398 + 0.257034i
\(545\) 142.091 + 246.109i 0.260718 + 0.451576i
\(546\) 592.634 1.08541
\(547\) 289.521 167.155i 0.529288 0.305585i −0.211438 0.977391i \(-0.567815\pi\)
0.740727 + 0.671807i \(0.234481\pi\)
\(548\) 222.364 + 385.146i 0.405774 + 0.702822i
\(549\) 123.545 213.985i 0.225036 0.389773i
\(550\) −392.252 + 226.467i −0.713185 + 0.411757i
\(551\) 113.602 85.3095i 0.206174 0.154827i
\(552\) −1250.00 −2.26449
\(553\) −396.681 + 687.072i −0.717326 + 1.24244i
\(554\) −230.859 −0.416713
\(555\) 757.360 437.262i 1.36461 0.787860i
\(556\) −54.9503 + 31.7256i −0.0988315 + 0.0570604i
\(557\) −303.180 525.123i −0.544309 0.942771i −0.998650 0.0519430i \(-0.983459\pi\)
0.454341 0.890828i \(-0.349875\pi\)
\(558\) 124.729 72.0122i 0.223528 0.129054i
\(559\) 65.0290i 0.116331i
\(560\) −486.178 280.695i −0.868175 0.501241i
\(561\) 216.614 + 375.186i 0.386121 + 0.668781i
\(562\) 23.9979 + 41.5656i 0.0427009 + 0.0739602i
\(563\) 136.112i 0.241762i 0.992667 + 0.120881i \(0.0385719\pi\)
−0.992667 + 0.120881i \(0.961428\pi\)
\(564\) 433.362 0.768373
\(565\) −47.1009 + 81.5812i −0.0833645 + 0.144392i
\(566\) −250.473 144.611i −0.442532 0.255496i
\(567\) 70.3069 + 40.5917i 0.123998 + 0.0715904i
\(568\) 101.275 + 58.4714i 0.178302 + 0.102943i
\(569\) 1007.04 1.76984 0.884922 0.465739i \(-0.154211\pi\)
0.884922 + 0.465739i \(0.154211\pi\)
\(570\) −388.341 517.132i −0.681299 0.907249i
\(571\) 433.551i 0.759284i 0.925133 + 0.379642i \(0.123953\pi\)
−0.925133 + 0.379642i \(0.876047\pi\)
\(572\) 364.634 210.521i 0.637471 0.368044i
\(573\) 446.725 773.750i 0.779624 1.35035i
\(574\) −610.111 352.248i −1.06291 0.613672i
\(575\) 356.899 + 206.056i 0.620694 + 0.358358i
\(576\) 478.542 + 828.860i 0.830803 + 1.43899i
\(577\) 459.998 0.797223 0.398612 0.917120i \(-0.369492\pi\)
0.398612 + 0.917120i \(0.369492\pi\)
\(578\) 263.542 + 456.469i 0.455956 + 0.789739i
\(579\) −428.293 + 247.275i −0.739711 + 0.427073i
\(580\) −104.000 −0.179310
\(581\) 938.336 1.61504
\(582\) 1084.70 626.251i 1.86374 1.07603i
\(583\) −609.107 + 351.668i −1.04478 + 0.603204i
\(584\) −139.636 + 241.856i −0.239102 + 0.414137i
\(585\) −156.000 270.200i −0.266667 0.461880i
\(586\) 431.588 0.736498
\(587\) −805.568 465.095i −1.37235 0.792326i −0.381125 0.924524i \(-0.624463\pi\)
−0.991223 + 0.132198i \(0.957797\pi\)
\(588\) 895.497 + 517.015i 1.52295 + 0.879278i
\(589\) 90.8297 10.9992i 0.154210 0.0186744i
\(590\) −116.566 + 67.2996i −0.197570 + 0.114067i
\(591\) −43.0575 24.8592i −0.0728553 0.0420630i
\(592\) −822.178 −1.38881
\(593\) 218.181 + 377.901i 0.367928 + 0.637270i 0.989241 0.146292i \(-0.0467340\pi\)
−0.621314 + 0.783562i \(0.713401\pi\)
\(594\) 1022.54 1.72144
\(595\) 153.315 88.5163i 0.257672 0.148767i
\(596\) 79.1366 137.069i 0.132780 0.229981i
\(597\) −898.451 −1.50494
\(598\) −331.770 191.548i −0.554800 0.320314i
\(599\) −618.142 + 356.885i −1.03196 + 0.595801i −0.917545 0.397633i \(-0.869832\pi\)
−0.114412 + 0.993433i \(0.536499\pi\)
\(600\) 505.443i 0.842405i
