Properties

Label 1110.2.ba.b.529.2
Level $1110$
Weight $2$
Character 1110.529
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 529.2
Character \(\chi\) \(=\) 1110.529
Dual form 1110.2.ba.b.619.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.16062 + 0.575954i) q^{5} -1.00000i q^{6} +(-1.29297 - 0.746494i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.16062 + 0.575954i) 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} +(2.15913 + 0.581519i) 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} +(0.581519 - 2.15913i) q^{20} +(0.746494 + 1.29297i) q^{21} +(-2.49619 - 4.32353i) q^{22} +7.83788 q^{23} +(0.866025 + 0.500000i) q^{24} +(4.33655 - 2.48883i) q^{25} +7.11776 q^{26} -1.00000i q^{27} +(1.29297 - 0.746494i) q^{28} +8.24378i q^{29} +(0.575954 + 2.16062i) q^{30} -0.925166i q^{31} +(0.500000 - 0.866025i) q^{32} +(4.32353 + 2.49619i) q^{33} +(-2.24427 + 3.88718i) q^{34} +(3.22355 + 0.868201i) q^{35} -1.00000 q^{36} +(4.87320 + 3.64031i) q^{37} +3.10196i q^{38} +(-6.16416 + 3.55888i) q^{39} +(2.16062 - 0.575954i) 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} +(4.32367 + 2.51115i) q^{50} -4.48853i q^{51} +(3.55888 + 6.16416i) q^{52} +(3.66104 - 2.11370i) q^{53} +(0.866025 - 0.500000i) q^{54} +(10.7866 - 2.87538i) 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} +(-4.13911 + 15.3682i) q^{65} +4.99238i q^{66} +(11.5321 + 6.65806i) q^{67} -4.48853 q^{68} +(-6.78780 - 3.91894i) q^{69} +(0.859892 + 3.22578i) 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} +(0.581519 - 2.15913i) 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} +(-6.69752 - 1.80385i) 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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 18q^{2} - 18q^{4} + 4q^{5} - 36q^{8} + 18q^{9} + O(q^{10}) \) \( 36q + 18q^{2} - 18q^{4} + 4q^{5} - 36q^{8} + 18q^{9} + 2q^{10} + 4q^{11} + 14q^{13} + 2q^{15} - 18q^{16} - 18q^{18} + 6q^{19} - 2q^{20} + 2q^{22} + 20q^{23} - 2q^{25} + 28q^{26} - 2q^{30} + 18q^{32} + 6q^{33} - 20q^{35} - 36q^{36} - 20q^{37} + 6q^{39} - 4q^{40} + 10q^{41} - 2q^{44} + 2q^{45} + 10q^{46} + 10q^{49} - 4q^{50} + 14q^{52} + 12q^{53} + 40q^{55} - 8q^{57} - 30q^{58} + 18q^{59} - 4q^{60} - 6q^{61} + 12q^{62} + 36q^{64} - 32q^{65} - 36q^{67} + 12q^{69} - 40q^{70} - 24q^{71} - 18q^{72} - 34q^{74} + 8q^{75} - 6q^{76} + 24q^{77} + 6q^{78} - 2q^{80} - 18q^{81} + 20q^{82} - 36q^{83} + 26q^{85} + 10q^{87} - 4q^{88} - 2q^{90} - 36q^{91} - 10q^{92} - 12q^{93} + 12q^{94} + 18q^{95} - 52q^{97} - 10q^{98} + 2q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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
\(5\) −2.16062 + 0.575954i −0.966258 + 0.257574i
\(6\) 1.00000i 0.408248i
\(7\) −1.29297 0.746494i −0.488695 0.282148i 0.235338 0.971914i \(-0.424380\pi\)
−0.724033 + 0.689765i \(0.757714\pi\)
\(8\) −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 0.354634 0.935005i \(-0.384605\pi\)
0.632421 0.774625i \(-0.282061\pi\)
\(14\) 1.49299i 0.399018i
\(15\) 2.15913 + 0.581519i 0.557485 + 0.150148i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 2.24427 + 3.88718i 0.544314 + 0.942780i 0.998650 + 0.0519493i \(0.0165434\pi\)
−0.454335 + 0.890831i \(0.650123\pi\)
\(18\) −0.500000 + 0.866025i −0.117851 + 0.204124i
\(19\) 2.68637 + 1.55098i 0.616296 + 0.355819i 0.775426 0.631439i \(-0.217535\pi\)
−0.159129 + 0.987258i \(0.550869\pi\)
\(20\) 0.581519 2.15913i 0.130032 0.482796i
\(21\) 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 \(-0.195550\pi\)
0.817155 + 0.576417i \(0.195550\pi\)
\(24\) 0.866025 + 0.500000i 0.176777 + 0.102062i
\(25\) 4.33655 2.48883i 0.867311 0.497767i
\(26\) 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 \(0.277466\pi\)
