Properties

Label 76.3.g.a.11.2
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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 11.2
Root \(2.73861 + 1.58114i\) of defining polynomial
Character \(\chi\) \(=\) 76.11
Dual form 76.3.g.a.7.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.00000 - 1.73205i) q^{2} +(4.23861 + 2.44716i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(1.73861 - 3.01137i) q^{5} -9.78866i q^{6} +10.0905i q^{7} +8.00000 q^{8} +(7.47723 + 12.9509i) q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.73205i) q^{2} +(4.23861 + 2.44716i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(1.73861 - 3.01137i) q^{5} -9.78866i q^{6} +10.0905i q^{7} +8.00000 q^{8} +(7.47723 + 12.9509i) q^{9} -6.95445 q^{10} -17.5434i q^{11} +(-16.9545 + 9.78866i) q^{12} +(-3.00000 - 5.19615i) q^{13} +(17.4772 - 10.0905i) q^{14} +(14.7386 - 8.50934i) q^{15} +(-8.00000 - 13.8564i) 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} +(-30.3861 + 17.5434i) 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} +(-34.9545 - 20.1810i) q^{28} +(-3.73861 - 6.47547i) q^{29} +(-29.4772 - 17.0187i) q^{30} +4.81544i q^{31} +(-16.0000 + 27.7128i) q^{32} +(42.9317 - 74.3598i) q^{33} +10.0911 q^{34} +(30.3861 + 17.5434i) q^{35} -59.8178 q^{36} -51.3861 q^{37} +(-30.3861 + 22.8185i) q^{38} -29.3660i q^{39} +(13.9089 - 24.0909i) q^{40} +(17.4545 - 30.2320i) q^{41} +98.7723 q^{42} +(-9.38613 - 5.41908i) q^{43} +(60.7723 + 35.0869i) q^{44} +52.0000 q^{45} +(55.2950 + 31.9246i) q^{46} +(19.1703 - 11.0680i) q^{47} -78.3093i q^{48} -52.8178 q^{49} +(12.9089 - 22.3589i) q^{50} +(-21.3861 + 12.3473i) q^{51} +24.0000 q^{52} +(20.0455 + 34.7199i) q^{53} +(50.4772 - 29.1430i) 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} +68.0747i q^{60} +(-8.26139 - 14.3091i) q^{61} +(8.34058 - 4.81544i) q^{62} +(-130.681 + 75.4488i) q^{63} +64.0000 q^{64} -20.8634 q^{65} -171.727 q^{66} +(83.0109 - 47.9263i) q^{67} +(-10.0911 - 17.4783i) q^{68} -156.249 q^{69} -70.1738i q^{70} +(-12.6594 - 7.30892i) q^{71} +(59.8178 + 103.607i) q^{72} +(-17.4545 + 30.2320i) q^{73} +(51.3861 + 89.0034i) q^{74} +63.1804i q^{75} +(69.9089 + 29.8118i) q^{76} +177.022 q^{77} +(-50.8634 + 29.3660i) q^{78} +(68.0911 + 39.3124i) q^{79} -55.6356 q^{80} +(-4.02277 + 6.96765i) q^{81} -69.8178 q^{82} -92.9922i q^{83} +(-98.7723 - 171.079i) q^{84} +(8.77226 + 15.1940i) q^{85} +21.6763i q^{86} -36.5960i q^{87} -140.348i q^{88} +(56.2495 + 97.4270i) q^{89} +(-52.0000 - 90.0666i) q^{90} +(52.4317 - 30.2714i) q^{91} -127.698i 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} +(52.8178 + 91.4831i) q^{98} +(227.204 - 131.176i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{2} + 6 q^{3} - 8 q^{4} - 4 q^{5} + 32 q^{8} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{2} + 6 q^{3} - 8 q^{4} - 4 q^{5} + 32 q^{8} + 8 q^{9} + 16 q^{10} - 24 q^{12} - 12 q^{13} + 48 q^{14} + 48 q^{15} - 32 q^{16} - 32 q^{17} + 16 q^{18} - 42 q^{19} - 16 q^{20} - 44 q^{21} - 12 q^{22} - 12 q^{23} + 48 q^{24} - 18 q^{25} - 24 q^{26} - 96 q^{28} - 4 q^{29} - 96 q^{30} - 64 q^{32} + 106 q^{33} + 128 q^{34} + 12 q^{35} - 64 q^{36} - 96 q^{37} - 12 q^{38} - 32 q^{40} + 26 q^{41} + 176 q^{42} + 72 q^{43} + 24 q^{44} + 208 q^{45} + 24 q^{46} - 36 q^{49} - 36 q^{50} + 24 q^{51} + 96 q^{52} + 124 q^{53} + 180 q^{54} - 288 q^{55} + 124 q^{57} - 8 q^{58} + 78 q^{59} - 44 q^{61} - 120 q^{62} - 216 q^{63} + 256 q^{64} + 48 q^{65} - 424 q^{66} + 102 q^{67} - 128 q^{68} - 384 q^{69} - 204 q^{71} + 64 q^{72} - 26 q^{73} + 96 q^{74} + 192 q^{76} + 248 q^{77} - 72 q^{78} + 360 q^{79} + 128 q^{80} - 38 q^{81} - 104 q^{82} - 176 q^{84} - 184 q^{85} - 16 q^{89} - 208 q^{90} + 144 q^{91} - 80 q^{93} - 24 q^{95} - 192 q^{96} - 234 q^{97} + 36 q^{98} + 624 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 1.73205i −0.500000 0.866025i
\(3\) 4.23861 + 2.44716i 1.41287 + 0.815721i 0.995658 0.0930873i \(-0.0296736\pi\)
0.417213 + 0.908809i \(0.363007\pi\)
\(4\) −2.00000 + 3.46410i −0.500000 + 0.866025i
\(5\) 1.73861 3.01137i 0.347723 0.602273i −0.638122 0.769935i \(-0.720288\pi\)
0.985845 + 0.167662i \(0.0536218\pi\)
\(6\) 9.78866i 1.63144i
\(7\) 10.0905i 1.44150i 0.693197 + 0.720749i \(0.256202\pi\)
−0.693197 + 0.720749i \(0.743798\pi\)
\(8\) 8.00000 1.00000
\(9\) 7.47723 + 12.9509i 0.830803 + 1.43899i
\(10\) −6.95445 −0.695445
\(11\) 17.5434i 1.59486i −0.603413 0.797429i \(-0.706193\pi\)
0.603413 0.797429i \(-0.293807\pi\)
\(12\) −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 \(0.907458\pi\)
\(14\) 17.4772 10.0905i 1.24837 0.720749i
\(15\) 14.7386 8.50934i 0.982574 0.567289i
\(16\) −8.00000 13.8564i −0.500000 0.866025i
\(17\) −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
\(22\) −30.3861 + 17.5434i −1.38119 + 0.797429i
\(23\) −27.6475 + 15.9623i −1.20207 + 0.694013i −0.961014 0.276499i \(-0.910826\pi\)
−0.241052 + 0.970512i \(0.577492\pi\)
\(24\) 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
\(28\) −34.9545 20.1810i −1.24837 0.720749i
\(29\) −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 \(0.0247475\pi\)
−0.996979 + 0.0776683i \(0.975252\pi\)
\(32\) −16.0000 + 27.7128i −0.500000 + 0.866025i
\(33\) 42.9317 74.3598i 1.30096 2.25333i
\(34\) 10.0911 0.296797
\(35\) 30.3861 + 17.5434i 0.868175 + 0.501241i
\(36\) −59.8178 −1.66161
\(37\) −51.3861 −1.38881 −0.694407 0.719582i \(-0.744333\pi\)
−0.694407 + 0.719582i \(0.744333\pi\)