\(601\) 21.9586 0.0365368 0.0182684 0.999833i \(-0.494185\pi\)
0.0182684 + 0.999833i \(0.494185\pi\)
\(602\) 109.362 189.421i 0.181665 0.314653i
\(603\) −1241.38 716.712i −2.05868 1.18858i
\(604\) 19.2617i 0.0318903i
\(605\) −324.725 + 562.440i −0.536735 + 0.929652i
\(606\) 1584.64i 2.61491i
\(607\) 305.012i 0.502492i 0.967923 + 0.251246i \(0.0808403\pi\)
−0.967923 + 0.251246i \(0.919160\pi\)
\(608\) 73.0932 + 603.590i 0.120219 + 0.992747i
\(609\) 369.271 0.606357
\(610\) −114.907 −0.188372
\(611\) 115.022 + 66.4078i 0.188252 + 0.108687i
\(612\) −301.814 −0.493160
\(613\) 499.043 864.369i 0.814100 1.41006i −0.0958719 0.995394i \(-0.530564\pi\)
0.909972 0.414669i \(-0.136103\pi\)
\(614\) 155.566 + 89.8162i 0.253365 + 0.146280i
\(615\) 594.104i 0.966022i
\(616\) 1416.17 2.29898
\(617\) 66.0683 + 114.434i 0.107080 + 0.185468i 0.914586 0.404391i \(-0.132517\pi\)
−0.807506 + 0.589859i \(0.799183\pi\)
\(618\) −815.996 + 1413.35i −1.32038 + 2.28697i
\(619\) 432.512i 0.698727i −0.936987 0.349363i \(-0.886398\pi\)
0.936987 0.349363i \(-0.113602\pi\)
\(620\) −58.0041 33.4887i −0.0935551 0.0540141i
\(621\) −465.190 805.733i −0.749098 1.29748i
\(622\) 690.268i 1.10976i
\(623\) 983.085 567.584i 1.57799 0.911050i
\(624\) 469.856i 0.752974i
\(625\) 67.8188 117.466i 0.108510 0.187945i
\(626\) −522.723 905.382i −0.835020 1.44630i
\(627\) 1500.65 + 639.936i 2.39339 + 1.02063i
\(628\) −116.182 + 201.233i −0.185003 + 0.320435i
\(629\) 129.636 224.535i 0.206098 0.356972i
\(630\) 1049.41i 1.66573i
\(631\) 592.283 341.955i 0.938642 0.541925i 0.0491077 0.998793i \(-0.484362\pi\)
0.889534 + 0.456868i \(0.151029\pi\)
\(632\) −544.729 314.499i −0.861913 0.497625i
\(633\) −721.202 1249.16i −1.13934 1.97339i
\(634\) −3.09317 5.35753i −0.00487882 0.00845037i
\(635\) 490.668i 0.772705i
\(636\) 784.876i 1.23408i
\(637\) 158.453 + 274.449i 0.248749 + 0.430847i
\(638\) 227.204 131.176i 0.356119 0.205605i
\(639\) 218.602i 0.342100i
\(640\) 222.542 385.455i 0.347723 0.602273i
\(641\) 197.363 341.843i 0.307899 0.533297i −0.670003 0.742358i \(-0.733707\pi\)
0.977903 + 0.209061i \(0.0670407\pi\)
\(642\) −888.950 + 1539.71i −1.38466 + 2.39830i
\(643\) −854.326 493.245i −1.32866 0.767100i −0.343564 0.939129i \(-0.611634\pi\)
−0.985092 + 0.172030i \(0.944968\pi\)
\(644\) −644.269 1115.91i −1.00042 1.73277i
\(645\) −184.451 −0.285971
\(646\) −176.364 75.2085i −0.273010 0.116422i
\(647\) 1173.93i 1.81442i 0.420674 + 0.907212i \(0.361794\pi\)
−0.420674 + 0.907212i \(0.638206\pi\)
\(648\) −32.1822 + 55.7412i −0.0496639 + 0.0860204i
\(649\) 169.771 294.052i 0.261589 0.453085i
\(650\) 77.4534 134.153i 0.119159 0.206390i
\(651\) 205.954 + 118.908i 0.316366 + 0.182654i
\(652\) 831.535i 1.27536i
\(653\) −847.540 −1.29792 −0.648959 0.760823i \(-0.724795\pi\)
−0.648959 + 0.760823i \(0.724795\pi\)
\(654\) 692.816 399.997i 1.05935 0.611617i
\(655\) 407.032 235.000i 0.621422 0.358778i
\(656\) 279.271 483.712i 0.425718 0.737366i
\(657\) −522.043 −0.794587