−0.643537 + 0.765415i \(0.722534\pi\)
\(30\) 0.575954 + 2.16062i 0.105154 + 0.394473i
\(31\) 0.925166i 0.166165i −0.996543 0.0830823i \(-0.973524\pi\)
0.996543 0.0830823i \(-0.0264764\pi\)
\(32\) 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
\(35\) 3.22355 + 0.868201i 0.544880 + 0.146753i
\(36\) −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
\(40\) 2.16062 0.575954i 0.341624 0.0910663i
\(41\) 3.23677 5.60626i 0.505499 0.875550i −0.494481 0.869189i \(-0.664642\pi\)
0.999980 0.00636146i \(-0.00202493\pi\)
\(42\) −0.746494 + 1.29297i −0.115187 + 0.199509i
\(43\) −8.04319 −1.22657 −0.613287 0.789860i \(-0.710153\pi\)
−0.613287 + 0.789860i \(0.710153\pi\)
\(44\) 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
\(50\) 4.32367 + 2.51115i 0.611459 + 0.355130i
\(51\) 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 \(-0.572899\pi\)
0.729903 + 0.683551i \(0.239565\pi\)
\(54\) 0.866025 0.500000i 0.117851 0.0680414i
\(55\) 10.7866 2.87538i 1.45447 0.387717i
\(56\) 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 −0.766343 0.642431i \(-0.777926\pi\)
0.173190 + 0.984888i \(0.444592\pi\)
\(60\) −1.58317 + 1.57910i −0.204387 + 0.203861i
\(61\) 8.38002 + 4.83821i 1.07295 + 0.619469i 0.928986 0.370114i \(-0.120681\pi\)
0.143965 + 0.989583i \(0.454015\pi\)
\(62\) 0.801217 0.462583i 0.101755 0.0587481i
\(63\) 1.49299i 0.188099i
\(64\) 1.00000 0.125000
\(65\) −4.13911 + 15.3682i −0.513394 + 1.90618i
\(66\) 4.99238i 0.614520i
\(67\) 11.5321 + 6.65806i 1.40887 + 0.813412i 0.995279 0.0970505i \(-0.0309408\pi\)
0.413592 + 0.910463i \(0.364274\pi\)
\(68\) −4.48853 −0.544314
\(69\) −6.78780 3.91894i −0.817155 0.471785i
\(70\) 0.859892 + 3.22578i 0.102777 + 0.385554i
\(71\) 0.259078 0.448736i 0.0307469 0.0532552i −0.850243 0.526391i \(-0.823545\pi\)
0.880989 + 0.473136i \(0.156878\pi\)
\(72\) −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 0.452218 0.891907i \(-0.350633\pi\)
−0.546305 + 0.837586i \(0.683966\pi\)
\(80\) 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 \(-0.501167\pi\)
0.864187 + 0.503171i \(0.167834\pi\)
\(84\) −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 −0.0947935 0.995497i \(-0.530219\pi\)
0.814729 + 0.579842i \(0.196886\pi\)
\(90\) 0.581519 2.15913i 0.0612975 0.227592i
\(91\) −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
\(95\) −6.69752 1.80385i −0.687151 0.185071i
\(96\) −0.866025 + 0.500000i −0.0883883 + 0.0510310i
\(97\) 9.48892 0.963454 0.481727 0.876321i \(-0.340010\pi\)
0.481727 + 0.876321i \(0.340010\pi\)
\(98\) 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 \(-0.584558\pi\)
−0.262534 + 0.964923i \(0.584558\pi\)
\(104\) −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 \(-0.242120\pi\)
−0.234829 + 0.972037i \(0.575453\pi\)
\(108\) 0.866025 + 0.500000i 0.0833333 + 0.0481125i
\(109\) −6.74554 + 3.89454i −0.646105 + 0.373029i −0.786962 0.617001i \(-0.788347\pi\)
0.140857 + 0.990030i \(0.455014\pi\)
\(110\) 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 \(-0.194238\pi\)
−0.906033 + 0.423206i \(0.860905\pi\)
\(114\) 1.55098 2.68637i 0.145262 0.251602i
\(115\) −16.9347 + 4.51426i −1.57917 + 0.420957i
\(116\) −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
\(120\) −2.15913 0.581519i −0.197101 0.0530852i
\(121\) 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 \(-0.532928\pi\)
0.809764 + 0.586755i \(0.199595\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 6.96561 + 4.02159i 0.613287 + 0.354082i
\(130\) −15.3788 + 4.09950i −1.34881 + 0.359550i
\(131\) −6.67622 + 3.85452i −0.583304 + 0.336771i −0.762445 0.647053i \(-0.776001\pi\)
0.179141 + 0.983823i \(0.442668\pi\)