\(38\) −30.3861 + 22.8185i −0.799635 + 0.600486i
\(39\) 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 \(0.0266881\pi\)
\(42\) 98.7723 2.35172
\(43\) −9.38613 5.41908i −0.218282 0.126025i 0.386872 0.922133i \(-0.373555\pi\)
−0.605155 + 0.796108i \(0.706889\pi\)
\(44\) 60.7723 + 35.0869i 1.38119 + 0.797429i
\(45\) 52.0000 1.15556
\(46\) 55.2950 + 31.9246i 1.20207 + 0.694013i
\(47\) 19.1703 11.0680i 0.407879 0.235489i −0.281999 0.959415i \(-0.590998\pi\)
0.689878 + 0.723926i \(0.257664\pi\)
\(48\) 78.3093i 1.63144i
\(49\) −52.8178 −1.07791
\(50\) 12.9089 22.3589i 0.258178 0.447177i
\(51\) −21.3861 + 12.3473i −0.419336 + 0.242104i
\(52\) 24.0000 0.461538
\(53\) 20.0455 + 34.7199i 0.378218 + 0.655093i 0.990803 0.135312i \(-0.0432037\pi\)
−0.612585 + 0.790405i \(0.709870\pi\)
\(54\) 50.4772 29.1430i 0.934763 0.539686i
\(55\) −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 0.635274 0.772287i \(-0.280887\pi\)
−0.351183 + 0.936307i \(0.614220\pi\)
\(60\) 68.0747i 1.13458i
\(61\) −8.26139 14.3091i −0.135433 0.234576i 0.790330 0.612681i \(-0.209909\pi\)
−0.925763 + 0.378105i \(0.876576\pi\)
\(62\) 8.34058 4.81544i 0.134525 0.0776683i
\(63\) −130.681 + 75.4488i −2.07430 + 1.19760i
\(64\) 64.0000 1.00000
\(65\) −20.8634 −0.320975
\(66\) −171.727 −2.60192
\(67\) 83.0109 47.9263i 1.23897 0.715319i 0.270085 0.962837i \(-0.412948\pi\)
0.968883 + 0.247518i \(0.0796149\pi\)
\(68\) −10.0911 17.4783i −0.148398 0.257034i
\(69\) −156.249 −2.26449
\(70\) 70.1738i 1.00248i
\(71\) −12.6594 7.30892i −0.178302 0.102943i 0.408193 0.912896i \(-0.366159\pi\)
−0.586495 + 0.809953i \(0.699492\pi\)
\(72\) 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 \(0.243520\pi\)
\(74\) 51.3861 + 89.0034i 0.694407 + 1.20275i
\(75\) 63.1804i 0.842405i
\(76\) 69.9089 + 29.8118i 0.919854 + 0.392261i
\(77\) 177.022 2.29898
\(78\) −50.8634 + 29.3660i −0.652094 + 0.376487i
\(79\) 68.0911 + 39.3124i 0.861913 + 0.497625i 0.864652 0.502371i \(-0.167539\pi\)
−0.00273968 + 0.999996i \(0.500872\pi\)
\(80\) −55.6356 −0.695445
\(81\) −4.02277 + 6.96765i −0.0496639 + 0.0860204i
\(82\) −69.8178 −0.851437
\(83\) 92.9922i 1.12039i −0.828361 0.560194i \(-0.810726\pi\)
0.828361 0.560194i \(-0.189274\pi\)
\(84\) −98.7723 171.079i −1.17586 2.03665i
\(85\) 8.77226 + 15.1940i 0.103203 + 0.178753i
\(86\) 21.6763i 0.252050i
\(87\) 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 \(0.615561\pi\)
\(90\) −52.0000 90.0666i −0.577778 1.00074i
\(91\) 52.4317 30.2714i 0.576172 0.332653i
\(92\) 127.698i 1.38803i
\(93\) −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 \(0.937410\pi\)
\(98\) 52.8178 + 91.4831i 0.538957 + 0.933501i
\(99\) 227.204 131.176i 2.29499 1.32501i
\(100\) −51.6356 −0.516356
\(101\) −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 \(0.300172\pi\)
−0.587349 + 0.809334i \(0.699828\pi\)
\(104\) −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 \(0.322633\pi\)
−0.528823 + 0.848732i \(0.677367\pi\)
\(108\) −100.954 58.2861i −0.934763 0.539686i
\(109\) −40.8634 + 70.7774i −0.374893 + 0.649334i −0.990311 0.138867i \(-0.955654\pi\)
0.615418 + 0.788201i \(0.288987\pi\)
\(110\) 122.005i 1.10914i
\(111\) −217.806 125.750i −1.96222 1.13289i
\(112\) 139.818 80.7238i 1.24837 0.720749i
\(113\) −27.0911 −0.239744 −0.119872 0.992789i \(-0.538248\pi\)
−0.119872 + 0.992789i \(0.538248\pi\)
\(114\) −184.636 + 22.3589i −1.61961 + 0.196130i
\(115\) 111.009i 0.965296i
\(116\) 29.9089 0.257835
\(117\) 44.8634 77.7056i 0.383447 0.664150i
\(118\) 38.7088i 0.328040i
\(119\) −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
\(124\) −16.6812 9.63087i −0.134525 0.0776683i
\(125\) 131.818 1.05454
\(126\) 261.362 + 150.898i 2.07430 + 1.19760i
\(127\) 122.204 70.5545i 0.962236 0.555547i 0.0653753 0.997861i \(-0.479176\pi\)
0.896860 + 0.442314i \(0.145842\pi\)
\(128\) −64.0000 110.851i −0.500000 0.866025i
\(129\) −26.5228 45.9388i −0.205603 0.356115i
\(130\) 20.8634 + 36.1364i 0.160487 + 0.277972i
\(131\) −117.056 67.5826i −0.893560 0.515897i −0.0184550 0.999830i \(-0.505875\pi\)
−0.875105 + 0.483932i \(0.839208\pi\)
\(132\) 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 \(0.700335\pi\)
\(138\) 156.249 + 270.632i 1.13224 + 1.96110i
\(139\) 13.7376 7.93139i 0.0988315 0.0570604i −0.449770 0.893145i \(-0.648494\pi\)
0.548601 + 0.836084i \(0.315161\pi\)
\(140\) −121.545 + 70.1738i −0.868175 + 0.501241i
\(141\) 108.341 0.768373
\(142\) 29.2357i 0.205885i
\(143\) −91.1584 + 52.6303i −0.637471 + 0.368044i
\(144\) 119.636 207.215i 0.830803 1.43899i
\(145\) −26.0000 −0.179310
\(146\) 69.8178 0.478204
\(147\) −223.874 129.254i −1.52295 0.879278i
\(148\) 102.772 178.007i 0.694407 1.20275i
\(149\) 19.7842 34.2672i 0.132780 0.229981i −0.791967 0.610563i \(-0.790943\pi\)
0.924747 + 0.380582i \(0.124276\pi\)
\(150\) 109.432 63.1804i 0.729545 0.421203i
\(151\) 4.81544i 0.0318903i 0.999873 + 0.0159452i \(0.00507571\pi\)
−0.999873 + 0.0159452i \(0.994924\pi\)
\(152\) −18.2733 150.898i −0.120219 0.992747i
\(153\) −75.4534 −0.493160
\(154\) −177.022 306.611i −1.14949 1.99098i
\(155\) 14.5010 + 8.37218i 0.0935551 + 0.0540141i
\(156\) 101.727 + 58.7319i 0.652094 + 0.376487i
\(157\) −29.0455 + 50.3084i −0.185003 + 0.320435i −0.943578 0.331151i \(-0.892563\pi\)
0.758574 + 0.651587i \(0.225896\pi\)
\(158\) 157.250i 0.995251i
\(159\) 196.219i 1.23408i
\(160\) 55.6356 + 96.3637i 0.347723 + 0.602273i
\(161\) −161.067 278.977i −1.00042 1.73277i
