Properties

Label 1110.2.ba.a.619.17
Level $1110$
Weight $2$
Character 1110.619
Analytic conductor $8.863$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.ba (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 619.17
Character \(\chi\) \(=\) 1110.619
Dual form 1110.2.ba.a.529.17

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.581519 + 2.15913i) q^{5} +1.00000i q^{6} +(1.29297 - 0.746494i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.581519 + 2.15913i) q^{5} +1.00000i q^{6} +(1.29297 - 0.746494i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.57910 - 1.58317i) q^{10} -4.99238 q^{11} +(-0.866025 - 0.500000i) q^{12} +(-3.55888 - 6.16416i) q^{13} +1.49299i q^{14} +(0.575954 + 2.16062i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.24427 + 3.88718i) q^{17} +(0.500000 + 0.866025i) q^{18} +(2.68637 - 1.55098i) q^{19} +(2.16062 - 0.575954i) q^{20} +(0.746494 - 1.29297i) q^{21} +(2.49619 - 4.32353i) q^{22} -7.83788 q^{23} +(0.866025 - 0.500000i) q^{24} +(-4.32367 - 2.51115i) q^{25} +7.11776 q^{26} -1.00000i q^{27} +(-1.29297 - 0.746494i) q^{28} -8.24378i q^{29} +(-2.15913 - 0.581519i) q^{30} +0.925166i q^{31} +(-0.500000 - 0.866025i) q^{32} +(-4.32353 + 2.49619i) q^{33} +(-2.24427 - 3.88718i) q^{34} +(0.859892 + 3.22578i) q^{35} -1.00000 q^{36} +(-4.87320 + 3.64031i) q^{37} +3.10196i q^{38} +(-6.16416 - 3.55888i) q^{39} +(-0.581519 + 2.15913i) q^{40} +(3.23677 + 5.60626i) q^{41} +(0.746494 + 1.29297i) q^{42} +8.04319 q^{43} +(2.49619 + 4.32353i) q^{44} +(1.57910 + 1.58317i) q^{45} +(3.91894 - 6.78780i) q^{46} -4.51871i q^{47} +1.00000i q^{48} +(-2.38549 + 4.13180i) q^{49} +(4.33655 - 2.48883i) q^{50} +4.48853i q^{51} +(-3.55888 + 6.16416i) q^{52} +(-3.66104 - 2.11370i) q^{53} +(0.866025 + 0.500000i) q^{54} +(2.90317 - 10.7792i) q^{55} +(1.29297 - 0.746494i) q^{56} +(1.55098 - 2.68637i) q^{57} +(7.13932 + 4.12189i) q^{58} +(-4.55609 - 2.63046i) q^{59} +(1.58317 - 1.57910i) q^{60} +(8.38002 - 4.83821i) q^{61} +(-0.801217 - 0.462583i) q^{62} -1.49299i q^{63} +1.00000 q^{64} +(15.3788 - 4.09950i) q^{65} -4.99238i q^{66} +(-11.5321 + 6.65806i) q^{67} +4.48853 q^{68} +(-6.78780 + 3.91894i) q^{69} +(-3.22355 - 0.868201i) q^{70} +(0.259078 + 0.448736i) q^{71} +(0.500000 - 0.866025i) q^{72} -13.8195i q^{73} +(-0.716002 - 6.04048i) q^{74} +(-4.99998 - 0.0128835i) q^{75} +(-2.68637 - 1.55098i) q^{76} +(-6.45498 + 3.72678i) q^{77} +(6.16416 - 3.55888i) q^{78} +(-0.836264 + 0.482817i) q^{79} +(-1.57910 - 1.58317i) q^{80} +(-0.500000 - 0.866025i) q^{81} -6.47355 q^{82} +(-7.83972 - 4.52626i) q^{83} -1.49299 q^{84} +(-7.08784 - 7.10613i) q^{85} +(-4.02159 + 6.96561i) q^{86} +(-4.12189 - 7.13932i) q^{87} -4.99238 q^{88} +(6.79186 + 3.92128i) q^{89} +(-2.16062 + 0.575954i) q^{90} +(-9.20301 - 5.31336i) q^{91} +(3.91894 + 6.78780i) q^{92} +(0.462583 + 0.801217i) q^{93} +(3.91331 + 2.25935i) q^{94} +(1.78658 + 6.70215i) q^{95} +(-0.866025 - 0.500000i) q^{96} -9.48892 q^{97} +(-2.38549 - 4.13180i) q^{98} +(-2.49619 + 4.32353i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 18q^{2} - 18q^{4} + 2q^{5} + 36q^{8} + 18q^{9} + O(q^{10}) \) \( 36q - 18q^{2} - 18q^{4} + 2q^{5} + 36q^{8} + 18q^{9} + 2q^{10} + 4q^{11} - 14q^{13} - 2q^{15} - 18q^{16} + 18q^{18} + 6q^{19} - 4q^{20} - 2q^{22} - 20q^{23} + 4q^{25} + 28q^{26} - 2q^{30} - 18q^{32} - 6q^{33} - 40q^{35} - 36q^{36} + 20q^{37} + 6q^{39} + 2q^{40} + 10q^{41} - 2q^{44} - 2q^{45} + 10q^{46} + 10q^{49} - 2q^{50} - 14q^{52} - 12q^{53} + 56q^{55} + 8q^{57} + 30q^{58} + 18q^{59} + 4q^{60} - 6q^{61} - 12q^{62} + 36q^{64} + 40q^{65} + 36q^{67} + 12q^{69} + 20q^{70} - 24q^{71} + 18q^{72} - 34q^{74} + 8q^{75} - 6q^{76} - 24q^{77} - 6q^{78} + 2q^{80} - 18q^{81} - 20q^{82} + 36q^{83} + 26q^{85} - 10q^{87} + 4q^{88} + 4q^{90} - 36q^{91} + 10q^{92} + 12q^{93} + 12q^{94} - 30q^{95} + 52q^{97} + 10q^{98} + 2q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 0.866025 0.500000i 0.500000 0.288675i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −0.581519 + 2.15913i −0.260063 + 0.965592i
\(6\) 1.00000i 0.408248i
\(7\) 1.29297 0.746494i 0.488695 0.282148i −0.235338 0.971914i \(-0.575620\pi\)
0.724033 + 0.689765i \(0.242286\pi\)
\(8\) 1.00000 0.353553
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) −1.57910 1.58317i −0.499355 0.500644i
\(11\) −4.99238 −1.50526 −0.752630 0.658443i \(-0.771215\pi\)
−0.752630 + 0.658443i \(0.771215\pi\)
\(12\) −0.866025 0.500000i −0.250000 0.144338i
\(13\) −3.55888 6.16416i −0.987055 1.70963i −0.632421 0.774625i \(-0.717939\pi\)
−0.354634 0.935005i \(-0.615395\pi\)
\(14\) 1.49299i 0.399018i
\(15\) 0.575954 + 2.16062i 0.148711 + 0.557870i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −2.24427 + 3.88718i −0.544314 + 0.942780i 0.454335 + 0.890831i \(0.349877\pi\)
−0.998650 + 0.0519493i \(0.983457\pi\)
\(18\) 0.500000 + 0.866025i 0.117851 + 0.204124i
\(19\) 2.68637 1.55098i 0.616296 0.355819i −0.159129 0.987258i \(-0.550869\pi\)
0.775426 + 0.631439i \(0.217535\pi\)
\(20\) 2.16062 0.575954i 0.483129 0.128787i
\(21\) 0.746494 1.29297i 0.162898 0.282148i
\(22\) 2.49619 4.32353i 0.532190 0.921780i
\(23\) −7.83788 −1.63431 −0.817155 0.576417i \(-0.804450\pi\)
−0.817155 + 0.576417i \(0.804450\pi\)
\(24\) 0.866025 0.500000i 0.176777 0.102062i
\(25\) −4.32367 2.51115i −0.864734 0.502230i
\(26\) 7.11776 1.39591
\(27\) 1.00000i 0.192450i
\(28\) −1.29297 0.746494i −0.244347 0.141074i
\(29\) 8.24378i 1.53083i −0.643537 0.765415i \(-0.722534\pi\)
0.643537 0.765415i \(-0.277466\pi\)
\(30\) −2.15913 0.581519i −0.394201 0.106170i
\(31\) 0.925166i 0.166165i 0.996543 + 0.0830823i \(0.0264764\pi\)
−0.996543 + 0.0830823i \(0.973524\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −4.32353 + 2.49619i −0.752630 + 0.434531i
\(34\) −2.24427 3.88718i −0.384888 0.666646i
\(35\) 0.859892 + 3.22578i 0.145348 + 0.545256i