\(132\) −4.32353 + 2.49619i −0.376315 + 0.217266i
\(133\) −2.31559 4.01072i −0.200787 0.347774i
\(134\) 13.3161i 1.15034i
\(135\) 0.575954 + 2.16062i 0.0495702 + 0.185957i
\(136\) −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 0.646105 0.763249i \(-0.276397\pi\)
−0.984045 + 0.177919i \(0.943064\pi\)
\(140\) −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
\(145\) −4.74803 17.8117i −0.394303 1.47918i
\(146\) 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 \(0.381493\pi\)
\(150\) −2.48883 4.33655i −0.203212 0.354078i
\(151\) 5.35526 9.27558i 0.435805 0.754836i −0.561556 0.827439i \(-0.689797\pi\)
0.997361 + 0.0726027i \(0.0231305\pi\)
\(152\) −2.68637 1.55098i −0.217894 0.125801i
\(153\) −2.24427 + 3.88718i −0.181438 + 0.314260i
\(154\) 7.45357i 0.600626i
\(155\) 0.532853 + 1.99893i 0.0427998 + 0.160558i
\(156\) 7.11776i 0.569877i
\(157\) −5.76364 + 3.32764i −0.459988 + 0.265574i −0.712039 0.702140i \(-0.752228\pi\)
0.252051 + 0.967714i \(0.418895\pi\)
\(158\) 0.965634i 0.0768217i
\(159\) −4.22740 −0.335255
\(160\) −0.581519 + 2.15913i −0.0459731 + 0.170694i
\(161\) −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 \(-0.201425\pi\)
−0.915357 + 0.402644i \(0.868091\pi\)
\(164\) 3.23677 + 5.60626i 0.252750 + 0.437775i
\(165\) −10.7792 2.90317i −0.839160 0.226011i
\(166\) 7.83972 + 4.52626i 0.608480 + 0.351306i
\(167\) 7.54017 13.0600i 0.583476 1.01061i −0.411588 0.911370i \(-0.635026\pi\)
0.995064 0.0992397i \(-0.0316411\pi\)
\(168\) −0.746494 1.29297i −0.0575933 0.0997544i
\(169\) −18.8312 32.6167i −1.44856 2.50897i
\(170\) 2.61017 9.69131i 0.200191 0.743290i
\(171\) 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 \(-0.900260\pi\)
−0.208711 + 0.977977i \(0.566927\pi\)
\(174\) 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 \(0.0740820\pi\)
−0.973039 + 0.230640i \(0.925918\pi\)
\(180\) 2.16062 0.575954i 0.161043 0.0429291i
\(181\) 4.96675 8.60266i 0.369176 0.639431i −0.620261 0.784395i \(-0.712973\pi\)
0.989437 + 0.144964i \(0.0463068\pi\)
\(182\) −9.20301 5.31336i −0.682173 0.393853i
\(183\) −4.83821 8.38002i −0.357651 0.619469i
\(184\) −7.83788 −0.577816
\(185\) −12.6258 5.05859i −0.928267 0.371915i
\(186\) −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
\(190\) −1.78658 6.70215i −0.129612 0.486225i
\(191\) 9.91473i 0.717404i −0.933452 0.358702i \(-0.883219\pi\)
0.933452 0.358702i \(-0.116781\pi\)
\(192\) −0.866025 0.500000i −0.0625000 0.0360844i
\(193\) 16.2324 1.16843 0.584217 0.811597i \(-0.301402\pi\)
0.584217 + 0.811597i \(0.301402\pi\)
\(194\) 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 \(-0.741045\pi\)
0.285888 + 0.958263i \(0.407711\pi\)
\(198\) 2.49619 4.32353i 0.177397 0.307260i
\(199\) 19.9907i 1.41710i 0.705660 + 0.708550i \(0.250650\pi\)
−0.705660 + 0.708550i \(0.749350\pi\)
\(200\) −4.33655 + 2.48883i −0.306641 + 0.175987i
\(201\) −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
\(205\) −3.76449 + 13.9772i −0.262923 + 0.976211i
\(206\) −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
\(210\) 0.868201 3.22355i 0.0599116 0.222446i
\(211\) −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
\(215\) 17.3783 4.63251i 1.18519 0.315934i
\(216\) 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
\(220\) −2.90317 + 10.7792i −0.195731 + 0.726733i
\(221\) 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
\(225\) 4.32367 + 2.51115i 0.288245 + 0.167410i
\(226\) 0.919606 1.59280i 0.0611713 0.105952i
\(227\) −9.89438 + 17.1376i −0.656713 + 1.13746i 0.324748 + 0.945800i \(0.394720\pi\)
−0.981461 + 0.191660i \(0.938613\pi\)
\(228\) 3.10196 0.205432
\(229\) 4.33595 7.51008i 0.286527 0.496280i −0.686451 0.727176i \(-0.740832\pi\)