\(162\) 16.0911 0.0993278
\(163\) 207.884i 1.27536i 0.770301 + 0.637680i \(0.220106\pi\)
−0.770301 + 0.637680i \(0.779894\pi\)
\(164\) 69.8178 + 120.928i 0.425718 + 0.737366i
\(165\) −149.283 258.566i −0.904746 1.56707i
\(166\) −161.067 + 92.9922i −0.970285 + 0.560194i
\(167\) 103.319 59.6512i 0.618676 0.357193i −0.157678 0.987491i \(-0.550401\pi\)
0.776353 + 0.630298i \(0.217067\pi\)
\(168\) −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 \(0.0769135\pi\)
\(174\) −63.3861 + 36.5960i −0.364288 + 0.210322i
\(175\) −112.806 + 65.1285i −0.644605 + 0.372163i
\(176\) −243.089 + 140.348i −1.38119 + 0.797429i
\(177\) 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 \(0.194473\pi\)
−0.819101 + 0.573649i \(0.805527\pi\)
\(180\) −104.000 + 180.133i −0.577778 + 1.00074i
\(181\) 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
\(186\) 47.1366 0.253423
\(187\) 76.6573 + 44.2581i 0.409932 + 0.236675i
\(188\) 88.5438i 0.470978i
\(189\) −294.067 −1.55591
\(190\) 15.8851 + 131.176i 0.0836057 + 0.690401i
\(191\) 182.548i 0.955748i −0.878428 0.477874i \(-0.841408\pi\)
0.878428 0.477874i \(-0.158592\pi\)
\(192\) 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 \(0.0823585\pi\)
\(194\) 255.909 1.31912
\(195\) −88.4317 51.0561i −0.453496 0.261826i
\(196\) 105.636 182.966i 0.538957 0.933501i
\(197\) 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 −0.843078 0.537792i \(-0.819259\pi\)
0.0442024 + 0.999023i \(0.485925\pi\)
\(200\) 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
\(204\) 98.7783i 0.484207i
\(205\) −60.6931 105.123i −0.296064 0.512797i
\(206\) 288.772 166.723i 1.40181 0.809334i
\(207\) −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 −0.246928 0.969034i \(-0.579421\pi\)
−0.962672 + 0.270671i \(0.912755\pi\)
\(212\) −160.364 −0.756436
\(213\) −35.7723 61.9594i −0.167945 0.290889i
\(214\) 314.590 181.629i 1.47005 0.848732i
\(215\) −32.6377 + 18.8434i −0.151803 + 0.0876436i
\(216\) 233.144i 1.07937i
\(217\) −48.5901 −0.223917
\(218\) 163.453 0.749786
\(219\) −147.965 + 85.4278i −0.675641 + 0.390081i
\(220\) 211.319 122.005i 0.960540 0.554568i
\(221\) 30.2733 0.136983
\(222\) 503.001i 2.26577i
\(223\) −28.9425 16.7100i −0.129787 0.0749327i 0.433701 0.901057i \(-0.357208\pi\)
−0.563488 + 0.826124i \(0.690541\pi\)
\(224\) −279.636 161.448i −1.24837 0.720749i
\(225\) −96.5228 + 167.182i −0.428990 + 0.743033i
\(226\) 27.0911 + 46.9232i 0.119872 + 0.207625i
\(227\) 27.1743i 0.119711i 0.998207 + 0.0598553i \(0.0190639\pi\)
−0.998207 + 0.0598553i \(0.980936\pi\)
\(228\) 223.362 + 297.439i 0.979659 + 1.30456i
\(229\) −251.818 −1.09964 −0.549821 0.835283i \(-0.685304\pi\)
−0.549821 + 0.835283i \(0.685304\pi\)
\(230\) 192.273 111.009i 0.835971 0.482648i
\(231\) 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 \(0.0517943\pi\)
\(234\) −179.453 −0.766895
\(235\) 76.9717i 0.327539i
\(236\) −67.0455 + 38.7088i −0.284091 + 0.164020i
\(237\) 192.408 + 333.260i 0.811848 + 1.40616i
\(238\) 101.824i 0.427832i
\(239\) 119.247i 0.498943i −0.968382 0.249471i \(-0.919743\pi\)
0.968382 0.249471i \(-0.0802569\pi\)
\(240\) −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 \(0.789458\pi\)
\(242\) 186.772 + 323.499i 0.771786 + 1.33677i
\(243\) 193.046 111.455i 0.794426 0.458662i
\(244\) 66.0911 0.270865
\(245\) −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
\(250\) −131.818 228.315i −0.527271 0.913261i
\(251\) 161.124 93.0248i 0.641927 0.370617i −0.143429 0.989661i \(-0.545813\pi\)
0.785356 + 0.619044i \(0.212480\pi\)
\(252\) 603.590i 2.39520i
\(253\) 280.034 + 485.032i 1.10685 + 1.91712i
\(254\) −244.408 141.109i −0.962236 0.555547i
\(255\) 85.8686i 0.336740i
\(256\) −128.000 + 221.703i −0.500000 + 0.866025i
\(257\) −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
\(260\) 41.7267 72.2728i 0.160487 0.277972i
\(261\) 55.9089 96.8371i 0.214210 0.371023i
\(262\) 270.330i 1.03179i
\(263\) −75.2376 43.4384i −0.286074 0.165165i 0.350096 0.936714i \(-0.386149\pi\)
−0.636170 + 0.771549i \(0.719482\pi\)
\(264\) 343.453 594.879i 1.30096 2.25333i
\(265\) 139.406 0.526060
\(266\) −230.249 306.611i −0.865600 1.15267i
\(267\) 550.607i 2.06220i
\(268\) 383.411i 1.43064i
\(269\) −97.6356 + 169.110i −0.362958 + 0.628661i −0.988446 0.151572i \(-0.951566\pi\)
0.625489 + 0.780233i \(0.284900\pi\)
\(270\) 202.674i 0.750644i
\(271\) 304.010 + 175.520i 1.12181 + 0.647676i 0.941862 0.336001i \(-0.109074\pi\)
0.179946 + 0.983677i \(0.442408\pi\)
\(272\) 80.7288 0.296797
\(273\) 296.317 1.08541
\(274\) 111.182 192.573i 0.405774 0.702822i
\(275\) 196.126 113.233i 0.713185 0.411757i
\(276\) 312.499 541.264i 1.13224 1.96110i
\(277\) −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 \(0.819737\pi\)
\(282\) −108.341 187.651i −0.384186 0.665430i
\(283\) 125.237 + 72.3053i 0.442532 + 0.255496i 0.704671 0.709534i \(-0.251095\pi\)
−0.262139 + 0.965030i \(0.584428\pi\)
\(284\) 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
\(288\) −478.542 −1.66161
\(289\) 131.771 + 228.234i 0.455956 + 0.789739i
\(290\) 26.0000 + 45.0333i 0.0896552 + 0.155287i
\(291\) −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 \(0.379957\pi\)
\(294\) 517.015i 1.75856i
\(295\) 58.2831 33.6498i 0.197570 0.114067i
\(296\) −411.089 −1.38881
\(297\) 511.269 1.72144
\(298\) −79.1366 −0.265559
\(299\) 165.885 + 95.7738i 0.554800 + 0.320314i
\(300\) −218.863 126.361i −0.729545 0.421203i