\(658\) 223.362 + 386.875i 0.339456 + 0.587956i
\(659\) 566.364 326.991i 0.859430 0.496192i −0.00439135 0.999990i \(-0.501398\pi\)
0.863821 + 0.503798i \(0.168064\pi\)
\(660\) −597.132 1034.26i −0.904746 1.56707i
\(661\) 154.170 + 267.031i 0.233238 + 0.403980i 0.958759 0.284220i \(-0.0917346\pi\)
−0.725521 + 0.688200i \(0.758401\pi\)
\(662\) 207.085i 0.312817i
\(663\) −128.317 74.0837i −0.193540 0.111740i
\(664\) 743.938i 1.12039i
\(665\) 261.501 613.221i 0.393235 0.922137i
\(666\) −768.451 1331.00i −1.15383 1.99849i
\(667\) −206.727 119.354i −0.309935 0.178941i
\(668\) −413.275 + 238.605i −0.618676 + 0.357193i
\(669\) −81.7842 141.654i −0.122248 0.211740i
\(670\) 666.603i 0.994930i
\(671\) 251.032 144.933i 0.374116 0.215996i
\(672\) −790.178 + 1368.63i −1.17586 + 2.03665i
\(673\) 110.273 0.163853 0.0819267 0.996638i \(-0.473893\pi\)
0.0819267 + 0.996638i \(0.473893\pi\)
\(674\) 496.406 859.800i 0.736507 1.27567i
\(675\) 325.803 188.102i 0.482671 0.278670i
\(676\) 266.000 460.726i 0.393491 0.681547i
\(677\) −910.356 −1.34469 −0.672346 0.740237i \(-0.734713\pi\)
−0.672346 + 0.740237i \(0.734713\pi\)
\(678\) 229.657 + 132.593i 0.338728 + 0.195564i
\(679\) 1118.14 + 645.561i 1.64675 + 0.950753i
\(680\) 70.1780 + 121.552i 0.103203 + 0.178753i
\(681\) −66.5000 + 115.181i −0.0976505 + 0.169136i
\(682\) 168.959 0.247740
\(683\) 289.407i 0.423729i 0.977299 + 0.211864i \(0.0679535\pi\)
−0.977299 + 0.211864i \(0.932047\pi\)
\(684\) −908.816 + 682.476i −1.32868 + 0.997772i
\(685\) 386.606 0.564388
\(686\) 77.0470i 0.112313i
\(687\) 1067.36 + 616.240i 1.55365 + 0.897001i
\(688\) 150.178 + 86.7053i 0.218282 + 0.126025i
\(689\) 120.273 208.319i 0.174562 0.302350i
\(690\) −543.315 + 941.049i −0.787413 + 1.36384i
\(691\) 308.668i 0.446698i −0.974739 0.223349i \(-0.928301\pi\)
0.974739 0.223349i \(-0.0716990\pi\)
\(692\) 192.547 333.500i 0.278247 0.481937i
\(693\) 1323.63 + 2292.60i 1.91000 + 3.30822i
\(694\) 968.703 + 559.281i 1.39583 + 0.805880i
\(695\) 55.1585i 0.0793647i
\(696\) 292.768i 0.420644i
\(697\) 88.0673 + 152.537i 0.126352 + 0.218848i
\(698\) −1014.54 −1.45350
\(699\) −697.440 + 402.667i −0.997769 + 0.576062i
\(700\) 451.224 260.514i 0.644605 0.372163i
\(701\) −606.075 + 1049.75i −0.864586 + 1.49751i 0.00287094 + 0.999996i \(0.499086\pi\)
−0.867457 + 0.497512i \(0.834247\pi\)
\(702\) −302.863 + 174.858i −0.431429 + 0.249086i
\(703\) −117.374 969.255i −0.166962 1.37874i
\(704\) 1122.78i 1.59486i
\(705\) 188.362 326.253i 0.267181 0.462770i
\(706\) −191.545 −0.271310
\(707\) −1414.65 + 816.749i −2.00092 + 1.15523i
\(708\) 189.453 + 328.143i 0.267590 + 0.463479i
\(709\) −457.689 792.740i −0.645541 1.11811i −0.984176 0.177193i \(-0.943298\pi\)
0.338635 0.940918i \(-0.390035\pi\)
\(710\) 88.0393 50.8295i 0.123999 0.0715909i
\(711\) 1175.79i 1.65371i
\(712\) 449.996 + 779.416i 0.632017 + 1.09468i
\(713\) −76.8654 133.135i −0.107806 0.186725i
\(714\) −249.180 431.593i −0.348992 0.604471i
\(715\) 366.015i 0.511909i
\(716\) 821.465i 1.14730i