0.972978 + 0.230896i \(0.0741657\pi\)
\(230\) −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
\(235\) 2.60257 + 9.76320i 0.169773 + 0.636881i
\(236\) 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 −0.433889 0.900966i \(-0.642859\pi\)
0.563315 + 0.826242i \(0.309526\pi\)
\(240\) −0.575954 2.16062i −0.0371777 0.139467i
\(241\) 18.1405 + 10.4734i 1.16853 + 0.674652i 0.953334 0.301919i \(-0.0976272\pi\)
0.215197 + 0.976571i \(0.430960\pi\)
\(242\) 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
\(250\) −10.7881 2.93540i −0.682300 0.185651i
\(251\) 17.3320i 1.09399i 0.837137 + 0.546993i \(0.184228\pi\)
−0.837137 + 0.546993i \(0.815772\pi\)
\(252\) 1.29297 + 0.746494i 0.0814492 + 0.0470247i
\(253\) −39.1297 −2.46006
\(254\) 7.96186 + 4.59678i 0.499572 + 0.288428i
\(255\) 2.58519 + 9.69801i 0.161891 + 0.607313i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 2.45518 + 4.25250i 0.153150 + 0.265263i 0.932384 0.361470i \(-0.117725\pi\)
−0.779234 + 0.626733i \(0.784392\pi\)
\(258\) 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 \(-0.530369\pi\)
−0.909718 + 0.415227i \(0.863702\pi\)
\(264\) −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 −0.954591 0.297920i \(-0.903707\pi\)
0.219289 0.975660i \(-0.429626\pi\)
\(272\) 2.24427 3.88718i 0.136079 0.235695i
\(273\) 10.6267 0.643159
\(274\) 4.59818 2.65476i 0.277786 0.160380i
\(275\) −21.6497 + 12.4252i −1.30553 + 0.749269i
\(276\) 6.78780 3.91894i 0.408578 0.235892i
\(277\) −12.6092 + 21.8397i −0.757611 + 1.31222i 0.186454 + 0.982464i \(0.440300\pi\)
−0.944066 + 0.329758i \(0.893033\pi\)
\(278\) 3.98426 6.90094i 0.238960 0.413891i
\(279\) 0.801217 0.462583i 0.0479676 0.0276941i
\(280\) −3.22355 0.868201i −0.192644 0.0518849i
\(281\) 3.24794 1.87520i 0.193756 0.111865i −0.399984 0.916522i \(-0.630984\pi\)
0.593740 + 0.804657i \(0.297651\pi\)
\(282\) −4.51871 −0.269085
\(283\) 15.0869 26.1313i 0.896824 1.55334i 0.0652929 0.997866i \(-0.479202\pi\)
0.831531 0.555478i \(-0.187465\pi\)
\(284\) 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 \(-0.0268385\pi\)
0.425291 + 0.905057i \(0.360172\pi\)
\(294\) −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
\(300\) 2.51115 4.32367i 0.144981 0.249627i
\(301\) 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
\(305\) −20.8926 5.62702i −1.19631 0.322202i
\(306\) −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 −0.916496 0.400044i \(-0.868995\pi\)
−0.111800 + 0.993731i \(0.535662\pi\)
\(312\) 6.16416 3.55888i 0.348977 0.201482i
\(313\) 7.90172 + 13.6862i 0.446632 + 0.773589i 0.998164 0.0605646i \(-0.0192901\pi\)
−0.551533 + 0.834153i \(0.685957\pi\)
\(314\) −5.76364 3.32764i −0.325261 0.187789i
\(315\) 0.859892 + 3.22578i 0.0484494 + 0.181752i
\(316\) 0.836264 0.482817i 0.0470435 0.0271606i
\(317\) 16.8545 9.73093i 0.946641 0.546543i 0.0546048 0.998508i \(-0.482610\pi\)
0.892036 + 0.451965i \(0.149277\pi\)
\(318\) −2.11370 3.66104i −0.118530 0.205301i
\(319\) 41.1561i 2.30430i
\(320\) −2.16062 + 0.575954i −0.120782 + 0.0321968i
\(321\) −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
\(330\) −2.87538 10.7866i −0.158285 0.593785i
\(331\) −3.62395 + 2.09229i −0.199190 + 0.115003i −0.596278 0.802778i \(-0.703354\pi\)
0.397087 + 0.917781i \(0.370021\pi\)
\(332\) 9.05253i 0.496822i
\(333\) −0.716002 + 6.04048i −0.0392367 + 0.331016i
\(334\) 15.0803 0.825160
\(335\) −28.7512 7.74358i −1.57085 0.423077i
\(336\) 0.746494 1.29297i 0.0407246 0.0705370i
\(337\) 11.0981 + 6.40748i 0.604551 + 0.349038i 0.770830 0.637041i \(-0.219842\pi\)
−0.166279 + 0.986079i \(0.553175\pi\)
\(338\) 18.8312 32.6167i 1.02428 1.77411i
\(339\) 1.83921i 0.0998923i