\(301\) 54.6812 94.7105i 0.181665 0.314653i
\(302\) 8.34058 4.81544i 0.0276178 0.0159452i
\(303\) 792.319i 2.61491i
\(304\) −243.089 + 182.548i −0.799635 + 0.600486i
\(305\) −57.4534 −0.188372
\(306\) 75.4534 + 130.689i 0.246580 + 0.427089i
\(307\) −77.7831 44.9081i −0.253365 0.146280i 0.367939 0.929850i \(-0.380064\pi\)
−0.621304 + 0.783569i \(0.713397\pi\)
\(308\) −354.043 + 613.221i −1.14949 + 1.99098i
\(309\) −407.998 + 706.673i −1.32038 + 2.28697i
\(310\) 33.4887i 0.108028i
\(311\) 345.134i 1.10976i −0.831932 0.554878i \(-0.812765\pi\)
0.831932 0.554878i \(-0.187235\pi\)
\(312\) 234.928i 0.752974i
\(313\) −261.361 452.691i −0.835020 1.44630i −0.894014 0.448039i \(-0.852123\pi\)
0.0589940 0.998258i \(-0.481211\pi\)
\(314\) 116.182 0.370007
\(315\) 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 \(0.834886\pi\)
\(318\) 339.861 196.219i 1.06875 0.617041i
\(319\) −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
\(326\) 360.065 207.884i 1.10449 0.637680i
\(327\) −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 \(0.0499916\pi\)
−0.987692 + 0.156408i \(0.950008\pi\)
\(332\) 322.135 + 185.984i 0.970285 + 0.560194i
\(333\) −384.226 665.498i −1.15383 1.99849i
\(334\) −206.638 119.302i −0.618676 0.357193i
\(335\) 333.301i 0.994930i
\(336\) 790.178 2.35172
\(337\) 248.203 429.900i 0.736507 1.27567i −0.217552 0.976049i \(-0.569807\pi\)
0.954059 0.299619i \(-0.0968595\pi\)
\(338\) −266.000 −0.786982
\(339\) −114.829 66.2964i −0.338728 0.195564i
\(340\) −70.1780 −0.206406
\(341\) 84.4793 0.247740
\(342\) −522.725 222.910i −1.52843 0.651783i
\(343\) 38.5235i 0.112313i
\(344\) −75.0890 43.3527i −0.218282 0.126025i
\(345\) −271.657 + 470.524i −0.787413 + 1.36384i
\(346\) −192.547 −0.556493
\(347\) −484.351 279.640i −1.39583 0.805880i −0.401873 0.915695i \(-0.631641\pi\)
−0.993952 + 0.109815i \(0.964974\pi\)
\(348\) 126.772 + 73.1920i 0.364288 + 0.210322i
\(349\) −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
\(352\) 486.178 + 280.695i 1.38119 + 0.797429i
\(353\) −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
\(356\) −449.996 −1.26403
\(357\) −124.590 215.796i −0.348992 0.604471i
\(358\) 355.705 205.366i 0.993589 0.573649i
\(359\) 185.715 + 107.222i 0.517311 + 0.298670i 0.735834 0.677162i \(-0.236790\pi\)
−0.218523 + 0.975832i \(0.570124\pi\)
\(360\) 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
\(364\) 242.172i 0.665306i
\(365\) 60.6931 + 105.123i 0.166282 + 0.288010i
\(366\) −140.067 + 80.8679i −0.382698 + 0.220951i
\(367\) 332.602 192.028i 0.906272 0.523237i 0.0270425 0.999634i \(-0.491391\pi\)
0.879230 + 0.476398i \(0.158058\pi\)
\(368\) 442.360 + 255.397i 1.20207 + 0.694013i
\(369\) 522.043 1.41475
\(370\) 357.362 0.965844
\(371\) −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 \(0.387551\pi\)
\(374\) 177.033i 0.473349i
\(375\) 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
\(378\) 294.067 + 509.339i 0.777956 + 1.34746i
\(379\) 118.568i 0.312845i −0.987690 0.156423i \(-0.950004\pi\)
0.987690 0.156423i \(-0.0499962\pi\)
\(380\) 211.319 158.690i 0.556102 0.417605i
\(381\) 690.634 1.81269
\(382\) −316.182 + 182.548i −0.827702 + 0.477874i
\(383\) −534.077 308.350i −1.39446 0.805090i −0.400652 0.916230i \(-0.631217\pi\)
−0.993805 + 0.111140i \(0.964550\pi\)
\(384\) 626.474i 1.63144i
\(385\) 307.772 533.077i 0.799408 1.38462i
\(386\) −202.091 −0.523552
\(387\) 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 \(-0.349113\pi\)
\(390\) 204.224i 0.523652i
\(391\) 161.077i 0.411962i
\(392\) −422.542 −1.07791
\(393\) −330.771 572.913i −0.841657 1.45779i
\(394\) −10.1584 17.5948i −0.0257827 0.0446569i
\(395\) 236.768 136.698i 0.599413 0.346071i
\(396\) 1049.41i 2.65003i
\(397\) 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 \(0.167425\pi\)
\(402\) −469.135 812.565i −1.16700 2.02131i
\(403\) 25.0217 14.4463i 0.0620887 0.0358469i
\(404\) 647.540 1.60282
\(405\) 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
\(412\) −577.545 333.445i −1.40181 0.809334i
\(413\) −97.6475 + 169.130i −0.236435 + 0.409517i
\(414\) 954.830i 2.30635i
\(415\) −280.034 161.677i −0.674780 0.389584i
\(416\) 192.000 0.461538
\(417\) 77.6377 0.186181
\(418\) 400.315 + 533.077i 0.957691 + 1.27530i
\(419\) 833.373i 1.98896i 0.104936 + 0.994479i \(0.466536\pi\)
−0.104936 + 0.994479i \(0.533464\pi\)
\(420\) −686.907 −1.63549
\(421\) 404.964 701.419i 0.961910 1.66608i 0.244214 0.969721i \(-0.421470\pi\)
0.717696 0.696356i \(-0.245197\pi\)
\(422\) 589.418i 1.39673i
\(423\) 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
\(428\) −629.180 363.257i −1.47005 0.848732i
\(429\) −515.180 −1.20089
\(430\) 65.2754 + 37.6868i 0.151803 + 0.0876436i
\(431\) −222.564 + 128.497i −0.516390 + 0.298138i −0.735456 0.677572i \(-0.763032\pi\)
0.219066 + 0.975710i \(0.429699\pi\)
\(432\) 403.818 233.144i 0.934763 0.539686i
\(433\) 121.137 + 209.815i 0.279761 + 0.484561i 0.971325 0.237754i \(-0.0764113\pi\)
−0.691564 + 0.722315i \(0.743078\pi\)
\(434\) 48.5901 + 84.1605i 0.111959 + 0.193918i
\(435\) −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 0.758046 0.652201i \(-0.226154\pi\)
−0.185800 + 0.982588i \(0.559488\pi\)
\(440\) −422.638 244.010i −0.960540 0.554568i
\(441\) −394.931 684.040i −0.895534 1.55111i
\(442\) −30.2733 52.4349i −0.0684916 0.118631i
\(443\) −187.649 + 108.339i −0.423586 + 0.244557i −0.696610 0.717450i \(-0.745309\pi\)
0.273024 + 0.962007i \(0.411976\pi\)