\(717\) 291.818 505.443i 0.406998 0.704942i
\(718\) −371.430 214.445i −0.517311 0.298670i
\(719\) 391.610 + 226.096i 0.544659 + 0.314459i 0.746965 0.664863i \(-0.231510\pi\)
−0.202306 + 0.979322i \(0.564844\pi\)
\(720\) 832.000 1.15556
\(721\) −1682.31 −2.33330
\(722\) −701.130 + 172.337i −0.971095 + 0.238694i
\(723\) 324.140i 0.448327i
\(724\) 431.770 + 747.848i 0.596368 + 1.03294i
\(725\) 48.2614 83.5912i 0.0665674 0.115298i
\(726\) 1583.31 + 914.125i 2.18087 + 1.25913i
\(727\) −1194.95 689.905i −1.64367 0.948975i −0.979512 0.201385i \(-0.935456\pi\)
−0.664161 0.747590i \(-0.731211\pi\)
\(728\) −419.453 + 242.172i −0.576172 + 0.332653i
\(729\) 1163.40 1.59589
\(730\) 121.386 + 210.247i 0.166282 + 0.288010i
\(731\) −47.3582 + 27.3423i −0.0647855 + 0.0374039i
\(732\) 323.472i 0.441901i
\(733\) 694.475 0.947442 0.473721 0.880675i \(-0.342910\pi\)
0.473721 + 0.880675i \(0.342910\pi\)
\(734\) −665.204 + 384.056i −0.906272 + 0.523237i
\(735\) 778.461 449.445i 1.05913 0.611489i
\(736\) 884.720 510.794i 1.20207 0.694013i
\(737\) −840.793 1456.30i −1.14083 1.97598i
\(738\) 1044.09 1.41475
\(739\) 699.757 + 404.005i 0.946897 + 0.546692i 0.892116 0.451807i \(-0.149220\pi\)
0.0547817 + 0.998498i \(0.482554\pi\)
\(740\) −357.362 + 618.970i −0.482922 + 0.836446i
\(741\) −553.907 + 67.0766i −0.747513 + 0.0905218i
\(742\) 700.681 404.538i 0.944314 0.545200i
\(743\) 348.962 + 201.473i 0.469666 + 0.271162i 0.716100 0.697998i \(-0.245925\pi\)
−0.246434 + 0.969160i \(0.579259\pi\)
\(744\) −94.2733 + 163.286i −0.126711 + 0.219471i
\(745\) −68.7940 119.155i −0.0923409 0.159939i
\(746\) 516.182 0.691933
\(747\) −1204.34 + 695.324i −1.61223 + 0.930822i
\(748\) −306.629 177.033i −0.409932 0.236675i
\(749\) −1832.72 −2.44689
\(750\) −1117.45 645.160i −1.48993 0.860213i
\(751\) −1181.79 + 682.308i −1.57362 + 0.908532i −0.577905 + 0.816104i \(0.696130\pi\)
−0.995719 + 0.0924285i \(0.970537\pi\)
\(752\) −306.725 + 177.088i −0.407879 + 0.235489i
\(753\) 910.588 1.20928
\(754\) −44.8634 + 77.7056i −0.0595005 + 0.103058i
\(755\) −14.5010 8.37218i −0.0192067 0.0110890i
\(756\) −1176.27 −1.55591
\(757\) −555.043 + 961.363i −0.733215 + 1.26996i 0.222288 + 0.974981i \(0.428648\pi\)
−0.955502 + 0.294984i \(0.904686\pi\)
\(758\) 237.137i 0.312845i
\(759\) 2741.15i 3.61153i
\(760\) 486.178 + 207.325i 0.639708 + 0.272796i
\(761\) 1268.49 1.66688 0.833438 0.552613i \(-0.186369\pi\)
0.833438 + 0.552613i \(0.186369\pi\)
\(762\) 1381.27 1.81269
\(763\) 714.178 + 412.331i 0.936013 + 0.540407i
\(764\) 730.192i 0.955748i
\(765\) −131.184 + 227.218i −0.171483 + 0.297017i
\(766\) 1068.15 + 616.699i 1.39446 + 0.805090i
\(767\) 116.126i 0.151403i
\(768\) −1085.08 626.474i −1.41287 0.815721i
\(769\) 542.816 + 940.184i 0.705872 + 1.22261i 0.966376 + 0.257134i \(0.0827781\pi\)
−0.260504 + 0.965473i \(0.583889\pi\)
\(770\) 615.545 1066.15i 0.799408 1.38462i
\(771\) 1486.53i 1.92805i
\(772\) 202.091 350.032i 0.261776 0.453409i
\(773\) 489.667 + 848.128i 0.633463 + 1.09719i 0.986838 + 0.161709i \(0.0517006\pi\)