\(340\) 9.69801 2.58519i 0.525948 0.140201i
\(341\) 4.61878i 0.250121i
\(342\) −2.68637 + 1.55098i −0.145262 + 0.0838673i
\(343\) 17.5739i 0.948904i
\(344\) 8.04319 0.433660
\(345\) 16.9230 + 4.55788i 0.911103 + 0.245388i
\(346\) −15.2577 8.80902i −0.820257 0.473576i
\(347\) −12.0755 −0.648247 −0.324123 0.946015i \(-0.605069\pi\)
−0.324123 + 0.946015i \(0.605069\pi\)
\(348\) 4.12189 + 7.13932i 0.220956 + 0.382708i
\(349\) 3.57899 + 6.19899i 0.191579 + 0.331824i 0.945774 0.324827i \(-0.105306\pi\)
−0.754195 + 0.656651i \(0.771973\pi\)
\(350\) −3.71580 6.47442i −0.198618 0.346072i
\(351\) −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 0.861422 + 0.507889i \(0.169574\pi\)
0.00913392 + 0.999958i \(0.497093\pi\)
\(354\) 2.63046 + 4.55609i 0.139808 + 0.242154i
\(355\) −0.301318 + 1.11877i −0.0159923 + 0.0593779i
\(356\) 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
\(365\) 7.95941 + 29.8587i 0.416614 + 1.56288i
\(366\) 4.83821 8.38002i 0.252897 0.438031i
\(367\) −1.34639 0.777339i −0.0702810 0.0405768i 0.464448 0.885601i \(-0.346253\pi\)
−0.534729 + 0.845024i \(0.679586\pi\)
\(368\) −3.91894 6.78780i −0.204289 0.353839i
\(369\) 6.47355 0.336999
\(370\) −1.93203 13.4636i −0.100441 0.699937i
\(371\) −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 \(-0.583748\pi\)
−0.966262 + 0.257560i \(0.917082\pi\)
\(374\) 11.2042 19.4063i 0.579357 1.00348i
\(375\) 10.8105 2.85192i 0.558251 0.147273i
\(376\) 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 0.933977 0.357332i \(-0.116314\pi\)
−0.776448 + 0.630182i \(0.782980\pi\)
\(380\) 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 0.0580512 0.998314i \(-0.481511\pi\)
0.835539 0.549431i \(-0.185155\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) −16.0932 4.33439i −0.820186 0.220901i
\(386\) 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 0.0207936 0.999784i \(-0.493381\pi\)
−0.855441 + 0.517900i \(0.826714\pi\)
\(390\) 15.3682 + 4.13911i 0.778197 + 0.209592i
\(391\) 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
\(395\) 2.08493 + 0.561535i 0.104904 + 0.0282539i
\(396\) 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
\(400\) −4.32367 2.51115i −0.216184 0.125557i
\(401\) 2.84609i 0.142127i −0.997472 0.0710634i \(-0.977361\pi\)
0.997472 0.0710634i \(-0.0226393\pi\)
\(402\) 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
\(405\) 0.581519 2.15913i 0.0288959 0.107288i
\(406\) 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 −0.159885 0.987136i \(-0.551112\pi\)
0.774942 + 0.632033i \(0.217779\pi\)
\(410\) −13.9869 + 3.72846i −0.690762 + 0.184136i
\(411\) −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 0.881314 0.472531i \(-0.156659\pi\)
−0.849881 + 0.526975i \(0.823326\pi\)
\(420\) 3.22578 0.859892i 0.157402 0.0419584i
\(421\) 40.0359i 1.95123i 0.219484 + 0.975616i \(0.429563\pi\)
−0.219484 + 0.975616i \(0.570437\pi\)
\(422\) −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
\(425\) 19.4069 + 11.2714i 0.941374 + 0.546742i
\(426\) −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 0.644814 0.764340i \(-0.276935\pi\)
−0.339531 + 0.940595i \(0.610268\pi\)
\(432\) −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
\(435\) −4.79391 + 17.7994i −0.229851 + 0.853415i
\(436\) 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 0.917331 0.398125i \(-0.130339\pi\)
0.113880 + 0.993495i \(0.463672\pi\)
\(440\) −10.7866 + 2.87538i −0.514233 + 0.137079i
\(441\) 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 0.628397 0.777893i \(-0.283711\pi\)
−0.359476 + 0.933154i \(0.617045\pi\)
\(450\) −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 −0.448681 0.893692i \(-0.648106\pi\)