\(444\) 871.224 503.001i 1.96222 1.13289i
\(445\) 391.184 0.879066
\(446\) 66.8399i 0.149865i
\(447\) 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 \(0.614394\pi\)
\(450\) 386.091 0.857980
\(451\) −530.373 306.211i −1.17599 0.678960i
\(452\) 54.1822 93.8463i 0.119872 0.207625i
\(453\) −11.7842 + 20.4108i −0.0260136 + 0.0450569i
\(454\) 47.0673 27.1743i 0.103672 0.0598553i
\(455\) 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 \(0.748379\pi\)
\(458\) 251.818 + 436.161i 0.549821 + 0.952317i
\(459\) −127.343 73.5213i −0.277435 0.160177i
\(460\) −384.547 222.018i −0.835971 0.482648i
\(461\) 109.907 190.364i 0.238410 0.412938i −0.721848 0.692051i \(-0.756707\pi\)
0.960258 + 0.279114i \(0.0900406\pi\)
\(462\) 1732.81i 3.75066i
\(463\) 66.7372i 0.144141i −0.997400 0.0720704i \(-0.977039\pi\)
0.997400 0.0720704i \(-0.0229606\pi\)
\(464\) −59.8178 + 103.607i −0.128918 + 0.223292i
\(465\) 40.9762 + 70.9728i 0.0881208 + 0.152630i
\(466\) −329.089 −0.706200
\(467\) 171.878i 0.368046i −0.982922 0.184023i \(-0.941088\pi\)
0.982922 0.184023i \(-0.0589121\pi\)
\(468\) 179.453 + 310.822i 0.383447 + 0.664150i
\(469\) 483.600 + 837.620i 1.03113 + 1.78597i
\(470\) −133.319 + 76.9717i −0.283657 + 0.163770i
\(471\) −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
\(478\) −206.542 + 119.247i −0.432097 + 0.249471i
\(479\) 19.8178 11.4418i 0.0413733 0.0238869i −0.479171 0.877722i \(-0.659063\pi\)
0.520544 + 0.853835i \(0.325729\pi\)
\(480\) 544.598i 1.13458i
\(481\) 154.158 + 267.010i 0.320496 + 0.555115i
\(482\) 66.2277 114.710i 0.137402 0.237987i
\(483\) 1576.63i 3.26425i
\(484\) 373.545 646.998i 0.771786 1.33677i
\(485\) 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 \(0.0479215\pi\)
−0.988689 + 0.149982i \(0.952079\pi\)
\(488\) −66.0911 114.473i −0.135433 0.234576i
\(489\) −508.726 + 881.139i −1.04034 + 1.80192i
\(490\) 367.319 0.749630
\(491\) 412.931 + 238.406i 0.840999 + 0.485551i 0.857604 0.514311i \(-0.171952\pi\)
−0.0166045 + 0.999862i \(0.505286\pi\)
\(492\) 683.423i 1.38907i
\(493\) 37.7267 0.0765248
\(494\) 209.727 + 89.4355i 0.424548 + 0.181044i
\(495\) 912.259i 1.84295i
\(496\) 66.7246 38.5235i 0.134525 0.0776683i
\(497\) 73.7505 127.740i 0.148391 0.257021i
\(498\) −910.269 −1.82785
\(499\) −501.621 289.611i −1.00525 0.580382i −0.0954538 0.995434i \(-0.530430\pi\)
−0.909798 + 0.415052i \(0.863764\pi\)
\(500\) −263.636 + 456.630i −0.527271 + 0.913261i
\(501\) 583.905 1.16548
\(502\) −322.247 186.050i −0.641927 0.370617i
\(503\) 181.830 104.979i 0.361490 0.208707i −0.308244 0.951307i \(-0.599741\pi\)
0.669734 + 0.742601i \(0.266408\pi\)
\(504\) −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
\(508\) 564.436i 1.11109i
\(509\) 70.9545 + 122.897i 0.139400 + 0.241447i 0.927270 0.374394i \(-0.122149\pi\)
−0.787870 + 0.615842i \(0.788816\pi\)
\(510\) 148.729 85.8686i 0.291625 0.168370i
\(511\) −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
\(516\) 212.182 0.411206
\(517\) −194.170 336.313i −0.375571 0.650508i
\(518\) −898.087 + 518.511i −1.73376 + 1.00099i
\(519\) 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 \(0.549901\pi\)
\(522\) −223.636 −0.428421
\(523\) −531.564 + 306.899i −1.01638 + 0.586804i −0.913052 0.407843i \(-0.866281\pi\)
−0.103323 + 0.994648i \(0.532948\pi\)
\(524\) 468.226 270.330i 0.893560 0.515897i
\(525\) −637.521 −1.21433
\(526\) 173.754i 0.330330i
\(527\) −21.0414 12.1483i −0.0399268 0.0230517i
\(528\) −1373.81 −2.60192
\(529\) 245.090 424.508i 0.463308 0.802473i
\(530\) −139.406 241.458i −0.263030 0.455581i
\(531\) 289.434i 0.545074i
\(532\) −300.816 + 705.414i −0.565443 + 1.32597i
\(533\) −209.453 −0.392971
\(534\) 953.679 550.607i 1.78592 1.03110i
\(535\) 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
\(538\) 390.542 0.725915
\(539\) 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 \(0.908045\pi\)
\(542\) 702.081i 1.29535i
\(543\) 1056.61i 1.94588i
\(544\) −80.7288 139.826i −0.148398 0.257034i
\(545\) 142.091 + 246.109i 0.260718 + 0.451576i
\(546\) −296.317 513.236i −0.542705 0.939992i
\(547\) −289.521 + 167.155i −0.529288 + 0.305585i −0.740727 0.671807i \(-0.765519\pi\)
0.211438 + 0.977391i \(0.432185\pi\)
\(548\) −444.729 −0.811549
\(549\) 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
\(554\) 115.430 + 199.930i 0.208357 + 0.360884i
\(555\) −757.360 + 437.262i −1.36461 + 0.787860i
\(556\) 63.4511i 0.114121i
\(557\) −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
\(560\) 561.390i 1.00248i
\(561\) 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 \(-0.961428\pi\)
0.992667 0.120881i \(-0.0385719\pi\)
\(564\) −216.681 + 375.303i −0.384186 + 0.665430i
\(565\) −47.1009 + 81.5812i −0.0833645 + 0.144392i
\(566\) 289.221i 0.510992i
\(567\) −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 \(0.154211\pi\)
\(570\) −253.679 + 594.879i −0.445051 + 1.04365i
\(571\) 433.551i 0.759284i −0.925133 0.379642i \(-0.876047\pi\)
0.925133 0.379642i \(-0.123953\pi\)
\(572\) 421.043i 0.736088i
\(573\) 446.725 773.750i 0.779624 1.35035i
\(574\) 704.495i 1.22734i
\(575\) −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
\(580\) 52.0000 90.0666i 0.0896552 0.155287i
\(581\) 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
\(586\) −215.794 373.766i −0.368249 0.637826i
\(587\) 805.568 + 465.095i 1.37235 + 0.792326i 0.991223 0.132198i \(-0.0422035\pi\)
0.381125 + 0.924524i \(0.375537\pi\)