−0.353375 + 0.935482i \(0.614966\pi\)
\(774\) 324.158i 0.418808i
\(775\) 53.8339 31.0810i 0.0694630 0.0401045i
\(776\) −511.818 + 886.494i −0.659559 + 1.14239i
\(777\) 1268.88 2197.77i 1.63305 2.82853i
\(778\) −421.909 730.768i −0.542299 0.939290i
\(779\) 610.111 + 260.175i 0.783197 + 0.333985i
\(780\) 353.727 + 204.224i 0.453496 + 0.261826i
\(781\) −128.224 + 222.090i −0.164179 + 0.284366i
\(782\) 322.154i 0.411962i
\(783\) −188.715 + 108.955i −0.241015 + 0.139150i
\(784\) −845.085 −1.07791
\(785\) 100.998 + 174.934i 0.128660 + 0.222845i
\(786\) −661.542 1145.83i −0.841657 1.45779i
\(787\) 92.7520i 0.117855i 0.998262 + 0.0589276i \(0.0187681\pi\)
−0.998262 + 0.0589276i \(0.981232\pi\)
\(788\) 40.6335 0.0515654
\(789\) −212.602 368.237i −0.269457 0.466714i
\(790\) −473.536 + 273.396i −0.599413 + 0.346071i
\(791\) 273.362i 0.345591i
\(792\) −1817.63 + 1049.41i −2.29499 + 1.32501i
\(793\) −49.5683 + 85.8549i −0.0625073 + 0.108266i
\(794\) 529.065 916.368i 0.666329 1.15412i
\(795\) −590.887 341.149i −0.743254 0.429118i
\(796\) 635.905 367.140i 0.798875 0.461231i
\(797\) 1276.61 1.60176 0.800882 0.598822i \(-0.204365\pi\)
0.800882 + 0.598822i \(0.204365\pi\)
\(798\) −1726.26 736.145i −2.16324 0.922488i
\(799\) 111.688i 0.139785i
\(800\) 206.542 + 357.742i 0.258178 + 0.447177i
\(801\) −841.180 + 1456.97i −1.05016 + 1.81893i
\(802\) −1.91098 + 3.30991i −0.00238276 + 0.00412707i
\(803\) −530.373 306.211i −0.660490 0.381334i
\(804\) 1876.54 2.33400
\(805\) −1120.13 −1.39147
\(806\) −50.0435 + 28.8926i −0.0620887 + 0.0358469i
\(807\) 827.679 477.861i 1.02562 0.592145i
\(808\) −647.540 1121.57i −0.801411 1.38809i
\(809\) −1144.13 −1.41425 −0.707125 0.707089i \(-0.750008\pi\)
−0.707125 + 0.707089i \(0.750008\pi\)
\(810\) 27.9762 + 48.4562i 0.0345385 + 0.0598224i
\(811\) −908.471 + 524.506i −1.12019 + 0.646740i −0.941448 0.337157i \(-0.890535\pi\)
−0.178738 + 0.983897i \(0.557201\pi\)
\(812\) −261.362 + 150.898i −0.321875 + 0.185834i
\(813\) 859.053 + 1487.92i 1.05665 + 1.83016i
\(814\) 1802.98i 2.21496i
\(815\) −626.014 361.429i −0.768115 0.443472i
\(816\) 342.178 197.557i 0.419336 0.242104i
\(817\) −80.7764 + 189.421i −0.0988695 + 0.231850i
\(818\) 285.863 + 495.130i 0.349466 + 0.605293i
\(819\) −784.087 452.693i −0.957371 0.552738i
\(820\) −242.772 420.494i −0.296064 0.512797i
\(821\) −200.770 347.744i −0.244543 0.423562i 0.717460 0.696600i \(-0.245305\pi\)
−0.962003 + 0.273038i \(0.911971\pi\)
\(822\) 1088.32i 1.32400i
\(823\) 243.748 140.728i 0.296171 0.170994i −0.344551 0.938768i \(-0.611969\pi\)
0.640721 + 0.767774i \(0.278635\pi\)
\(824\) 1333.78i 1.61867i
\(825\) 1108.40 1.34352
\(826\) −195.295 + 338.261i −0.236435 + 0.409517i
\(827\) 551.534 318.428i 0.666909 0.385040i −0.127995 0.991775i \(-0.540854\pi\)
0.794904 + 0.606735i \(0.207521\pi\)
\(828\) 1653.81 + 954.830i 1.99736 + 1.15318i
\(829\) −52.2774 −0.0630608 −0.0315304 0.999503i \(-0.510038\pi\)
−0.0315304 + 0.999503i \(0.510038\pi\)