0.998300 0.0582764i \(-0.0185605\pi\)
\(458\) 8.67189 0.405211
\(459\) 3.88718 2.24427i 0.181438 0.104753i
\(460\) 4.55788 16.9230i 0.212512 0.789038i
\(461\) 9.55328 5.51559i 0.444941 0.256887i −0.260750 0.965406i \(-0.583970\pi\)
0.705691 + 0.708520i \(0.250637\pi\)
\(462\) 3.72678 6.45498i 0.173386 0.300313i
\(463\) 6.03232 10.4483i 0.280346 0.485573i −0.691124 0.722736i \(-0.742884\pi\)
0.971470 + 0.237163i \(0.0762175\pi\)
\(464\) 7.13932 4.12189i 0.331435 0.191354i
\(465\) 0.538002 1.99755i 0.0249492 0.0926342i
\(466\) −1.85101 + 1.06868i −0.0857462 + 0.0495056i
\(467\) −8.08233 −0.374005 −0.187003 0.982359i \(-0.559877\pi\)
−0.187003 + 0.982359i \(0.559877\pi\)
\(468\) −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 −0.795651 0.605755i \(-0.792871\pi\)
0.126774 + 0.991932i \(0.459538\pi\)
\(480\) 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
\(485\) −20.5020 + 5.46518i −0.930946 + 0.248161i
\(486\) 0.866025 + 0.500000i 0.0392837 + 0.0226805i
\(487\) −33.2218 −1.50542 −0.752711 0.658351i \(-0.771254\pi\)
−0.752711 + 0.658351i \(0.771254\pi\)
\(488\) −8.38002 4.83821i −0.379346 0.219015i
\(489\) 2.78270i 0.125838i
\(490\) −2.77442 + 10.3012i −0.125336 + 0.465360i
\(491\) 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 0.143555 0.989642i \(-0.454147\pi\)
−0.785278 + 0.619143i \(0.787480\pi\)
\(500\) −2.85192 10.8105i −0.127542 0.483459i
\(501\) −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 −0.999557 0.0297718i \(-0.990522\pi\)
0.473995 0.880527i \(-0.342811\pi\)
\(504\) 1.49299i 0.0665030i
\(505\) −18.3529 + 4.89231i −0.816693 + 0.217705i
\(506\) −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 0.810087 0.586310i \(-0.199420\pi\)
−0.912803 + 0.408401i \(0.866087\pi\)
\(510\) −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
\(515\) 11.5136 3.06917i 0.507351 0.135244i
\(516\) −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
\(520\) 4.13911 15.3682i 0.181512 0.673938i
\(521\) −10.8756 + 18.8371i −0.476468 + 0.825267i −0.999636 0.0269626i \(-0.991416\pi\)
0.523169 + 0.852229i \(0.324750\pi\)
\(522\) −7.13932 4.12189i −0.312480 0.180410i
\(523\) 16.7885 29.0785i 0.734108 1.27151i −0.221005 0.975273i \(-0.570934\pi\)
0.955113 0.296240i \(-0.0957329\pi\)
\(524\) 7.70903i 0.336771i
\(525\) 6.45519 + 3.74911i 0.281727 + 0.163625i
\(526\) 18.8193i 0.820563i
\(527\) 3.59629 2.07632i 0.156657 0.0904458i
\(528\) 4.99238i 0.217266i
\(529\) 38.4323 1.67097
\(530\) −9.12750 2.45832i −0.396473 0.106782i
\(531\) −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
\(535\) −12.6256 3.40045i −0.545851 0.147014i
\(536\) −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
\(540\) −2.15913 0.581519i −0.0929141 0.0250246i
\(541\) 2.98441i 0.128310i −0.997940 0.0641548i \(-0.979565\pi\)
0.997940 0.0641548i \(-0.0204352\pi\)
\(542\) 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 \(-0.361539\pi\)
0.421401 + 0.906874i \(0.361539\pi\)
\(548\) 4.59818 + 2.65476i 0.196425 + 0.113406i
\(549\) 9.67642i 0.412979i
\(550\) −21.5854 12.5366i −0.920406 0.534563i
\(551\) −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
\(555\) 8.40496 + 10.6938i 0.356771 + 0.453925i
\(556\) 7.96852 0.337941
\(557\) −6.44022 11.1548i −0.272881 0.472643i 0.696717 0.717346i \(-0.254643\pi\)
−0.969598 + 0.244702i \(0.921310\pi\)
\(558\) 0.801217 + 0.462583i 0.0339182 + 0.0195827i
\(559\) −28.6247 + 49.5795i −1.21070 + 2.09699i
\(560\) −0.859892 3.22578i −0.0363371 0.136314i
\(561\) 22.4085i 0.946086i
\(562\) 3.24794 + 1.87520i 0.137006 + 0.0791004i
\(563\) 4.71733 0.198812 0.0994059 0.995047i \(-0.468306\pi\)
0.0994059 + 0.995047i \(0.468306\pi\)