\(588\) 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
\(592\) 411.089 + 712.027i 0.694407 + 1.20275i
\(593\) 218.181 + 377.901i 0.367928 + 0.637270i 0.989241 0.146292i \(-0.0467340\pi\)
−0.621314 + 0.783562i \(0.713401\pi\)
\(594\) −511.269 885.544i −0.860722 1.49082i
\(595\) −153.315 + 88.5163i −0.257672 + 0.148767i
\(596\) 79.1366 + 137.069i 0.132780 + 0.229981i
\(597\) −898.451 −1.50494
\(598\) 383.095i 0.640627i
\(599\) 618.142 356.885i 1.03196 0.595801i 0.114412 0.993433i \(-0.463501\pi\)
0.917545 + 0.397633i \(0.130168\pi\)
\(600\) 505.443i 0.842405i
\(601\) 21.9586 0.0365368 0.0182684 0.999833i \(-0.494185\pi\)
0.0182684 + 0.999833i \(0.494185\pi\)
\(602\) −218.725 −0.363330
\(603\) 1241.38 + 716.712i 2.05868 + 1.18858i
\(604\) −16.6812 9.63087i −0.0276178 0.0159452i
\(605\) −324.725 + 562.440i −0.536735 + 0.929652i
\(606\) −1372.34 + 792.319i −2.26458 + 1.30746i
\(607\) 305.012i 0.502492i −0.967923 0.251246i \(-0.919160\pi\)
0.967923 0.251246i \(-0.0808403\pi\)
\(608\) 559.271 + 238.495i 0.919854 + 0.392261i
\(609\) 369.271 0.606357
\(610\) 57.4534 + 99.5122i 0.0941859 + 0.163135i
\(611\) −115.022 66.4078i −0.188252 0.108687i
\(612\) 150.907 261.378i 0.246580 0.427089i
\(613\) 499.043 864.369i 0.814100 1.41006i −0.0958719 0.995394i \(-0.530564\pi\)
0.909972 0.414669i \(-0.136103\pi\)
\(614\) 179.632i 0.292561i
\(615\) 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 \(0.799183\pi\)
\(618\) 1631.99 2.64076
\(619\) 432.512i 0.698727i 0.936987 + 0.349363i \(0.113602\pi\)
−0.936987 + 0.349363i \(0.886398\pi\)
\(620\) −58.0041 + 33.4887i −0.0935551 + 0.0540141i
\(621\) −465.190 805.733i −0.749098 1.29748i
\(622\) −597.790 + 345.134i −0.961077 + 0.554878i
\(623\) −983.085 + 567.584i −1.57799 + 0.911050i
\(624\) −406.907 + 234.928i −0.652094 + 0.376487i
\(625\) 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
\(630\) 908.816 524.705i 1.44256 0.832865i
\(631\) −592.283 + 341.955i −0.938642 + 0.541925i −0.889534 0.456868i \(-0.848971\pi\)
−0.0491077 + 0.998793i \(0.515638\pi\)
\(632\) 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
\(636\) −679.723 392.438i −1.06875 0.617041i
\(637\) 158.453 + 274.449i 0.248749 + 0.430847i
\(638\) 227.204 + 131.176i 0.356119 + 0.205605i
\(639\) 218.602i 0.342100i
\(640\) −445.085 −0.695445
\(641\) 197.363 341.843i 0.307899 0.533297i −0.670003 0.742358i \(-0.733707\pi\)
0.977903 + 0.209061i \(0.0670407\pi\)
\(642\) 1777.90 2.76932
\(643\) 854.326 + 493.245i 1.32866 + 0.767100i 0.985092 0.172030i \(-0.0550325\pi\)
0.343564 + 0.939129i \(0.388366\pi\)
\(644\) 1288.54 2.00084
\(645\) −184.451 −0.285971
\(646\) −23.0497 190.340i −0.0356806 0.294644i
\(647\) 1173.93i 1.81442i −0.420674 0.907212i \(-0.638206\pi\)
0.420674 0.907212i \(-0.361794\pi\)
\(648\) −32.1822 + 55.7412i −0.0496639 + 0.0860204i
\(649\) 169.771 294.052i 0.261589 0.453085i
\(650\) −154.907 −0.238318
\(651\) −205.954 118.908i −0.316366 0.182654i
\(652\) −720.130 415.767i −1.10449 0.637680i
\(653\) −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
\(656\) −558.542 −0.851437
\(657\) −522.043 −0.794587
\(658\) 223.362 386.875i 0.339456 0.587956i
\(659\) −566.364 + 326.991i −0.859430 + 0.496192i −0.863821 0.503798i \(-0.831936\pi\)
0.00439135 + 0.999990i \(0.498602\pi\)
\(660\) 1194.26 1.80949
\(661\) 154.170 + 267.031i 0.233238 + 0.403980i 0.958759 0.284220i \(-0.0917346\pi\)
−0.725521 + 0.688200i \(0.758401\pi\)
\(662\) 179.341 103.542i 0.270907 0.156408i
\(663\) 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
\(668\) 477.209i 0.714385i
\(669\) −81.7842 141.654i −0.122248 0.211740i
\(670\) −577.295 + 333.301i −0.861634 + 0.497465i
\(671\) −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 \(0.473893\pi\)
\(674\) −992.812 −1.47301
\(675\) −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 \(0.734713\pi\)
\(678\) 265.185i 0.391129i
\(679\) −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
\(682\) −84.4793 146.322i −0.123870 0.214549i
\(683\) 289.407i 0.423729i −0.977299 0.211864i \(-0.932047\pi\)
0.977299 0.211864i \(-0.0679535\pi\)
\(684\) 136.634 + 1128.30i 0.199757 + 1.64955i
\(685\) 386.606 0.564388
\(686\) −66.7246 + 38.5235i −0.0972662 + 0.0561567i
\(687\) −1067.36 616.240i −1.55365 0.897001i
\(688\) 173.411i 0.252050i
\(689\) 120.273 208.319i 0.174562 0.302350i
\(690\) 1086.63 1.57483
\(691\) 308.668i 0.446698i 0.974739 + 0.223349i \(0.0716990\pi\)
−0.974739 + 0.223349i \(0.928301\pi\)
\(692\) 192.547 + 333.500i 0.278247 + 0.481937i
\(693\) 1323.63 + 2292.60i 1.91000 + 3.30822i
\(694\) 1118.56i 1.61176i
\(695\) 55.1585i 0.0793647i
\(696\) 292.768i 0.420644i
\(697\) 88.0673 + 152.537i 0.126352 + 0.218848i
\(698\) 507.271 + 878.620i 0.726750 + 1.25877i
\(699\) 697.440 402.667i 0.997769 0.576062i
\(700\) 521.028i 0.744326i
\(701\) −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
\(706\) 95.7723 + 165.882i 0.135655 + 0.234961i
\(707\) 1414.65 816.749i 2.00092 1.15523i
\(708\) −378.907 −0.535179
\(709\) −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
\(716\) −711.410 410.733i −0.993589 0.573649i
\(717\) 291.818 505.443i 0.406998 0.704942i
\(718\) 428.890i 0.597340i
\(719\) −391.610 226.096i −0.544659 0.314459i 0.202306 0.979322i \(-0.435156\pi\)
−0.746965 + 0.664863i \(0.768490\pi\)
\(720\) −416.000 720.533i −0.577778 1.00074i
\(721\) −1682.31 −2.33330
\(722\) 499.814 + 521.028i 0.692263 + 0.721646i
\(723\) 324.140i 0.448327i