\(830\) 560.067 + 323.355i 0.674780 + 0.389584i
\(831\) 489.261 + 282.475i 0.588762 + 0.339922i
\(832\) −192.000 332.554i −0.230769 0.399704i
\(833\) 133.247 230.791i 0.159961 0.277060i
\(834\) 155.275 0.186181
\(835\) 414.841i 0.496816i
\(836\) −1323.63 + 160.288i −1.58329 + 0.191732i
\(837\) −140.336 −0.167666
\(838\) 1666.75i 1.98896i
\(839\) 934.461 + 539.511i 1.11378 + 0.643041i 0.939806 0.341709i \(-0.111006\pi\)
0.173974 + 0.984750i \(0.444339\pi\)
\(840\) 686.907 + 1189.76i 0.817746 + 1.41638i
\(841\) 392.546 679.909i 0.466760 0.808453i
\(842\) 809.929 1402.84i 0.961910 1.66608i
\(843\) 117.454i 0.139328i
\(844\) 1020.90 + 589.418i 1.20960 + 0.698363i
\(845\) −231.236 400.512i −0.273651 0.473978i
\(846\) −573.362 331.031i −0.677733 0.391289i
\(847\) 1884.62i 2.22506i
\(848\) 320.729 + 555.519i 0.378218 + 0.655093i
\(849\) 353.886 + 612.949i 0.416827 + 0.721966i
\(850\) −130.265 −0.153253
\(851\) −1420.70 + 820.241i −1.66945 + 0.963855i
\(852\) −143.089 247.837i −0.167945 0.290889i
\(853\) 120.683 209.029i 0.141481 0.245052i −0.786574 0.617497i \(-0.788147\pi\)
0.928055 + 0.372444i \(0.121480\pi\)
\(854\) −288.772 + 166.723i −0.338141 + 0.195226i
\(855\) 118.776 + 980.834i 0.138920 + 1.14717i
\(856\) 1453.03i 1.69746i
\(857\) −282.045 + 488.515i −0.329107 + 0.570030i −0.982335 0.187132i \(-0.940081\pi\)
0.653228 + 0.757161i \(0.273414\pi\)
\(858\) −1030.36 −1.20089
\(859\) 794.551 458.734i 0.924972 0.534033i 0.0397544 0.999209i \(-0.487342\pi\)
0.885218 + 0.465176i \(0.154009\pi\)
\(860\) 130.551 75.3735i 0.151803 0.0876436i
\(861\) 862.008 + 1493.04i 1.00117 + 1.73408i
\(862\) 445.128 256.995i 0.516390 0.298138i
\(863\) 467.620i 0.541854i 0.962600 + 0.270927i \(0.0873301\pi\)
−0.962600 + 0.270927i \(0.912670\pi\)
\(864\) 932.577i 1.07937i
\(865\) −167.382 289.914i −0.193505 0.335161i
\(866\) 242.273 + 419.630i 0.279761 + 0.484561i
\(867\) 1289.86i 1.48773i
\(868\) −194.360 −0.223917
\(869\) 689.675 1194.55i 0.793642 1.37463i
\(870\) 220.408 + 127.253i 0.253342 + 0.146267i
\(871\) 498.065 + 287.558i 0.571831 + 0.330147i
\(872\) −326.907 + 566.219i −0.374893 + 0.649334i
\(873\) −1913.49 −2.19185
\(874\) 728.471 + 970.065i 0.833491 + 1.10991i
\(875\) 1330.11i 1.52012i
\(876\) 591.861 341.711i 0.675641 0.390081i
\(877\) −753.758 + 1305.55i −0.859474 + 1.48865i 0.0129583 + 0.999916i \(0.495875\pi\)
−0.872432 + 0.488736i \(0.837458\pi\)
\(878\) −502.432 290.079i −0.572246 0.330386i
\(879\) −914.667 528.083i −1.04058 0.600777i
\(880\) 845.275 + 488.020i 0.960540 + 0.554568i
\(881\) −279.998 −0.317818 −0.158909 0.987293i \(-0.550798\pi\)
−0.158909 + 0.987293i \(0.550798\pi\)
\(882\) −789.861 1368.08i −0.895534 1.55111i
\(883\) −305.052 + 176.122i −0.345473 + 0.199459i −0.662689 0.748894i \(-0.730585\pi\)
0.317217 + 0.948353i \(0.397252\pi\)
\(884\) 121.093 0.136983
\(885\) 329.386 0.372188
\(886\) 375.297 216.678i 0.423586 0.244557i
\(887\) 79.7702 46.0553i 0.0899326 0.0519226i −0.454359 0.890819i \(-0.650132\pi\)