\(564\) −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 \(0.324727\pi\)
−0.523230 + 0.852191i \(0.675273\pi\)
\(570\) −1.80385 + 6.69752i −0.0755548 + 0.280528i
\(571\) 5.57259 + 9.65201i 0.233206 + 0.403924i 0.958750 0.284252i \(-0.0917451\pi\)
−0.725544 + 0.688176i \(0.758412\pi\)
\(572\) −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
\(575\) 33.9894 19.5072i 1.41746 0.813506i
\(576\) 0.500000 + 0.866025i 0.0208333 + 0.0360844i
\(577\) 18.0545 + 31.2713i 0.751619 + 1.30184i 0.947038 + 0.321122i \(0.104060\pi\)
−0.195419 + 0.980720i \(0.562607\pi\)
\(578\) −3.14690 −0.130894
\(579\) −14.0577 8.11621i −0.584217 0.337298i
\(580\) 17.7994 + 4.79391i 0.739079 + 0.199056i
\(581\) −13.5153 −0.560710
\(582\) 9.48892i 0.393329i
\(583\) −18.2773 + 10.5524i −0.756969 + 0.437036i
\(584\) 13.8195i 0.571856i
\(585\) −15.3788 + 4.09950i −0.635834 + 0.169493i
\(586\) 28.1011i 1.16084i
\(587\) 15.0657 26.0945i 0.621827 1.07704i −0.367318 0.930095i \(-0.619724\pi\)
0.989145 0.146941i \(-0.0469427\pi\)
\(588\) −4.13180 2.38549i −0.170392 0.0983761i
\(589\) 1.43491 2.48534i 0.0591245 0.102407i
\(590\) 11.3590 + 3.05933i 0.467643 + 0.125951i
\(591\) 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
\(595\) 3.85965 + 14.4790i 0.158230 + 0.593581i
\(596\) −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 0.235092 + 0.971973i \(0.424461\pi\)
−0.959300 + 0.282390i \(0.908873\pi\)
\(600\) 4.99998 + 0.0128835i 0.204123 + 0.000525966i
\(601\) 17.9480 + 31.0868i 0.732114 + 1.26806i 0.955978 + 0.293438i \(0.0947994\pi\)
−0.223864 + 0.974620i \(0.571867\pi\)
\(602\) 12.0084i 0.489425i
\(603\) 13.3161i 0.542275i
\(604\) 5.35526 + 9.27558i 0.217902 + 0.377418i
\(605\) −30.0843 + 8.01952i −1.22310 + 0.326040i
\(606\) 8.49427i 0.345056i
\(607\) 20.3935 + 35.3226i 0.827746 + 1.43370i 0.899802 + 0.436298i \(0.143711\pi\)
−0.0720560 + 0.997401i \(0.522956\pi\)
\(608\) 2.68637 1.55098i 0.108947 0.0629005i
\(609\) −10.6589 + 6.15393i −0.431921 + 0.249370i
\(610\) −5.57317 20.9071i −0.225651 0.846502i
\(611\) −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 \(-0.814910\pi\)
0.0578469 + 0.998325i \(0.481576\pi\)
\(614\) 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 \(-0.595657\pi\)
0.679208 + 0.733945i \(0.262323\pi\)
\(618\) 5.32885i 0.214358i
\(619\) 43.9421 1.76618 0.883092 0.469200i \(-0.155458\pi\)
0.883092 + 0.469200i \(0.155458\pi\)
\(620\) −1.99755 0.538002i −0.0802236 0.0216067i
\(621\) 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
\(625\) 12.6114 21.5859i 0.504456 0.863437i
\(626\) −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 −0.205098 0.978741i \(-0.565751\pi\)
0.745066 + 0.666991i \(0.232418\pi\)
\(632\) 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 0.611330 0.791376i \(-0.290635\pi\)
−0.991017 + 0.133740i \(0.957301\pi\)
\(642\) 2.92376 5.06411i 0.115392 0.199864i
\(643\) 29.7837 1.17456 0.587278 0.809385i \(-0.300199\pi\)
0.587278 + 0.809385i \(0.300199\pi\)
\(644\) 10.1341 5.85093i 0.399340 0.230559i
\(645\) −17.3663 4.67727i −0.683797 0.184167i
\(646\) −12.0579 + 6.96161i −0.474410 + 0.273901i
\(647\) 9.75527 16.8966i 0.383519 0.664275i −0.608043 0.793904i \(-0.708045\pi\)
0.991563 + 0.129629i \(0.0413787\pi\)
\(648\) 0.500000 0.866025i 0.0196419 0.0340207i
\(649\) 22.7458 13.1323i 0.892850 0.515487i
\(650\) 30.8665 17.7149i 1.21069 0.694836i
\(651\) 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 \(-0.913949\pi\)
0.713118 + 0.701044i \(0.247283\pi\)
\(654\) 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 −0.692004 0.721894i \(-0.743272\pi\)
0.971180 + 0.238346i \(0.0766051\pi\)
\(660\) 7.90382 7.88348i 0.307656 0.306864i
\(661\) 21.4678 + 12.3944i 0.834999 + 0.482087i 0.855561 0.517702i \(-0.173212\pi\)