\(724\) −863.540 −1.19274
\(725\) 48.2614 83.5912i 0.0665674 0.115298i
\(726\) 1828.25i 2.51825i
\(727\) 1194.95 + 689.905i 1.64367 + 0.948975i 0.979512 + 0.201385i \(0.0645444\pi\)
0.664161 + 0.747590i \(0.268789\pi\)
\(728\) 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
\(732\) 280.135 + 161.736i 0.382698 + 0.220951i
\(733\) 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
\(736\) 1021.59i 1.38803i
\(737\) −840.793 1456.30i −1.14083 1.97598i
\(738\) −522.043 904.206i −0.707376 1.22521i
\(739\) −699.757 404.005i −0.946897 0.546692i −0.0547817 0.998498i \(-0.517446\pi\)
−0.892116 + 0.451807i \(0.850780\pi\)
\(740\) −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 0.246434 0.969160i \(-0.420741\pi\)
−0.716100 + 0.697998i \(0.754075\pi\)
\(744\) −94.2733 + 163.286i −0.126711 + 0.219471i
\(745\) −68.7940 119.155i −0.0923409 0.159939i
\(746\) −258.091 447.027i −0.345967 0.599232i
\(747\) 1204.34 695.324i 1.61223 0.930822i
\(748\) −306.629 + 177.033i −0.409932 + 0.236675i
\(749\) −1832.72 −2.44689
\(750\) 1290.32i 1.72043i
\(751\) 1181.79 682.308i 1.57362 0.908532i 0.577905 0.816104i \(-0.303870\pi\)
0.995719 0.0924285i \(-0.0294629\pi\)
\(752\) −306.725 177.088i −0.407879 0.235489i
\(753\) 910.588 1.20928
\(754\) 89.7267 0.119001
\(755\) 14.5010 + 8.37218i 0.0192067 + 0.0110890i
\(756\) 588.135 1018.68i 0.777956 1.34746i
\(757\) −555.043 + 961.363i −0.733215 + 1.26996i 0.222288 + 0.974981i \(0.428648\pi\)
−0.955502 + 0.294984i \(0.904686\pi\)
\(758\) −205.366 + 118.568i −0.270932 + 0.156423i
\(759\) 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 \(0.186369\pi\)
\(762\) −690.634 1196.21i −0.906343 1.56983i
\(763\) −714.178 412.331i −0.936013 0.540407i
\(764\) 632.364 + 365.096i 0.827702 + 0.477874i
\(765\) −131.184 + 227.218i −0.171483 + 0.297017i
\(766\) 1233.40i 1.61018i
\(767\) 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 \(0.583889\pi\)
\(770\) −1231.09 −1.59882
\(771\) 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 \(0.614966\pi\)
\(774\) −280.729 + 162.079i −0.362699 + 0.209404i
\(775\) −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
\(782\) −278.994 + 161.077i −0.356770 + 0.205981i
\(783\) 188.715 108.955i 0.241015 0.139150i
\(784\) 422.542 + 731.865i 0.538957 + 0.933501i
\(785\) 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 \(-0.981232\pi\)
0.998262 0.0589276i \(-0.0187681\pi\)
\(788\) −20.3168 + 35.1897i −0.0257827 + 0.0446569i
\(789\) −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
\(794\) −1058.13 −1.33266
\(795\) 590.887 + 341.149i 0.743254 + 0.429118i
\(796\) 734.280i 0.922462i
\(797\) 1276.61 1.60176 0.800882 0.598822i \(-0.204365\pi\)
0.800882 + 0.598822i \(0.204365\pi\)
\(798\) −225.612 1863.06i −0.282722 2.33466i
\(799\) 111.688i 0.139785i
\(800\) −413.085 −0.516356
\(801\) −841.180 + 1456.97i −1.05016 + 1.81893i
\(802\) 3.82195 0.00476553
\(803\) 530.373 + 306.211i 0.660490 + 0.381334i
\(804\) −938.269 + 1625.13i −1.16700 + 2.02131i
\(805\) −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 0.178738 0.983897i \(-0.442799\pi\)
0.941448 + 0.337157i \(0.109465\pi\)
\(812\) 301.795i 0.371669i
\(813\) 859.053 + 1487.92i 1.05665 + 1.83016i
\(814\) 1561.43 901.489i 1.91821 1.10748i
\(815\) 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
\(820\) 485.545 0.592127
\(821\) −200.770 347.744i −0.244543 0.423562i 0.717460 0.696600i \(-0.245305\pi\)
−0.962003 + 0.273038i \(0.911971\pi\)
\(822\) 942.517 544.162i 1.14661 0.661998i
\(823\) −243.748 + 140.728i −0.296171 + 0.170994i −0.640721 0.767774i \(-0.721365\pi\)
0.344551 + 0.938768i \(0.388031\pi\)
\(824\) 1333.78i 1.61867i
\(825\) 1108.40 1.34352
\(826\) 390.590 0.472869
\(827\) −551.534 + 318.428i −0.666909 + 0.385040i −0.794904 0.606735i \(-0.792479\pi\)
0.127995 + 0.991775i \(0.459146\pi\)
\(828\) 1653.81 954.830i 1.99736 1.15318i
\(829\) −52.2774 −0.0630608 −0.0315304 0.999503i \(-0.510038\pi\)
−0.0315304 + 0.999503i \(0.510038\pi\)
\(830\) 646.710i 0.779169i
\(831\) −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
\(834\) −77.6377 134.472i −0.0930907 0.161238i
\(835\) 414.841i 0.496816i
\(836\) 523.002 1226.44i 0.625601 1.46704i
\(837\) −140.336 −0.167666
\(838\) 1443.45 833.373i 1.72249 0.994479i
\(839\) −934.461 539.511i −1.11378 0.643041i −0.173974 0.984750i \(-0.555661\pi\)
−0.939806 + 0.341709i \(0.888994\pi\)
\(840\) 686.907 + 1189.76i 0.817746 + 1.41638i
\(841\) 392.546 679.909i 0.466760 0.808453i
\(842\) −1619.86 −1.92382
\(843\) 117.454i 0.139328i
\(844\) 1020.90 589.418i 1.20960 0.698363i
\(845\) −231.236 400.512i −0.273651 0.473978i
\(846\) 662.062i 0.782579i
\(847\) 1884.62i 2.22506i
\(848\) 320.729 555.519i 0.378218 0.655093i
\(849\) 353.886 + 612.949i 0.416827 + 0.721966i
\(850\) 65.1325 + 112.813i 0.0766265 + 0.132721i
\(851\) 1420.70 820.241i 1.66945 0.963855i
\(852\) 286.178 0.335890
\(853\) 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 \(0.273414\pi\)
\(858\) 515.180 + 892.318i 0.600443 + 1.04000i
\(859\) −794.551 + 458.734i −0.924972 + 0.534033i −0.885218 0.465176i \(-0.845991\pi\)
−0.0397544 + 0.999209i \(0.512658\pi\)
\(860\) 150.747i 0.175287i
\(861\) 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 \(-0.912670\pi\)
0.962600 0.270927i \(-0.0873301\pi\)
\(864\) −807.636 466.289i −0.934763 0.539686i
\(865\) −167.382 289.914i −0.193505 0.335161i
\(866\) 242.273 419.630i 0.279761 0.484561i