\(36\) −1.00000 −0.166667
\(37\) −4.87320 + 3.64031i −0.801150 + 0.598464i
\(38\) 3.10196i 0.503204i
\(39\) −6.16416 3.55888i −0.987055 0.569877i
\(40\) −0.581519 + 2.15913i −0.0919463 + 0.341388i
\(41\) 3.23677 + 5.60626i 0.505499 + 0.875550i 0.999980 + 0.00636146i \(0.00202493\pi\)
−0.494481 + 0.869189i \(0.664642\pi\)
\(42\) 0.746494 + 1.29297i 0.115187 + 0.199509i
\(43\) 8.04319 1.22657 0.613287 0.789860i \(-0.289847\pi\)
0.613287 + 0.789860i \(0.289847\pi\)
\(44\) 2.49619 + 4.32353i 0.376315 + 0.651797i
\(45\) 1.57910 + 1.58317i 0.235398 + 0.236006i
\(46\) 3.91894 6.78780i 0.577816 1.00081i
\(47\) 4.51871i 0.659121i −0.944134 0.329560i \(-0.893099\pi\)
0.944134 0.329560i \(-0.106901\pi\)
\(48\) 1.00000i 0.144338i
\(49\) −2.38549 + 4.13180i −0.340785 + 0.590257i
\(50\) 4.33655 2.48883i 0.613281 0.351974i
\(51\) 4.48853i 0.628520i
\(52\) −3.55888 + 6.16416i −0.493528 + 0.854815i
\(53\) −3.66104 2.11370i −0.502882 0.290339i 0.227021 0.973890i \(-0.427101\pi\)
−0.729903 + 0.683551i \(0.760435\pi\)
\(54\) 0.866025 + 0.500000i 0.117851 + 0.0680414i
\(55\) 2.90317 10.7792i 0.391463 1.45347i
\(56\) 1.29297 0.746494i 0.172780 0.0997544i
\(57\) 1.55098 2.68637i 0.205432 0.355819i
\(58\) 7.13932 + 4.12189i 0.937439 + 0.541230i
\(59\) −4.55609 2.63046i −0.593153 0.342457i 0.173190 0.984888i \(-0.444592\pi\)
−0.766343 + 0.642431i \(0.777926\pi\)
\(60\) 1.58317 1.57910i 0.204387 0.203861i
\(61\) 8.38002 4.83821i 1.07295 0.619469i 0.143965 0.989583i \(-0.454015\pi\)
0.928986 + 0.370114i \(0.120681\pi\)
\(62\) −0.801217 0.462583i −0.101755 0.0587481i
\(63\) 1.49299i 0.188099i
\(64\) 1.00000 0.125000
\(65\) 15.3788 4.09950i 1.90750 0.508480i
\(66\) 4.99238i 0.614520i
\(67\) −11.5321 + 6.65806i −1.40887 + 0.813412i −0.995279 0.0970505i \(-0.969059\pi\)
−0.413592 + 0.910463i \(0.635726\pi\)
\(68\) 4.48853 0.544314
\(69\) −6.78780 + 3.91894i −0.817155 + 0.471785i
\(70\) −3.22355 0.868201i −0.385288 0.103770i
\(71\) 0.259078 + 0.448736i 0.0307469 + 0.0532552i 0.880989 0.473136i \(-0.156878\pi\)
−0.850243 + 0.526391i \(0.823545\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) 13.8195i 1.61745i −0.588185 0.808726i \(-0.700157\pi\)
0.588185 0.808726i \(-0.299843\pi\)
\(74\) −0.716002 6.04048i −0.0832335 0.702191i
\(75\) −4.99998 0.0128835i −0.577348 0.00148766i
\(76\) −2.68637 1.55098i −0.308148 0.177909i
\(77\) −6.45498 + 3.72678i −0.735613 + 0.424707i
\(78\) 6.16416 3.55888i 0.697953 0.402964i
\(79\) −0.836264 + 0.482817i −0.0940870 + 0.0543212i −0.546305 0.837586i \(-0.683966\pi\)
0.452218 + 0.891907i \(0.350633\pi\)
\(80\) −1.57910 1.58317i −0.176549 0.177004i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −6.47355 −0.714884
\(83\) −7.83972 4.52626i −0.860521 0.496822i 0.00366573 0.999993i \(-0.498833\pi\)
−0.864187 + 0.503171i \(0.832166\pi\)
\(84\) −1.49299 −0.162898
\(85\) −7.08784 7.10613i −0.768784 0.770768i
\(86\) −4.02159 + 6.96561i −0.433660 + 0.751121i
\(87\) −4.12189 7.13932i −0.441913 0.765415i
\(88\) −4.99238 −0.532190
\(89\) 6.79186 + 3.92128i 0.719935 + 0.415655i 0.814729 0.579842i \(-0.196886\pi\)
−0.0947935 + 0.995497i \(0.530219\pi\)
\(90\) −2.16062 + 0.575954i −0.227749 + 0.0607109i
\(91\) −9.20301 5.31336i −0.964738 0.556992i
\(92\) 3.91894 + 6.78780i 0.408578 + 0.707677i
\(93\) 0.462583 + 0.801217i 0.0479676 + 0.0830823i
\(94\) 3.91331 + 2.25935i 0.403628 + 0.233034i
\(95\) 1.78658 + 6.70215i 0.183300 + 0.687626i
\(96\) −0.866025 0.500000i −0.0883883 0.0510310i
\(97\) −9.48892 −0.963454 −0.481727 0.876321i \(-0.659990\pi\)
−0.481727 + 0.876321i \(0.659990\pi\)
\(98\) −2.38549 4.13180i −0.240971 0.417374i
\(99\) −2.49619 + 4.32353i −0.250877 + 0.434531i
\(100\) −0.0128835 + 4.99998i −0.00128835 + 0.499998i
\(101\) 8.49427 0.845211 0.422606 0.906314i \(-0.361116\pi\)
0.422606 + 0.906314i \(0.361116\pi\)
\(102\) −3.88718 2.24427i −0.384888 0.222215i
\(103\) 5.32885 0.525068 0.262534 0.964923i \(-0.415442\pi\)
0.262534 + 0.964923i \(0.415442\pi\)
\(104\) −3.55888 6.16416i −0.348977 0.604445i
\(105\) 2.35758 + 2.36366i 0.230076 + 0.230670i
\(106\) 3.66104 2.11370i 0.355591 0.205301i
\(107\) −5.06411 + 2.92376i −0.489566 + 0.282651i −0.724394 0.689386i \(-0.757880\pi\)
0.234829 + 0.972037i \(0.424547\pi\)
\(108\) −0.866025 + 0.500000i −0.0833333 + 0.0481125i
\(109\) −6.74554 3.89454i −0.646105 0.373029i 0.140857 0.990030i \(-0.455014\pi\)
−0.786962 + 0.617001i \(0.788347\pi\)
\(110\) 7.88348 + 7.90382i 0.751660 + 0.753599i
\(111\) −2.40016 + 5.58921i −0.227813 + 0.530504i
\(112\) 1.49299i 0.141074i
\(113\) 0.919606 1.59280i 0.0865092 0.149838i −0.819524 0.573045i \(-0.805762\pi\)
0.906033 + 0.423206i \(0.139095\pi\)
\(114\) 1.55098 + 2.68637i 0.145262 + 0.251602i
\(115\) 4.55788 16.9230i 0.425024 1.57808i
\(116\) −7.13932 + 4.12189i −0.662869 + 0.382708i
\(117\) −7.11776 −0.658037
\(118\) 4.55609 2.63046i 0.419423 0.242154i
\(119\) 6.70132i 0.614309i
\(120\) 0.575954 + 2.16062i 0.0525772 + 0.197237i
\(121\) 13.9239 1.26581
\(122\) 9.67642i 0.876062i
\(123\) 5.60626 + 3.23677i 0.505499 + 0.291850i
\(124\) 0.801217 0.462583i 0.0719514 0.0415412i
\(125\) 7.93619 7.87508i 0.709834 0.704369i
\(126\) 1.29297 + 0.746494i 0.115187 + 0.0665030i
\(127\) −7.96186 4.59678i −0.706501 0.407899i 0.103263 0.994654i \(-0.467072\pi\)
−0.809764 + 0.586755i \(0.800405\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 6.96561 4.02159i 0.613287 0.354082i
\(130\) −4.13911 + 15.3682i −0.363024 + 1.34788i
\(131\) −6.67622 3.85452i −0.583304 0.336771i 0.179141 0.983823i \(-0.442668\pi\)
−0.762445 + 0.647053i \(0.776001\pi\)
\(132\) 4.32353 + 2.49619i 0.376315 + 0.217266i
\(133\) 2.31559 4.01072i 0.200787 0.347774i
\(134\) 13.3161i 1.15034i
\(135\) 2.15913 + 0.581519i 0.185828 + 0.0500492i
\(136\) −2.24427 + 3.88718i −0.192444 + 0.333323i