0.544292 + 0.838896i \(0.316798\pi\)
\(888\) 1742.45 + 1006.00i 1.96222 + 1.13289i
\(889\) 711.929 + 1233.10i 0.800820 + 1.38706i
\(890\) 782.369 0.879066
\(891\) −122.237 70.5733i −0.137190 0.0792068i
\(892\) 115.770 + 66.8399i 0.129787 + 0.0749327i
\(893\) −252.554 336.313i −0.282816 0.376610i
\(894\) −335.430 + 193.660i −0.375201 + 0.216622i
\(895\) −618.433 357.053i −0.690987 0.398941i
\(896\) 1291.58i 1.44150i
\(897\) 468.748 + 811.896i 0.522574 + 0.905124i
\(898\) −631.640 −0.703385
\(899\) −31.1822 + 18.0030i −0.0346854 + 0.0200256i
\(900\) −386.091 + 668.729i −0.428990 + 0.743033i
\(901\) −202.282 −0.224508
\(902\) 1060.75 + 612.422i 1.17599 + 0.678960i
\(903\) −463.545 + 267.628i −0.513338 + 0.296376i
\(904\) −216.729 −0.239744
\(905\) 750.681 0.829482
\(906\) −23.5683 + 40.8215i −0.0260136 + 0.0450569i
\(907\) −1071.41 618.580i −1.18127 0.682007i −0.224962 0.974367i \(-0.572226\pi\)
−0.956308 + 0.292360i \(0.905559\pi\)
\(908\) 108.697i 0.119711i
\(909\) 1210.45 2096.56i 1.33163 2.30645i
\(910\) 421.043i 0.462684i
\(911\) 391.450i 0.429693i 0.976648 + 0.214846i \(0.0689251\pi\)
−0.976648 + 0.214846i \(0.931075\pi\)
\(912\) 583.636 1368.63i 0.639951 1.50069i
\(913\) −1631.40 −1.78686
\(914\) −1285.99 −1.40699
\(915\) 243.523 + 140.598i 0.266145 + 0.153659i
\(916\) −1007.27 −1.09964
\(917\) 681.940 1181.16i 0.743665 1.28806i
\(918\) 254.685 + 147.043i 0.277435 + 0.160177i
\(919\) 166.723i 0.181418i −0.995877 0.0907088i \(-0.971087\pi\)
0.995877 0.0907088i \(-0.0289132\pi\)
\(920\) 888.072i 0.965296i
\(921\) −219.795 380.696i −0.238648 0.413351i
\(922\) 219.814 380.728i 0.238410 0.412938i
\(923\) 87.7070i 0.0950239i
\(924\) −3001.31 1732.81i −3.24817 1.87533i
\(925\) −331.669 574.468i −0.358561 0.621046i
\(926\) 133.474i 0.144141i
\(927\) 2159.22 1246.62i 2.32925 1.34479i
\(928\) −119.636 207.215i −0.128918 0.223292i
\(929\) −99.9969 + 173.200i −0.107639 + 0.186437i −0.914813 0.403877i \(-0.867662\pi\)
0.807174 + 0.590313i \(0.200996\pi\)
\(930\) 81.9524 + 141.946i 0.0881208 + 0.152630i
\(931\) −120.644 996.260i −0.129586 1.07010i
\(932\) 329.089 569.999i 0.353100 0.611587i
\(933\) 844.600 1462.89i 0.905252 1.56794i
\(934\) 343.755i 0.368046i
\(935\) −266.555 + 153.896i −0.285085 + 0.164594i
\(936\) 358.907 621.645i 0.383447 0.664150i
\(937\) 526.676 + 912.230i 0.562087 + 0.973564i 0.997314 + 0.0732431i \(0.0233349\pi\)
−0.435227 + 0.900321i \(0.643332\pi\)
\(938\) 967.200 + 1675.24i 1.03113 + 1.78597i
\(939\) 2558.38i 2.72457i
\(940\) 307.887i 0.327539i
\(941\) 18.6356 + 32.2778i 0.0198040 + 0.0343016i 0.875758 0.482751i \(-0.160362\pi\)
−0.855954 + 0.517053i \(0.827029\pi\)
\(942\) 492.451 284.317i 0.522772 0.301823i
\(943\) 1114.45i 1.18182i
\(944\) −268.182 154.835i −0.284091 0.164020i
\(945\) −511.269 + 885.544i −0.541026 + 0.937084i
\(946\) −190.139 + 329.330i −0.200992 + 0.348129i
\(947\) −66.9503 38.6538i −0.0706973 0.0408171i 0.464235 0.885712i \(-0.346329\pi\)
−0.534932 + 0.844895i \(0.679663\pi\)