\(867\) 1289.86i 1.48773i
\(868\) 97.1801 168.321i 0.111959 0.193918i
\(869\) 689.675 1194.55i 0.793642 1.37463i
\(870\) 254.505i 0.292535i
\(871\) −498.065 287.558i −0.571831 0.330147i
\(872\) −326.907 + 566.219i −0.374893 + 0.649334i
\(873\) −1913.49 −2.19185
\(874\) 475.865 1115.91i 0.544468 1.27678i
\(875\) 1330.11i 1.52012i
\(876\) 683.423i 0.780163i
\(877\) −753.758 + 1305.55i −0.859474 + 1.48865i 0.0129583 + 0.999916i \(0.495875\pi\)
−0.872432 + 0.488736i \(0.837458\pi\)
\(878\) 580.158i 0.660772i
\(879\) 914.667 + 528.083i 1.04058 + 0.600777i
\(880\) 976.040i 1.10914i
\(881\) −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 −0.317217 0.948353i \(-0.602748\pi\)
0.662689 + 0.748894i \(0.269415\pi\)
\(884\) −60.5466 + 104.870i −0.0684916 + 0.118631i
\(885\) 329.386 0.372188
\(886\) 375.297 + 216.678i 0.423586 + 0.244557i
\(887\) −79.7702 + 46.0553i −0.0899326 + 0.0519226i −0.544292 0.838896i \(-0.683202\pi\)
0.454359 + 0.890819i \(0.349868\pi\)
\(888\) −1742.45 1006.00i −1.96222 1.13289i
\(889\) 711.929 + 1233.10i 0.800820 + 1.38706i
\(890\) −391.184 677.551i −0.439533 0.761293i
\(891\) 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
\(896\) 1118.54 645.791i 1.24837 0.720749i
\(897\) 468.748 + 811.896i 0.522574 + 0.905124i
\(898\) 315.820 + 547.016i 0.351693 + 0.609149i
\(899\) 31.1822 18.0030i 0.0346854 0.0200256i
\(900\) −386.091 668.729i −0.428990 0.743033i
\(901\) −202.282 −0.224508
\(902\) 1224.84i 1.35792i
\(903\) 463.545 267.628i 0.513338 0.296376i
\(904\) −216.729 −0.239744
\(905\) 750.681 0.829482
\(906\) 47.1366 0.0520272
\(907\) 1071.41 + 618.580i 1.18127 + 0.682007i 0.956308 0.292360i \(-0.0944407\pi\)
0.224962 + 0.974367i \(0.427774\pi\)
\(908\) −94.1346 54.3486i −0.103672 0.0598553i
\(909\) 1210.45 2096.56i 1.33163 2.30645i
\(910\) −364.634 + 210.521i −0.400696 + 0.231342i
\(911\) 391.450i 0.429693i −0.976648 0.214846i \(-0.931075\pi\)
0.976648 0.214846i \(-0.0689251\pi\)
\(912\) −1477.08 + 178.871i −1.61961 + 0.196130i
\(913\) −1631.40 −1.78686
\(914\) 642.996 + 1113.70i 0.703497 + 1.21849i
\(915\) −243.523 140.598i −0.266145 0.153659i
\(916\) 503.636 872.322i 0.549821 0.952317i
\(917\) 681.940 1181.16i 0.743665 1.28806i
\(918\) 294.085i 0.320354i
\(919\) 166.723i 0.181418i 0.995877 + 0.0907088i \(0.0289132\pi\)
−0.995877 + 0.0907088i \(0.971087\pi\)
\(920\) 888.072i 0.965296i
\(921\) −219.795 380.696i −0.238648 0.413351i
\(922\) −439.627 −0.476819
\(923\) 87.7070i 0.0950239i
\(924\) −3001.31 + 1732.81i −3.24817 + 1.87533i
\(925\) −331.669 574.468i −0.358561 0.621046i
\(926\) −115.592 + 66.7372i −0.124830 + 0.0720704i
\(927\) −2159.22 + 1246.62i −2.32925 + 1.34479i
\(928\) 239.271 0.257835
\(929\) −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
\(934\) −297.701 + 171.878i −0.318737 + 0.184023i
\(935\) 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
\(940\) 266.638 + 153.943i 0.283657 + 0.163770i
\(941\) 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
\(944\) 309.670i 0.328040i
\(945\) −511.269 + 885.544i −0.541026 + 0.937084i
\(946\) 380.277 0.401985
\(947\) 66.9503 + 38.6538i 0.0706973 + 0.0408171i 0.534932 0.844895i \(-0.320337\pi\)
−0.464235 + 0.885712i \(0.653671\pi\)
\(948\) −1539.26 −1.62370
\(949\) 209.453 0.220710
\(950\) −451.224 192.419i −0.474972 0.202546i
\(951\) 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 \(0.966037\pi\)
\(954\) 1199.08 1.25690
\(955\) −549.718 317.380i −0.575621 0.332335i
\(956\) 413.085 + 238.495i 0.432097 + 0.249471i
\(957\) −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
\(964\) −264.911 −0.274804
\(965\) −175.679 304.285i −0.182051 0.315321i
\(966\) −2730.81 + 1576.63i −2.82692 + 1.63212i
\(967\) 1025.02 + 591.795i 1.06000 + 0.611991i 0.925432 0.378913i \(-0.123702\pi\)
0.134567 + 0.990904i \(0.457035\pi\)
\(968\) −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 0.141911 0.989879i \(-0.454675\pi\)
−0.786306 + 0.617838i \(0.788009\pi\)
\(972\) 891.639i 0.917324i
\(973\) 80.0316 + 138.619i 0.0822524 + 0.142465i
\(974\) 253.022 146.082i 0.259776 0.149982i
\(975\) 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 \(0.732858\pi\)
\(978\) 2034.90 2.08068
\(979\) 1709.20 986.809i 1.74587 1.00798i
\(980\) −367.319 636.215i −0.374815 0.649199i
\(981\) −1222.18 −1.24585
\(982\) 953.622i 0.971102i
\(983\) −857.727 495.209i −0.872560 0.503773i −0.00436204 0.999990i \(-0.501388\pi\)
−0.868198 + 0.496218i \(0.834722\pi\)
\(984\) 1183.72 683.423i 1.20297 0.694535i
\(985\) 17.6615 30.5906i 0.0179305 0.0310565i
\(986\) −37.7267 65.3446i −0.0382624 0.0662724i
\(987\) 1093.21i 1.10761i
\(988\) −54.8199 452.693i −0.0554857 0.458191i
\(989\) 346.004 0.349853
\(990\) −1580.08 + 912.259i −1.59604 + 0.921474i
\(991\) 974.899 + 562.858i 0.983752 + 0.567970i 0.903401 0.428797i \(-0.141062\pi\)
0.0803514 + 0.996767i \(0.474396\pi\)
\(992\) −133.449 77.0470i −0.134525 0.0776683i
\(993\) −253.385 + 438.876i −0.255171 + 0.441970i
\(994\) −295.002 −0.296783
\(995\) 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 \(-0.388420\pi\)
\(998\) 1158.44i 1.16076i
\(999\) 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.a.11.2 yes 4
4.3 odd 2 76.3.g.b.11.1 yes 4
19.7 even 3 76.3.g.b.7.1 yes 4
76.7 odd 6 inner 76.3.g.a.7.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
76.3.g.a.7.2 4 76.7 odd 6 inner
76.3.g.a.11.2 yes 4 1.1 even 1 trivial
76.3.g.b.7.1 yes 4 19.7 even 3
76.3.g.b.11.1 yes 4 4.3 odd 2