\(137\) 5.30952i 0.453623i −0.973939 0.226812i \(-0.927170\pi\)
0.973939 0.226812i \(-0.0728301\pi\)
\(138\) 7.83788i 0.667205i
\(139\) −3.98426 + 6.90094i −0.337941 + 0.585330i −0.984045 0.177919i \(-0.943064\pi\)
0.646105 + 0.763249i \(0.276397\pi\)
\(140\) 2.36366 2.35758i 0.199766 0.199252i
\(141\) −2.25935 3.91331i −0.190272 0.329560i
\(142\) −0.518156 −0.0434827
\(143\) 17.7673 + 30.7738i 1.48578 + 2.57344i
\(144\) 0.500000 + 0.866025i 0.0416667 + 0.0721688i
\(145\) 17.7994 + 4.79391i 1.47816 + 0.398113i
\(146\) 11.9681 + 6.90976i 0.990484 + 0.571856i
\(147\) 4.77099i 0.393504i
\(148\) 5.58921 + 2.40016i 0.459430 + 0.197292i
\(149\) 8.88053 0.727521 0.363760 0.931493i \(-0.381493\pi\)
0.363760 + 0.931493i \(0.381493\pi\)
\(150\) 2.51115 4.32367i 0.205034 0.353026i
\(151\) 5.35526 + 9.27558i 0.435805 + 0.754836i 0.997361 0.0726027i \(-0.0231305\pi\)
−0.561556 + 0.827439i \(0.689797\pi\)
\(152\) 2.68637 1.55098i 0.217894 0.125801i
\(153\) 2.24427 + 3.88718i 0.181438 + 0.314260i
\(154\) 7.45357i 0.600626i
\(155\) −1.99755 0.538002i −0.160447 0.0432133i
\(156\) 7.11776i 0.569877i
\(157\) 5.76364 + 3.32764i 0.459988 + 0.265574i 0.712039 0.702140i \(-0.247772\pi\)
−0.252051 + 0.967714i \(0.581105\pi\)
\(158\) 0.965634i 0.0768217i
\(159\) −4.22740 −0.335255
\(160\) 2.16062 0.575954i 0.170812 0.0455331i
\(161\) −10.1341 + 5.85093i −0.798679 + 0.461118i
\(162\) 1.00000 0.0785674
\(163\) 1.39135 2.40989i 0.108979 0.188757i −0.806378 0.591401i \(-0.798575\pi\)
0.915357 + 0.402644i \(0.131909\pi\)
\(164\) 3.23677 5.60626i 0.252750 0.437775i
\(165\) −2.87538 10.7866i −0.223848 0.839739i
\(166\) 7.83972 4.52626i 0.608480 0.351306i
\(167\) −7.54017 13.0600i −0.583476 1.01061i −0.995064 0.0992397i \(-0.968359\pi\)
0.411588 0.911370i \(-0.364974\pi\)
\(168\) 0.746494 1.29297i 0.0575933 0.0997544i
\(169\) −18.8312 + 32.6167i −1.44856 + 2.50897i
\(170\) 9.69801 2.58519i 0.743803 0.198275i
\(171\) 3.10196i 0.237213i
\(172\) −4.02159 6.96561i −0.306644 0.531123i
\(173\) 15.2577 + 8.80902i 1.16002 + 0.669737i 0.951309 0.308240i \(-0.0997400\pi\)
0.208711 + 0.977977i \(0.433073\pi\)
\(174\) 8.24378 0.624959
\(175\) −7.46491 0.0192349i −0.564294 0.00145402i
\(176\) 2.49619 4.32353i 0.188158 0.325898i
\(177\) −5.26092 −0.395435
\(178\) −6.79186 + 3.92128i −0.509071 + 0.293912i
\(179\) 6.17151i 0.461280i −0.973039 0.230640i \(-0.925918\pi\)
0.973039 0.230640i \(-0.0740820\pi\)
\(180\) 0.581519 2.15913i 0.0433439 0.160932i
\(181\) 4.96675 + 8.60266i 0.369176 + 0.639431i 0.989437 0.144964i \(-0.0463068\pi\)
−0.620261 + 0.784395i \(0.712973\pi\)
\(182\) 9.20301 5.31336i 0.682173 0.393853i
\(183\) 4.83821 8.38002i 0.357651 0.619469i
\(184\) −7.83788 −0.577816
\(185\) −5.02604 12.6388i −0.369522 0.929222i
\(186\) −0.925166 −0.0678364
\(187\) 11.2042 19.4063i 0.819335 1.41913i
\(188\) −3.91331 + 2.25935i −0.285408 + 0.164780i
\(189\) −0.746494 1.29297i −0.0542994 0.0940494i
\(190\) −6.69752 1.80385i −0.485889 0.130865i
\(191\) 9.91473i 0.717404i 0.933452 + 0.358702i \(0.116781\pi\)
−0.933452 + 0.358702i \(0.883219\pi\)
\(192\) 0.866025 0.500000i 0.0625000 0.0360844i
\(193\) −16.2324 −1.16843 −0.584217 0.811597i \(-0.698598\pi\)
−0.584217 + 0.811597i \(0.698598\pi\)
\(194\) 4.74446 8.21765i 0.340633 0.589993i
\(195\) 11.2687 11.2397i 0.806965 0.804888i
\(196\) 4.77099 0.340785
\(197\) 5.62897 + 3.24989i 0.401047 + 0.231545i 0.686936 0.726718i \(-0.258955\pi\)
−0.285888 + 0.958263i \(0.592289\pi\)
\(198\) −2.49619 4.32353i −0.177397 0.307260i
\(199\) 19.9907i 1.41710i −0.705660 0.708550i \(-0.749350\pi\)
0.705660 0.708550i \(-0.250650\pi\)
\(200\) −4.32367 2.51115i −0.305730 0.177565i
\(201\) −6.65806 + 11.5321i −0.469624 + 0.813412i
\(202\) −4.24713 + 7.35625i −0.298827 + 0.517584i
\(203\) −6.15393 10.6589i −0.431921 0.748109i
\(204\) 3.88718 2.24427i 0.272157 0.157130i
\(205\) −13.9869 + 3.72846i −0.976886 + 0.260407i
\(206\) −2.66443 + 4.61492i −0.185639 + 0.321537i
\(207\) −3.91894 + 6.78780i −0.272385 + 0.471785i
\(208\) 7.11776 0.493528
\(209\) −13.4114 + 7.74308i −0.927686 + 0.535600i
\(210\) −3.22578 + 0.859892i −0.222600 + 0.0593382i
\(211\) −3.12799 −0.215339 −0.107670 0.994187i \(-0.534339\pi\)
−0.107670 + 0.994187i \(0.534339\pi\)
\(212\) 4.22740i 0.290339i
\(213\) 0.448736 + 0.259078i 0.0307469 + 0.0177517i
\(214\) 5.84753i 0.399729i
\(215\) −4.67727 + 17.3663i −0.318987 + 1.18437i
\(216\) 1.00000i 0.0680414i
\(217\) 0.690630 + 1.19621i 0.0468830 + 0.0812038i
\(218\) 6.74554 3.89454i 0.456865 0.263771i
\(219\) −6.90976 11.9681i −0.466918 0.808726i
\(220\) −10.7866 + 2.87538i −0.727235 + 0.193858i
\(221\) 31.9483 2.14907
\(222\) −3.64031 4.87320i −0.244322 0.327068i
\(223\) 27.7499i 1.85827i 0.369741 + 0.929135i \(0.379446\pi\)
−0.369741 + 0.929135i \(0.620554\pi\)
\(224\) −1.29297 0.746494i −0.0863899 0.0498772i
\(225\) −4.33655 + 2.48883i −0.289104 + 0.165922i
\(226\) 0.919606 + 1.59280i 0.0611713 + 0.105952i
\(227\) 9.89438 + 17.1376i 0.656713 + 1.13746i 0.981461 + 0.191660i \(0.0613870\pi\)
−0.324748 + 0.945800i \(0.605280\pi\)
\(228\) −3.10196 −0.205432
\(229\) 4.33595 + 7.51008i 0.286527 + 0.496280i 0.972978 0.230896i \(-0.0741657\pi\)
−0.686451 + 0.727176i \(0.740832\pi\)
\(230\) 12.3768 + 12.4087i 0.816102 + 0.818207i
\(231\) −3.72678 + 6.45498i −0.245204 + 0.424707i
\(232\) 8.24378i 0.541230i
\(233\) 2.13736i 0.140023i 0.997546 + 0.0700115i \(0.0223036\pi\)
−0.997546 + 0.0700115i \(0.977696\pi\)
\(234\) 3.55888 6.16416i 0.232651 0.402964i
\(235\) 9.75647 + 2.62771i 0.636442 + 0.171413i
\(236\) 5.26092i 0.342457i
\(237\) −0.482817 + 0.836264i −0.0313623 + 0.0543212i
\(238\) −5.80351 3.35066i −0.376186 0.217191i
\(239\) 2.00088 + 1.15521i 0.129426 + 0.0747241i 0.563315 0.826242i \(-0.309526\pi\)
−0.433889 + 0.900966i \(0.642859\pi\)
\(240\) −2.15913 0.581519i −0.139371 0.0375369i