\(948\) 769.631 + 1333.04i 0.811848 + 1.40616i
\(949\) 209.453 0.220710
\(950\) −392.252 + 294.562i −0.412896 + 0.310065i
\(951\) 15.1390i 0.0159190i
\(952\) 352.729 + 203.648i 0.370513 + 0.213916i
\(953\) −561.682 + 972.862i −0.589383 + 1.02084i 0.404930 + 0.914348i \(0.367296\pi\)
−0.994313 + 0.106494i \(0.966037\pi\)
\(954\) −599.540 + 1038.43i −0.628449 + 1.08851i
\(955\) 549.718 + 317.380i 0.575621 + 0.332335i
\(956\) 476.989i 0.498943i
\(957\) −642.020 −0.670867
\(958\) −39.6356 + 22.8836i −0.0413733 + 0.0238869i
\(959\) 971.578 560.941i 1.01312 0.584923i
\(960\) −943.271 + 544.598i −0.982574 + 0.567289i
\(961\) 937.812 0.975871
\(962\) 308.317 + 534.020i 0.320496 + 0.555115i
\(963\) 2352.26 1358.08i 2.44264 1.41026i
\(964\) 132.455 + 229.420i 0.137402 + 0.237987i
\(965\) −175.679 304.285i −0.182051 0.315321i
\(966\) 3153.26i 3.26425i
\(967\) −1025.02 591.795i −1.06000 0.611991i −0.134567 0.990904i \(-0.542965\pi\)
−0.925432 + 0.378913i \(0.876298\pi\)
\(968\) −1494.18 −1.54357
\(969\) 281.746 + 375.186i 0.290760 + 0.387189i
\(970\) 444.926 + 770.635i 0.458687 + 0.794469i
\(971\) 625.708 + 361.252i 0.644395 + 0.372042i 0.786306 0.617838i \(-0.211991\pi\)
−0.141911 + 0.989879i \(0.545325\pi\)
\(972\) −772.182 + 445.820i −0.794426 + 0.458662i
\(973\) 80.0316 + 138.619i 0.0822524 + 0.142465i
\(974\) 292.164i 0.299963i
\(975\) −328.295 + 189.541i −0.336713 + 0.194401i
\(976\) −132.182 228.946i −0.135433 0.234576i
\(977\) −1305.31 −1.33604 −0.668021 0.744143i \(-0.732858\pi\)
−0.668021 + 0.744143i \(0.732858\pi\)
\(978\) −1017.45 + 1762.28i −1.04034 + 1.80192i
\(979\) −1709.20 + 986.809i −1.74587 + 1.00798i
\(980\) −367.319 + 636.215i −0.374815 + 0.649199i
\(981\) −1222.18 −1.24585
\(982\) −825.861 476.811i −0.840999 0.485551i
\(983\) 857.727 + 495.209i 0.872560 + 0.503773i 0.868198 0.496218i \(-0.165278\pi\)
0.00436204 + 0.999990i \(0.498612\pi\)
\(984\) −1183.72 + 683.423i −1.20297 + 0.694535i
\(985\) 17.6615 30.5906i 0.0179305 0.0310565i
\(986\) 75.4534 0.0765248
\(987\) 1093.21i 1.10761i
\(988\) 364.634 273.822i 0.369062 0.277148i
\(989\) 346.004 0.349853
\(990\) 1824.52i 1.84295i
\(991\) −974.899 562.858i −0.983752 0.567970i −0.0803514 0.996767i \(-0.525604\pi\)
−0.903401 + 0.428797i \(0.858938\pi\)
\(992\) 154.094i 0.155337i
\(993\) −253.385 + 438.876i −0.255171 + 0.441970i
\(994\) 147.501 255.479i 0.148391 0.257021i
\(995\) 638.314i 0.641522i
\(996\) 910.269 1576.63i 0.913925 1.58296i
\(997\) −639.734 1108.05i −0.641659 1.11139i −0.985062 0.172199i \(-0.944913\pi\)
0.343403 0.939188i \(-0.388420\pi\)
\(998\) 1003.24 + 579.222i 1.00525 + 0.580382i
\(999\) 1497.55i 1.49905i
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 76.3.g.b.11.1 yes 4
4.3 odd 2 76.3.g.a.11.2 yes 4
19.7 even 3 76.3.g.a.7.2 4
76.7 odd 6 inner 76.3.g.b.7.1 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
76.3.g.a.7.2 4 19.7 even 3
76.3.g.a.11.2 yes 4 4.3 odd 2
76.3.g.b.7.1 yes 4 76.7 odd 6 inner
76.3.g.b.11.1 yes 4 1.1 even 1 trivial