−0.0205623 + 0.999789i \(0.506546\pi\)
\(662\) −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
\(670\) −7.66948 28.7711i −0.296298 1.11152i
\(671\) −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 \(-0.267570\pi\)
−0.311713 + 0.950176i \(0.600903\pi\)
\(674\) 12.8150i 0.493614i
\(675\) −2.48883 4.33655i −0.0957953 0.166914i
\(676\) 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 −0.996676 0.0814698i \(-0.974039\pi\)
0.427783 0.903881i \(-0.359295\pi\)
\(684\) −2.68637 1.55098i −0.102716 0.0593031i
\(685\) 3.05804 + 11.4719i 0.116842 + 0.438317i
\(686\) −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
\(690\) 4.51426 + 16.9347i 0.171855 + 0.644692i
\(691\) 16.1943 + 28.0494i 0.616060 + 1.06705i 0.990197 + 0.139675i \(0.0446056\pi\)
−0.374137 + 0.927373i \(0.622061\pi\)
\(692\) 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
\(700\) 3.74911 6.45519i 0.141703 0.243983i
\(701\) −22.1818 + 12.8066i −0.837793 + 0.483700i −0.856514 0.516125i \(-0.827374\pi\)
0.0187202 + 0.999825i \(0.494041\pi\)
\(702\) 7.11776i 0.268642i
\(703\) 7.44520 + 17.3375i 0.280801 + 0.653895i
\(704\) −4.99238 −0.188158
\(705\) 2.62771 9.75647i 0.0989654 0.367450i
\(706\) −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 \(-0.761080\pi\)
0.731286 0.682071i \(-0.238920\pi\)
\(710\) −1.11954 + 0.298434i −0.0420155 + 0.0112000i
\(711\) 0.965634i 0.0362141i
\(712\) −6.79186 + 3.92128i −0.254536 + 0.146956i
\(713\) 7.25134i 0.271565i
\(714\) −6.70132 −0.250791
\(715\) 20.6640 76.7237i 0.772791 2.86930i
\(716\) −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 0.817487 0.575948i \(-0.195367\pi\)
−0.907529 + 0.419990i \(0.862033\pi\)
\(720\) −0.581519 + 2.15913i −0.0216719 + 0.0804660i
\(721\) 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
\(725\) 20.5174 + 35.7496i 0.761997 + 1.32771i
\(726\) 13.9239i 0.516764i
\(727\) −1.93804 + 3.35679i −0.0718780 + 0.124496i −0.899724 0.436459i \(-0.856233\pi\)
0.827846 + 0.560955i \(0.189566\pi\)
\(728\) 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 \(-0.505113\pi\)
−0.873944 + 0.486026i \(0.838446\pi\)
\(734\) 1.55468i 0.0573842i
\(735\) −2.74787 10.3083i −0.101357 0.380227i
\(736\) 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 \(0.815905\pi\)
\(740\) 10.6938 8.40496i 0.393111 0.308973i
\(741\) −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 \(-0.159940\pi\)
0.0211303 + 0.999777i \(0.493274\pi\)
\(744\) 0.462583 0.801217i 0.0169591 0.0293740i
\(745\) −19.1874 + 5.11477i −0.702973 + 0.187391i
\(746\) 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
\(755\) −6.22837 + 23.1254i −0.226674 + 0.841619i
\(756\) −0.746494 1.29297i −0.0271497 0.0470247i
\(757\) −20.2892 35.1419i −0.737423 1.27725i −0.953652 0.300911i \(-0.902709\pi\)
0.216230 0.976343i \(-0.430624\pi\)
\(758\) −3.06678 + 5.31181i −0.111390 + 0.192934i
\(759\) 33.8873 + 19.5649i 1.23003 + 0.710159i
\(760\) 6.69752 + 1.80385i 0.242945 + 0.0654324i
\(761\) −0.220861 0.382543i −0.00800622 0.0138672i 0.861995 0.506918i \(-0.169215\pi\)
−0.870001 + 0.493050i \(0.835882\pi\)
\(762\) −4.59678 7.96186i −0.166524 0.288428i
\(763\) 11.6290 0.420998
\(764\) 8.58641 + 4.95736i 0.310645 + 0.179351i
\(765\) 2.61017 9.69131i 0.0943708 0.350390i
\(766\) 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 \(-0.985159\pi\)
0.998913 0.0466082i \(-0.0148412\pi\)
\(770\) −4.29291 16.1043i −0.154706 0.580360i
\(771\) 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 \(-0.634023\pi\)
−0.994746 + 0.102374i \(0.967356\pi\)
\(774\) 4.02159 6.96561i 0.144553 0.250374i
\(775\) −2.30258 4.01203i −0.0827113 0.144116i
\(776\) −9.48892 −0.340633