\(241\) 18.1405 10.4734i 1.16853 0.674652i 0.215197 0.976571i \(-0.430960\pi\)
0.953334 + 0.301919i \(0.0976272\pi\)
\(242\) −6.96195 + 12.0585i −0.447531 + 0.775147i
\(243\) −0.866025 0.500000i −0.0555556 0.0320750i
\(244\) −8.38002 4.83821i −0.536476 0.309735i
\(245\) −7.53387 7.55331i −0.481321 0.482563i
\(246\) −5.60626 + 3.23677i −0.357442 + 0.206369i
\(247\) −19.1210 11.0395i −1.21664 0.702426i
\(248\) 0.925166i 0.0587481i
\(249\) −9.05253 −0.573681
\(250\) 2.85192 + 10.8105i 0.180371 + 0.683715i
\(251\) 17.3320i 1.09399i −0.837137 0.546993i \(-0.815772\pi\)
0.837137 0.546993i \(-0.184228\pi\)
\(252\) −1.29297 + 0.746494i −0.0814492 + 0.0470247i
\(253\) 39.1297 2.46006
\(254\) 7.96186 4.59678i 0.499572 0.288428i
\(255\) −9.69131 2.61017i −0.606894 0.163455i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −2.45518 + 4.25250i −0.153150 + 0.265263i −0.932384 0.361470i \(-0.882275\pi\)
0.779234 + 0.626733i \(0.215608\pi\)
\(258\) 8.04319i 0.500747i
\(259\) −3.58341 + 8.34462i −0.222662 + 0.518509i
\(260\) −11.2397 11.2687i −0.697054 0.698852i
\(261\) −7.13932 4.12189i −0.441913 0.255138i
\(262\) 6.67622 3.85452i 0.412458 0.238133i
\(263\) 16.2980 9.40967i 1.00498 0.580225i 0.0952619 0.995452i \(-0.469631\pi\)
0.909718 + 0.415227i \(0.136298\pi\)
\(264\) −4.32353 + 2.49619i −0.266095 + 0.153630i
\(265\) 6.69271 6.67549i 0.411130 0.410072i
\(266\) 2.31559 + 4.01072i 0.141978 + 0.245913i
\(267\) 7.84256 0.479957
\(268\) 11.5321 + 6.65806i 0.704436 + 0.406706i
\(269\) 12.5071 0.762571 0.381285 0.924457i \(-0.375482\pi\)
0.381285 + 0.924457i \(0.375482\pi\)
\(270\) −1.58317 + 1.57910i −0.0963489 + 0.0961010i
\(271\) −12.1046 + 20.9658i −0.735302 + 1.27358i 0.219289 + 0.975660i \(0.429626\pi\)
−0.954591 + 0.297920i \(0.903707\pi\)
\(272\) −2.24427 3.88718i −0.136079 0.235695i
\(273\) −10.6267 −0.643159
\(274\) 4.59818 + 2.65476i 0.277786 + 0.160380i
\(275\) 21.5854 + 12.5366i 1.30165 + 0.755987i
\(276\) 6.78780 + 3.91894i 0.408578 + 0.235892i
\(277\) 12.6092 + 21.8397i 0.757611 + 1.31222i 0.944066 + 0.329758i \(0.106967\pi\)
−0.186454 + 0.982464i \(0.559700\pi\)
\(278\) −3.98426 6.90094i −0.238960 0.413891i
\(279\) 0.801217 + 0.462583i 0.0479676 + 0.0276941i
\(280\) 0.859892 + 3.22578i 0.0513884 + 0.192777i
\(281\) 3.24794 + 1.87520i 0.193756 + 0.111865i 0.593740 0.804657i \(-0.297651\pi\)
−0.399984 + 0.916522i \(0.630984\pi\)
\(282\) 4.51871 0.269085
\(283\) −15.0869 26.1313i −0.896824 1.55334i −0.831531 0.555478i \(-0.812535\pi\)
−0.0652929 0.997866i \(-0.520798\pi\)
\(284\) 0.259078 0.448736i 0.0153734 0.0266276i
\(285\) 4.89830 + 4.91094i 0.290150 + 0.290899i
\(286\) −35.5346 −2.10120
\(287\) 8.37007 + 4.83246i 0.494070 + 0.285251i
\(288\) −1.00000 −0.0589256
\(289\) −1.57345 2.72530i −0.0925560 0.160312i
\(290\) −13.0513 + 13.0178i −0.766401 + 0.764429i
\(291\) −8.21765 + 4.74446i −0.481727 + 0.278125i
\(292\) −11.9681 + 6.90976i −0.700378 + 0.404363i
\(293\) −24.3362 + 14.0505i −1.42174 + 0.820841i −0.996448 0.0842159i \(-0.973161\pi\)
−0.425291 + 0.905057i \(0.639828\pi\)
\(294\) −4.13180 2.38549i −0.240971 0.139125i
\(295\) 8.32896 8.30753i 0.484931 0.483683i
\(296\) −4.87320 + 3.64031i −0.283249 + 0.211589i
\(297\) 4.99238i 0.289688i
\(298\) −4.44026 + 7.69076i −0.257218 + 0.445514i
\(299\) 27.8941 + 48.3139i 1.61316 + 2.79407i
\(300\) 2.48883 + 4.33655i 0.143693 + 0.250371i
\(301\) 10.3996 6.00419i 0.599421 0.346076i
\(302\) −10.7105 −0.616321
\(303\) 7.35625 4.24713i 0.422606 0.243992i
\(304\) 3.10196i 0.177909i
\(305\) 5.57317 + 20.9071i 0.319119 + 1.19713i
\(306\) −4.48853 −0.256592
\(307\) 13.0437i 0.744446i −0.928143 0.372223i \(-0.878596\pi\)
0.928143 0.372223i \(-0.121404\pi\)
\(308\) 6.45498 + 3.72678i 0.367807 + 0.212353i
\(309\) 4.61492 2.66443i 0.262534 0.151574i
\(310\) 1.46470 1.46093i 0.0831893 0.0829752i
\(311\) −18.1342 10.4698i −1.02830 0.593687i −0.111800 0.993731i \(-0.535662\pi\)
−0.916496 + 0.400044i \(0.868995\pi\)
\(312\) −6.16416 3.55888i −0.348977 0.201482i
\(313\) −7.90172 + 13.6862i −0.446632 + 0.773589i −0.998164 0.0605646i \(-0.980710\pi\)
0.551533 + 0.834153i \(0.314043\pi\)
\(314\) −5.76364 + 3.32764i −0.325261 + 0.187789i
\(315\) 3.22355 + 0.868201i 0.181627 + 0.0489176i
\(316\) 0.836264 + 0.482817i 0.0470435 + 0.0271606i
\(317\) −16.8545 9.73093i −0.946641 0.546543i −0.0546048 0.998508i \(-0.517390\pi\)
−0.892036 + 0.451965i \(0.850723\pi\)
\(318\) 2.11370 3.66104i 0.118530 0.205301i
\(319\) 41.1561i 2.30430i
\(320\) −0.581519 + 2.15913i −0.0325079 + 0.120699i
\(321\) −2.92376 + 5.06411i −0.163189 + 0.282651i
\(322\) 11.7019i 0.652119i
\(323\) 13.9232i 0.774709i
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) −0.0917014 + 35.5887i −0.00508668 + 1.97410i
\(326\) 1.39135 + 2.40989i 0.0770597 + 0.133471i
\(327\) −7.78907 −0.430737
\(328\) 3.23677 + 5.60626i 0.178721 + 0.309554i
\(329\) −3.37319 5.84253i −0.185970 0.322109i
\(330\) 10.7792 + 2.90317i 0.593375 + 0.159814i
\(331\) −3.62395 2.09229i −0.199190 0.115003i 0.397087 0.917781i \(-0.370021\pi\)
−0.596278 + 0.802778i \(0.703354\pi\)
\(332\) 9.05253i 0.496822i
\(333\) 0.716002 + 6.04048i 0.0392367 + 0.331016i
\(334\) 15.0803 0.825160
\(335\) −7.66948 28.7711i −0.419028 1.57193i
\(336\) 0.746494 + 1.29297i 0.0407246 + 0.0705370i
\(337\) −11.0981 + 6.40748i −0.604551 + 0.349038i −0.770830 0.637041i \(-0.780158\pi\)
0.166279 + 0.986079i \(0.446825\pi\)
\(338\) −18.8312 32.6167i −1.02428 1.77411i
\(339\) 1.83921i 0.0998923i
\(340\) −2.61017 + 9.69131i −0.141556 + 0.525585i
\(341\) 4.61878i 0.250121i
\(342\) 2.68637 + 1.55098i 0.145262 + 0.0838673i
\(343\) 17.5739i 0.948904i
\(344\) 8.04319 0.433660
\(345\) −4.51426 16.9347i −0.243039 0.911732i
\(346\) −15.2577 + 8.80902i −0.820257 + 0.473576i
\(347\) 12.0755 0.648247 0.324123 0.946015i \(-0.394931\pi\)
0.324123 + 0.946015i \(0.394931\pi\)
\(348\) −4.12189 + 7.13932i −0.220956 + 0.382708i
\(349\) 3.57899 6.19899i 0.191579 0.331824i −0.754195 0.656651i \(-0.771973\pi\)
0.945774 + 0.324827i \(0.105306\pi\)
\(350\) 3.74911 6.45519i 0.200399 0.345044i
\(351\) −6.16416 + 3.55888i −0.329018 + 0.189959i
\(352\) 2.49619 + 4.32353i 0.133047 + 0.230445i
\(353\) −16.3563 + 28.3299i −0.870556 + 1.50785i −0.00913392 + 0.999958i \(0.502907\pi\)
−0.861422 + 0.507889i \(0.830426\pi\)
\(354\) 2.63046 4.55609i 0.139808 0.242154i
\(355\) −1.11954 + 0.298434i −0.0594189 + 0.0158392i
\(356\) 7.84256i 0.415655i
\(357\) 3.35066 + 5.80351i 0.177336 + 0.307155i
\(358\) 5.34469 + 3.08576i 0.282475 + 0.163087i
\(359\) −26.3836 −1.39247 −0.696236 0.717813i \(-0.745143\pi\)
−0.696236 + 0.717813i \(0.745143\pi\)
\(360\) 1.57910 + 1.58317i 0.0832259 + 0.0834406i
\(361\) −4.68893 + 8.12147i −0.246786 + 0.427446i
\(362\) −9.93350 −0.522093
\(363\) 12.0585 6.96195i 0.632905 0.365408i
\(364\) 10.6267i 0.556992i
\(365\) 29.8381 + 8.03632i 1.56180 + 0.420640i
\(366\) 4.83821 + 8.38002i 0.252897 + 0.438031i
\(367\) 1.34639 0.777339i 0.0702810 0.0405768i −0.464448 0.885601i \(-0.653747\pi\)
0.534729 + 0.845024i \(0.320414\pi\)
\(368\) 3.91894 6.78780i 0.204289 0.353839i
\(369\) 6.47355 0.336999
\(370\) 13.4585 + 1.96671i 0.699676 + 0.102244i
\(371\) −6.31146 −0.327675
\(372\) 0.462583 0.801217i 0.0239838 0.0415412i
\(373\) 23.6846 13.6743i 1.22634 0.708028i 0.260078 0.965588i \(-0.416252\pi\)
0.966262 + 0.257560i \(0.0829184\pi\)
\(374\) 11.2042 + 19.4063i 0.579357 + 1.00348i
\(375\) 2.93540 10.7881i 0.151584 0.557096i
\(376\) 4.51871i 0.233034i
\(377\) −50.8159 + 29.3386i −2.61715 + 1.51101i
\(378\) 1.49299 0.0767910
\(379\) 3.06678 5.31181i 0.157530 0.272849i −0.776448 0.630182i \(-0.782980\pi\)
0.933977 + 0.357332i \(0.116314\pi\)
\(380\) 4.91094 4.89830i 0.251926 0.251278i
\(381\) −9.19357 −0.471001
\(382\) −8.58641 4.95736i −0.439319 0.253641i
\(383\) −17.4879 30.2900i −0.893591 1.54774i −0.835539 0.549431i \(-0.814845\pi\)
−0.0580512 0.998314i \(-0.518489\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) −4.29291 16.1043i −0.218787 0.820753i
\(386\) 8.11621 14.0577i 0.413104 0.715517i
\(387\) 4.02159 6.96561i 0.204429 0.354082i
\(388\) 4.74446 + 8.21765i 0.240864 + 0.417188i
\(389\) −16.4618 + 9.50424i −0.834648 + 0.481884i −0.855441 0.517900i \(-0.826714\pi\)
0.0207936 + 0.999784i \(0.493381\pi\)
\(390\) 4.09950 + 15.3788i 0.207586 + 0.778734i
\(391\) 17.5903 30.4673i 0.889579 1.54080i
\(392\) −2.38549 + 4.13180i −0.120486 + 0.208687i
\(393\) −7.70903 −0.388869
\(394\) −5.62897 + 3.24989i −0.283583 + 0.163727i
\(395\) −0.556161 2.08637i −0.0279835 0.104977i
\(396\) 4.99238 0.250877
\(397\) 15.0132i 0.753492i −0.926317 0.376746i \(-0.877043\pi\)
0.926317 0.376746i \(-0.122957\pi\)
\(398\) 17.3124 + 9.99533i 0.867793 + 0.501021i
\(399\) 4.63118i 0.231849i
\(400\) 4.33655 2.48883i 0.216828 0.124442i
\(401\) 2.84609i 0.142127i 0.997472 + 0.0710634i \(0.0226393\pi\)
−0.997472 + 0.0710634i \(0.977361\pi\)
\(402\) −6.65806 11.5321i −0.332074 0.575169i
\(403\) 5.70287 3.29255i 0.284080 0.164014i
\(404\) −4.24713 7.35625i −0.211303 0.365987i
\(405\) 2.16062 0.575954i 0.107362 0.0286194i
\(406\) 12.3079 0.610829
\(407\) 24.3289 18.1738i 1.20594 0.900844i
\(408\) 4.48853i 0.222215i
\(409\) 12.4387 + 7.18152i 0.615057 + 0.355103i 0.774942 0.632033i \(-0.217779\pi\)
−0.159885 + 0.987136i \(0.551112\pi\)
\(410\) 3.76449 13.9772i 0.185915 0.690286i
\(411\) −2.65476 4.59818i −0.130950 0.226812i
\(412\) −2.66443 4.61492i −0.131267 0.227361i
\(413\) −7.85450 −0.386495
\(414\) −3.91894 6.78780i −0.192605 0.333602i
\(415\) 14.3317 14.2949i 0.703517 0.701707i
\(416\) −3.55888 + 6.16416i −0.174488 + 0.302223i
\(417\) 7.96852i 0.390220i
\(418\) 15.4862i 0.757453i
\(419\) 0.643425 1.11444i 0.0314334 0.0544442i −0.849881 0.526975i \(-0.823326\pi\)
0.881314 + 0.472531i \(0.156659\pi\)
\(420\) 0.868201 3.22355i 0.0423639 0.157293i
\(421\) 40.0359i 1.95123i −0.219484 0.975616i \(-0.570437\pi\)
0.219484 0.975616i \(-0.429563\pi\)
\(422\) 1.56399 2.70892i 0.0761340 0.131868i
\(423\) −3.91331 2.25935i −0.190272 0.109853i
\(424\) −3.66104 2.11370i −0.177796 0.102650i
\(425\) 19.4648 11.1712i 0.944179 0.541883i
\(426\) −0.448736 + 0.259078i −0.0217413 + 0.0125524i
\(427\) 7.22339 12.5113i 0.349564 0.605463i
\(428\) 5.06411 + 2.92376i 0.244783 + 0.141325i
\(429\) 30.7738 + 17.7673i 1.48578 + 0.857813i
\(430\) −12.7010 12.7338i −0.612497 0.614077i
\(431\) 6.33783 3.65915i 0.305283 0.176255i −0.339531 0.940595i \(-0.610268\pi\)
0.644814 + 0.764340i \(0.276935\pi\)
\(432\) 0.866025 + 0.500000i 0.0416667 + 0.0240563i
\(433\) 7.62286i 0.366332i 0.983082 + 0.183166i \(0.0586345\pi\)
−0.983082 + 0.183166i \(0.941365\pi\)
\(434\) −1.38126 −0.0663026
\(435\) 17.8117 4.74803i 0.854004 0.227651i
\(436\) 7.78907i 0.373029i
\(437\) −21.0555 + 12.1564i −1.00722 + 0.581519i
\(438\) 13.8195 0.660322
\(439\) 21.6063 12.4744i 1.03121 0.595370i 0.113880 0.993495i \(-0.463672\pi\)
0.917331 + 0.398125i \(0.130339\pi\)
\(440\) 2.90317 10.7792i 0.138403 0.513878i
\(441\) 2.38549 + 4.13180i 0.113595 + 0.196752i
\(442\) −15.9741 + 27.6680i −0.759812 + 1.31603i
\(443\) 18.3769i 0.873111i −0.899677 0.436555i \(-0.856198\pi\)
0.899677 0.436555i \(-0.143802\pi\)
\(444\) 6.04048 0.716002i 0.286668 0.0339799i
\(445\) −12.4161 + 12.3842i −0.588582 + 0.587067i
\(446\) −24.0321 13.8749i −1.13795 0.656998i
\(447\) 7.69076 4.44026i 0.363760 0.210017i
\(448\) 1.29297 0.746494i 0.0610869 0.0352685i
\(449\) 5.69834 3.28994i 0.268921 0.155262i −0.359476 0.933154i \(-0.617045\pi\)
0.628397 + 0.777893i \(0.283711\pi\)
\(450\) 0.0128835 4.99998i 0.000607333 0.235701i
\(451\) −16.1592 27.9886i −0.760908 1.31793i
\(452\) −1.83921 −0.0865092
\(453\) 9.27558 + 5.35526i 0.435805 + 0.251612i
\(454\) −19.7888 −0.928732
\(455\) 16.8240 16.7807i 0.788719 0.786690i
\(456\) 1.55098 2.68637i 0.0726312 0.125801i
\(457\) −11.7495 20.3508i −0.549619 0.951968i −0.998300 0.0582764i \(-0.981440\pi\)
0.448681 0.893692i \(-0.351894\pi\)
\(458\) −8.67189 −0.405211
\(459\) 3.88718 + 2.24427i 0.181438 + 0.104753i
\(460\) −16.9347 + 4.51426i −0.789583 + 0.210478i
\(461\) 9.55328 + 5.51559i 0.444941 + 0.256887i 0.705691 0.708520i \(-0.250637\pi\)
−0.260750 + 0.965406i \(0.583970\pi\)
\(462\) −3.72678 6.45498i −0.173386 0.300313i
\(463\) −6.03232 10.4483i −0.280346 0.485573i 0.691124 0.722736i \(-0.257116\pi\)
−0.971470 + 0.237163i \(0.923782\pi\)
\(464\) 7.13932 + 4.12189i 0.331435 + 0.191354i
\(465\) −1.99893 + 0.532853i −0.0926982 + 0.0247105i
\(466\) −1.85101 1.06868i −0.0857462 0.0495056i
\(467\) 8.08233 0.374005 0.187003 0.982359i \(-0.440123\pi\)
0.187003 + 0.982359i \(0.440123\pi\)
\(468\) 3.55888 + 6.16416i 0.164509 + 0.284938i
\(469\) −9.94041 + 17.2173i −0.459005 + 0.795021i
\(470\) −7.15390 + 7.13549i −0.329985 + 0.329136i
\(471\) 6.65528 0.306659
\(472\) −4.55609 2.63046i −0.209711 0.121077i
\(473\) −40.1547 −1.84631
\(474\) −0.482817 0.836264i −0.0221765 0.0384109i
\(475\) −15.5097 0.0399640i −0.711635 0.00183367i
\(476\) 5.80351 3.35066i 0.266004 0.153577i
\(477\) −3.66104 + 2.11370i −0.167627 + 0.0967797i
\(478\) −2.00088 + 1.15521i −0.0915180 + 0.0528379i
\(479\) −14.6391 8.45188i −0.668877 0.386176i 0.126774 0.991932i \(-0.459538\pi\)
−0.795651 + 0.605755i \(0.792871\pi\)
\(480\) 1.58317 1.57910i 0.0722617 0.0720757i
\(481\) 39.7826 + 17.0838i 1.81393 + 0.778953i
\(482\) 20.9468i 0.954102i
\(483\) −5.85093 + 10.1341i −0.266226 + 0.461118i
\(484\) −6.96195 12.0585i −0.316452 0.548112i
\(485\) 5.51799 20.4878i 0.250559 0.930303i
\(486\) 0.866025 0.500000i 0.0392837 0.0226805i
\(487\) 33.2218 1.50542 0.752711 0.658351i \(-0.228746\pi\)
0.752711 + 0.658351i \(0.228746\pi\)
\(488\) 8.38002 4.83821i 0.379346 0.219015i
\(489\) 2.78270i 0.125838i
\(490\) 10.3083 2.74787i 0.465681 0.124136i
\(491\) 2.40662 0.108609 0.0543046 0.998524i \(-0.482706\pi\)
0.0543046 + 0.998524i \(0.482706\pi\)
\(492\) 6.47355i 0.291850i
\(493\) 32.0451 + 18.5012i 1.44324 + 0.833253i
\(494\) 19.1210 11.0395i 0.860292 0.496690i
\(495\) −7.88348 7.90382i −0.354336 0.355250i
\(496\) −0.801217 0.462583i −0.0359757 0.0207706i
\(497\) 0.669958 + 0.386800i 0.0300517 + 0.0173504i
\(498\) 4.52626 7.83972i 0.202827 0.351306i
\(499\) −14.3350 + 8.27632i −0.641723 + 0.370499i −0.785278 0.619143i \(-0.787480\pi\)
0.143555 + 0.989642i \(0.454147\pi\)
\(500\) −10.7881 2.93540i −0.482459 0.131275i
\(501\) −13.0600 7.54017i −0.583476 0.336870i
\(502\) 15.0099 + 8.66600i 0.669927 + 0.386782i
\(503\) 11.7871 20.4159i 0.525562 0.910299i −0.473995 0.880527i \(-0.657189\pi\)
0.999557 0.0297718i \(-0.00947807\pi\)
\(504\) 1.49299i 0.0665030i
\(505\) −4.93958 + 18.3402i −0.219808 + 0.816129i
\(506\) −19.5649 + 33.8873i −0.869764 + 1.50648i
\(507\) 37.6625i 1.67265i
\(508\) 9.19357i 0.407899i
\(509\) −2.31738 + 4.01382i −0.102716 + 0.177909i −0.912803 0.408401i \(-0.866087\pi\)
0.810087 + 0.586310i \(0.199420\pi\)
\(510\) 7.10613 7.08784i 0.314665 0.313855i
\(511\) −10.3162 17.8682i −0.456361 0.790441i
\(512\) 1.00000 0.0441942
\(513\) −1.55098 2.68637i −0.0684774 0.118606i
\(514\) −2.45518 4.25250i −0.108293 0.187570i
\(515\) −3.09883 + 11.5057i −0.136551 + 0.507001i
\(516\) −6.96561 4.02159i −0.306644 0.177041i
\(517\) 22.5591i 0.992149i
\(518\) −5.43494 7.27563i −0.238798 0.319673i
\(519\) 17.6180 0.773346
\(520\) 15.3788 4.09950i 0.674403 0.179775i
\(521\) −10.8756 18.8371i −0.476468 0.825267i 0.523169 0.852229i \(-0.324750\pi\)
−0.999636 + 0.0269626i \(0.991416\pi\)
\(522\) 7.13932 4.12189i 0.312480 0.180410i
\(523\) −16.7885 29.0785i −0.734108 1.27151i −0.955113 0.296240i \(-0.904267\pi\)
0.221005 0.975273i \(-0.429066\pi\)
\(524\) 7.70903i 0.336771i
\(525\) −6.47442 + 3.71580i −0.282567 + 0.162171i
\(526\) 18.8193i 0.820563i
\(527\) −3.59629 2.07632i −0.156657 0.0904458i
\(528\) 4.99238i 0.217266i
\(529\) 38.4323 1.67097
\(530\) 2.43479 + 9.13381i 0.105760 + 0.396747i
\(531\) −4.55609 + 2.63046i −0.197718 + 0.114152i
\(532\) −4.63118 −0.200787
\(533\) 23.0386 39.9040i 0.997911 1.72843i
\(534\) −3.92128 + 6.79186i −0.169690 + 0.293912i
\(535\) −3.36790 12.6343i −0.145607 0.546228i
\(536\) −11.5321 + 6.65806i −0.498111 + 0.287585i
\(537\) −3.08576 5.34469i −0.133160 0.230640i
\(538\) −6.25354 + 10.8315i −0.269609 + 0.466977i
\(539\) 11.9093 20.6275i 0.512970 0.888490i
\(540\) −0.575954 2.16062i −0.0247851 0.0929783i
\(541\) 2.98441i 0.128310i 0.997940 + 0.0641548i \(0.0204352\pi\)
−0.997940 + 0.0641548i \(0.979565\pi\)
\(542\) −12.1046 20.9658i −0.519937 0.900557i
\(543\) 8.60266 + 4.96675i 0.369176 + 0.213144i
\(544\) 4.48853 0.192444
\(545\) 12.3315 12.2997i 0.528222 0.526863i
\(546\) 5.31336 9.20301i 0.227391 0.393853i
\(547\) −19.7115 −0.842802 −0.421401 0.906874i \(-0.638461\pi\)
−0.421401 + 0.906874i \(0.638461\pi\)
\(548\) −4.59818 + 2.65476i −0.196425 + 0.113406i
\(549\) 9.67642i 0.412979i
\(550\) −21.6497 + 12.4252i −0.923148 + 0.529813i
\(551\) −12.7859 22.1459i −0.544698 0.943445i
\(552\) −6.78780 + 3.91894i −0.288908 + 0.166801i
\(553\) −0.720840 + 1.24853i −0.0306532 + 0.0530930i
\(554\) −25.2183 −1.07142
\(555\) −10.6721 8.43249i −0.453004 0.357939i
\(556\) 7.96852 0.337941
\(557\) 6.44022 11.1548i 0.272881 0.472643i −0.696717 0.717346i \(-0.745357\pi\)
0.969598 + 0.244702i \(0.0786902\pi\)
\(558\) −0.801217 + 0.462583i −0.0339182 + 0.0195827i
\(559\) −28.6247 49.5795i −1.21070 2.09699i
\(560\) −3.22355 0.868201i −0.136220 0.0366882i
\(561\) 22.4085i 0.946086i
\(562\) −3.24794 + 1.87520i −0.137006 + 0.0791004i
\(563\) −4.71733 −0.198812 −0.0994059 0.995047i \(-0.531694\pi\)
−0.0994059 + 0.995047i \(0.531694\pi\)
\(564\) −2.25935 + 3.91331i −0.0951359 + 0.164780i
\(565\) 2.90430 + 2.91179i 0.122185 + 0.122500i
\(566\) 30.1738 1.26830
\(567\) −1.29297 0.746494i −0.0542994 0.0313498i
\(568\) 0.259078 + 0.448736i 0.0108707 + 0.0188286i
\(569\) 40.6559i 1.70438i −0.523230 0.852191i \(-0.675273\pi\)
0.523230 0.852191i \(-0.324727\pi\)
\(570\) −6.70215 + 1.78658i −0.280722 + 0.0748318i
\(571\) 5.57259 9.65201i 0.233206 0.403924i −0.725544 0.688176i \(-0.758412\pi\)
0.958750 + 0.284252i \(0.0917451\pi\)
\(572\) 17.7673 30.7738i 0.742888 1.28672i
\(573\) 4.95736 + 8.58641i 0.207097 + 0.358702i
\(574\) −8.37007 + 4.83246i −0.349360 + 0.201703i
\(575\) 33.8884 + 19.6821i 1.41324 + 0.820800i
\(576\) 0.500000 0.866025i 0.0208333 0.0360844i
\(577\) −18.0545 + 31.2713i −0.751619 + 1.30184i 0.195419 + 0.980720i \(0.437393\pi\)
−0.947038 + 0.321122i \(0.895940\pi\)
\(578\) 3.14690 0.130894
\(579\) −14.0577 + 8.11621i −0.584217 + 0.337298i
\(580\) −4.74803 17.8117i −0.197151 0.739589i
\(581\) −13.5153 −0.560710
\(582\) 9.48892i 0.393329i
\(583\) 18.2773 + 10.5524i 0.756969 + 0.437036i
\(584\) 13.8195i 0.571856i
\(585\) 4.13911 15.3682i 0.171131 0.635395i
\(586\) 28.1011i 1.16084i
\(587\) −15.0657 26.0945i −0.621827 1.07704i −0.989145 0.146941i \(-0.953057\pi\)
0.367318 0.930095i \(-0.380276\pi\)
\(588\) 4.13180 2.38549i 0.170392 0.0983761i
\(589\) 1.43491 + 2.48534i 0.0591245 + 0.102407i
\(590\) 3.03005 + 11.3669i 0.124745 + 0.467966i
\(591\) 6.49977 0.267365
\(592\) −0.716002 6.04048i −0.0294275 0.248262i
\(593\) 20.9906i 0.861981i 0.902356 + 0.430991i \(0.141836\pi\)
−0.902356 + 0.430991i \(0.858164\pi\)
\(594\) −4.32353 2.49619i −0.177397 0.102420i
\(595\) −14.4690 3.89695i −0.593172 0.159759i
\(596\) −4.44026 7.69076i −0.181880 0.315026i
\(597\) −9.99533 17.3124i −0.409082 0.708550i
\(598\) −55.7881 −2.28135
\(599\) −17.7246 30.6999i −0.724207 1.25436i −0.959300 0.282390i \(-0.908873\pi\)
0.235092 0.971973i \(-0.424461\pi\)
\(600\) −4.99998 0.0128835i −0.204123 0.000525966i
\(601\) 17.9480 31.0868i 0.732114 1.26806i −0.223864 0.974620i \(-0.571867\pi\)
0.955978 0.293438i \(-0.0947994\pi\)
\(602\) 12.0084i 0.489425i
\(603\) 13.3161i 0.542275i
\(604\) 5.35526 9.27558i 0.217902 0.377418i
\(605\) −8.09702 + 30.0635i −0.329191 + 1.22225i
\(606\) 8.49427i 0.345056i
\(607\) −20.3935 + 35.3226i −0.827746 + 1.43370i 0.0720560 + 0.997401i \(0.477044\pi\)
−0.899802 + 0.436298i \(0.856289\pi\)
\(608\) −2.68637 1.55098i −0.108947 0.0629005i
\(609\) −10.6589 6.15393i −0.431921 0.249370i
\(610\) −20.8926 5.62702i −0.845918 0.227831i
\(611\) −27.8540 + 16.0815i −1.12685 + 0.650589i
\(612\) 2.24427 3.88718i 0.0907190 0.157130i
\(613\) 19.2575 + 11.1183i 0.777805 + 0.449066i 0.835652 0.549260i \(-0.185090\pi\)
−0.0578469 + 0.998325i \(0.518424\pi\)
\(614\) 11.2962 + 6.52187i 0.455878 + 0.263201i
\(615\) −10.2488 + 10.2224i −0.413270 + 0.412206i
\(616\) −6.45498 + 3.72678i −0.260079 + 0.150156i
\(617\) −9.51843 5.49547i −0.383197 0.221239i 0.296011 0.955184i \(-0.404343\pi\)
−0.679208 + 0.733945i \(0.737677\pi\)
\(618\) 5.32885i 0.214358i
\(619\) 43.9421 1.76618 0.883092 0.469200i \(-0.155458\pi\)
0.883092 + 0.469200i \(0.155458\pi\)
\(620\) 0.532853 + 1.99893i 0.0213999 + 0.0802790i
\(621\) 7.83788i 0.314523i
\(622\) 18.1342 10.4698i 0.727115 0.419800i
\(623\) 11.7088 0.469105
\(624\) 6.16416 3.55888i 0.246764 0.142469i
\(625\) 12.3883 + 21.7148i 0.495530 + 0.868591i
\(626\) −7.90172 13.6862i −0.315816 0.547010i
\(627\) −7.74308 + 13.4114i −0.309229 + 0.535600i
\(628\) 6.65528i 0.265574i
\(629\) −3.21380 27.1129i −0.128142 1.08106i
\(630\) −2.36366 + 2.35758i −0.0941705 + 0.0939281i
\(631\) 13.5638 + 7.83107i 0.539967 + 0.311750i 0.745066 0.666991i \(-0.232418\pi\)
−0.205098 + 0.978741i \(0.565751\pi\)
\(632\) −0.836264 + 0.482817i −0.0332648 + 0.0192054i
\(633\) −2.70892 + 1.56399i −0.107670 + 0.0621631i
\(634\) 16.8545 9.73093i 0.669376 0.386464i
\(635\) 14.5550 14.5176i 0.577598 0.576112i
\(636\) 2.11370 + 3.66104i 0.0838137 + 0.145170i
\(637\) 33.9587 1.34549
\(638\) −35.6422 20.5780i −1.41109 0.814693i
\(639\) 0.518156 0.0204979
\(640\) −1.57910 1.58317i −0.0624194 0.0625805i
\(641\) −9.61289 + 16.6500i −0.379686 + 0.657636i −0.991017 0.133740i \(-0.957301\pi\)
0.611330 + 0.791376i \(0.290635\pi\)
\(642\) −2.92376 5.06411i −0.115392 0.199864i
\(643\) −29.7837 −1.17456 −0.587278 0.809385i \(-0.699801\pi\)
−0.587278 + 0.809385i \(0.699801\pi\)
\(644\) 10.1341 + 5.85093i 0.399340 + 0.230559i
\(645\) 4.63251 + 17.3783i 0.182405 + 0.684269i
\(646\) −12.0579 6.96161i −0.474410 0.273901i
\(647\) −9.75527 16.8966i −0.383519 0.664275i 0.608043 0.793904i \(-0.291955\pi\)
−0.991563 + 0.129629i \(0.958621\pi\)
\(648\) −0.500000 0.866025i −0.0196419 0.0340207i
\(649\) 22.7458 + 13.1323i 0.892850 + 0.515487i
\(650\) −30.7748 17.8737i −1.20709 0.701066i
\(651\) 1.19621 + 0.690630i 0.0468830 + 0.0270679i
\(652\) −2.78270 −0.108979
\(653\) 6.40287 + 11.0901i 0.250563 + 0.433989i 0.963681 0.267056i \(-0.0860508\pi\)
−0.713118 + 0.701044i \(0.752717\pi\)
\(654\) 3.89454 6.74554i 0.152288 0.263771i
\(655\) 12.2047 12.1733i 0.476879 0.475652i
\(656\) −6.47355 −0.252750
\(657\) −11.9681 6.90976i −0.466918 0.269575i
\(658\) 6.74637 0.263001
\(659\) 7.16675 + 12.4132i 0.279177 + 0.483548i 0.971180 0.238346i \(-0.0766051\pi\)
−0.692004 + 0.721894i \(0.743272\pi\)
\(660\) −7.90382 + 7.88348i −0.307656 + 0.306864i
\(661\) 21.4678 12.3944i 0.834999 0.482087i −0.0205623 0.999789i \(-0.506546\pi\)
0.855561 + 0.517702i \(0.173212\pi\)
\(662\) 3.62395 2.09229i 0.140849 0.0813192i
\(663\) 27.6680 15.9741i 1.07454 0.620384i
\(664\) −7.83972 4.52626i −0.304240 0.175653i
\(665\) 7.31310 + 7.33197i 0.283590 + 0.284322i
\(666\) −5.58921 2.40016i −0.216577 0.0930044i
\(667\) 64.6137i 2.50185i
\(668\) −7.54017 + 13.0600i −0.291738 + 0.505305i
\(669\) 13.8749 + 24.0321i 0.536436 + 0.929135i
\(670\) 28.7512 + 7.74358i 1.11076 + 0.299161i
\(671\) −41.8363 + 24.1542i −1.61507 + 0.932462i
\(672\) −1.49299 −0.0575933
\(673\) −9.21745 + 5.32170i −0.355307 + 0.205136i −0.667020 0.745040i \(-0.732430\pi\)
0.311713 + 0.950176i \(0.399097\pi\)
\(674\) 12.8150i 0.493614i
\(675\) −2.51115 + 4.32367i −0.0966542 + 0.166418i
\(676\) 37.6625 1.44856
\(677\) 21.2505i 0.816725i −0.912820 0.408362i \(-0.866100\pi\)
0.912820 0.408362i \(-0.133900\pi\)
\(678\) 1.59280 + 0.919606i 0.0611713 + 0.0353172i
\(679\) −12.2689 + 7.08342i −0.470835 + 0.271837i
\(680\) −7.08784 7.10613i −0.271806 0.272508i
\(681\) 17.1376 + 9.89438i 0.656713 + 0.379153i
\(682\) 3.99998 + 2.30939i 0.153167 + 0.0884312i
\(683\) 14.8676 25.7514i 0.568893 0.985351i −0.427783 0.903881i \(-0.640705\pi\)
0.996676 0.0814698i \(-0.0259614\pi\)
\(684\) −2.68637 + 1.55098i −0.102716 + 0.0593031i
\(685\) 11.4639 + 3.08759i 0.438015 + 0.117971i
\(686\) −15.2195 8.78697i −0.581082 0.335488i
\(687\) 7.51008 + 4.33595i 0.286527 + 0.165427i
\(688\) −4.02159 + 6.96561i −0.153322 + 0.265561i
\(689\) 30.0896i 1.14632i
\(690\) 16.9230 + 4.55788i 0.644247 + 0.173515i
\(691\) 16.1943 28.0494i 0.616060 1.06705i −0.374137 0.927373i \(-0.622061\pi\)
0.990197 0.139675i \(-0.0446056\pi\)
\(692\) 17.6180i 0.669737i
\(693\) 7.45357i 0.283138i
\(694\) −6.03775 + 10.4577i −0.229190 + 0.396969i
\(695\) −12.5831 12.6156i −0.477304 0.478535i
\(696\) −4.12189 7.13932i −0.156240 0.270615i
\(697\) −29.0567 −1.10060
\(698\) 3.57899 + 6.19899i 0.135467 + 0.234635i
\(699\) 1.06868 + 1.85101i 0.0404212 + 0.0700115i
\(700\) 3.71580 + 6.47442i 0.140444 + 0.244710i
\(701\) −22.1818 12.8066i −0.837793 0.483700i 0.0187202 0.999825i \(-0.494041\pi\)
−0.856514 + 0.516125i \(0.827374\pi\)
\(702\) 7.11776i 0.268642i
\(703\) −7.44520 + 17.3375i −0.280801 + 0.653895i
\(704\) −4.99238 −0.188158
\(705\) 9.76320 2.60257i 0.367704 0.0980183i
\(706\) −16.3563 28.3299i −0.615576 1.06621i
\(707\) 10.9828 6.34092i 0.413051 0.238475i
\(708\) 2.63046 + 4.55609i 0.0988588 + 0.171229i
\(709\) 36.3231i 1.36414i 0.731286 + 0.682071i \(0.238920\pi\)
−0.731286 + 0.682071i \(0.761080\pi\)
\(710\) 0.301318 1.11877i 0.0113082 0.0419865i
\(711\) 0.965634i 0.0362141i
\(712\) 6.79186 + 3.92128i 0.254536 + 0.146956i
\(713\) 7.25134i 0.271565i
\(714\) −6.70132 −0.250791
\(715\) −76.7767 + 20.4663i −2.87129 + 0.765395i
\(716\) −5.34469 + 3.08576i −0.199740 + 0.115320i
\(717\) 2.31041 0.0862840
\(718\) 13.1918 22.8488i 0.492313 0.852711i
\(719\) −2.41440 + 4.18186i −0.0900419 + 0.155957i −0.907529 0.419990i \(-0.862033\pi\)
0.817487 + 0.575948i \(0.195367\pi\)
\(720\) −2.16062 + 0.575954i −0.0805215 + 0.0214645i
\(721\) 6.89002 3.97796i 0.256598 0.148147i
\(722\) −4.68893 8.12147i −0.174504 0.302250i
\(723\) 10.4734 18.1405i 0.389510 0.674652i
\(724\) 4.96675 8.60266i 0.184588 0.319715i
\(725\) −20.7014 + 35.6434i −0.768829 + 1.32376i
\(726\) 13.9239i 0.516764i
\(727\) 1.93804 + 3.35679i 0.0718780 + 0.124496i 0.899724 0.436459i \(-0.143767\pi\)
−0.827846 + 0.560955i \(0.810434\pi\)
\(728\) −9.20301 5.31336i −0.341086 0.196926i
\(729\) −1.00000 −0.0370370
\(730\) −21.8787 + 21.8224i −0.809768 + 0.807684i
\(731\) −18.0511 + 31.2653i −0.667642 + 1.15639i
\(732\) −9.67642 −0.357651
\(733\) 24.0960 13.9118i 0.890006 0.513845i 0.0160613 0.999871i \(-0.494887\pi\)
0.873944 + 0.486026i \(0.161554\pi\)
\(734\) 1.55468i 0.0573842i
\(735\) −10.3012 2.77442i −0.379965 0.102336i
\(736\) 3.91894 + 6.78780i 0.144454 + 0.250202i
\(737\) 57.5727 33.2396i 2.12072 1.22440i
\(738\) −3.23677 + 5.60626i −0.119147 + 0.206369i
\(739\) −45.5267 −1.67473 −0.837364 0.546646i \(-0.815905\pi\)
−0.837364 + 0.546646i \(0.815905\pi\)
\(740\) −8.43249 + 10.6721i −0.309984 + 0.392313i
\(741\) −22.0790 −0.811091
\(742\) 3.15573 5.46588i 0.115850 0.200659i
\(743\) −24.4648 + 14.1248i −0.897527 + 0.518188i −0.876397 0.481589i \(-0.840060\pi\)
−0.0211303 + 0.999777i \(0.506726\pi\)
\(744\) 0.462583 + 0.801217i 0.0169591 + 0.0293740i
\(745\) −5.16420 + 19.1742i −0.189201 + 0.702488i
\(746\) 27.3486i 1.00130i
\(747\) −7.83972 + 4.52626i −0.286840 + 0.165607i
\(748\) −22.4085 −0.819335
\(749\) −4.36514 + 7.56065i −0.159499 + 0.276260i
\(750\) 7.87508 + 7.93619i 0.287557 + 0.289789i
\(751\) 14.1263 0.515474 0.257737 0.966215i \(-0.417023\pi\)
0.257737 + 0.966215i \(0.417023\pi\)
\(752\) 3.91331 + 2.25935i 0.142704 + 0.0823901i
\(753\) −8.66600 15.0099i −0.315806 0.546993i
\(754\) 58.6772i 2.13690i
\(755\) −23.1413 + 6.16876i −0.842200 + 0.224504i
\(756\) −0.746494 + 1.29297i −0.0271497 + 0.0470247i
\(757\) 20.2892 35.1419i 0.737423 1.27725i −0.216230 0.976343i \(-0.569376\pi\)
0.953652 0.300911i \(-0.0972907\pi\)
\(758\) 3.06678 + 5.31181i 0.111390 + 0.192934i
\(759\) 33.8873 19.5649i 1.23003 0.710159i
\(760\) 1.78658 + 6.70215i 0.0648062 + 0.243112i
\(761\) −0.220861 + 0.382543i −0.00800622 + 0.0138672i −0.870001 0.493050i \(-0.835882\pi\)
0.861995 + 0.506918i \(0.169215\pi\)
\(762\) 4.59678 7.96186i 0.166524 0.288428i
\(763\) −11.6290 −0.420998
\(764\) 8.58641 4.95736i 0.310645 0.179351i
\(765\) −9.69801 + 2.58519i −0.350632 + 0.0934676i
\(766\) 34.9758 1.26373
\(767\) 37.4460i 1.35210i
\(768\) −0.866025 0.500000i −0.0312500 0.0180422i
\(769\) 2.58497i 0.0932163i 0.998913 + 0.0466082i \(0.0148412\pi\)
−0.998913 + 0.0466082i \(0.985159\pi\)
\(770\) 16.0932 + 4.33439i 0.579959 + 0.156201i
\(771\) 4.91036i 0.176842i
\(772\) 8.11621 + 14.0577i 0.292109 + 0.505947i
\(773\) 39.0202 22.5283i 1.40346 0.810288i 0.408715 0.912662i \(-0.365977\pi\)
0.994746 + 0.102374i \(0.0326438\pi\)
\(774\) 4.02159 + 6.96561i 0.144553 + 0.250374i
\(775\) 2.32323 4.00011i 0.0834528 0.143688i
\(776\) −9.48892 −0.340633