Properties

Label 1110.2.x.d.751.8
Level $1110$
Weight $2$
Character 1110.751
Analytic conductor $8.863$
Analytic rank $0$
Dimension $16$
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.x (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 60 x^{14} + 1362 x^{12} + 15028 x^{10} + 86441 x^{8} + 260376 x^{6} + 382684 x^{4} + 224224 x^{2} + 38416\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 751.8
Root \(-3.78749i\) of defining polynomial
Character \(\chi\) \(=\) 1110.751
Dual form 1110.2.x.d.841.8

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(1.89374 - 3.28006i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(1.89374 - 3.28006i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +1.00000 q^{10} -3.84038 q^{11} +(0.500000 + 0.866025i) q^{12} +(5.82335 + 3.36212i) q^{13} -3.78749i q^{14} +(-0.866025 + 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(4.14609 - 2.39374i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(-4.79142 - 2.76633i) q^{19} +(0.866025 - 0.500000i) q^{20} +(1.89374 + 3.28006i) q^{21} +(-3.32587 + 1.92019i) q^{22} -8.45628i q^{23} +(0.866025 + 0.500000i) q^{24} +(0.500000 + 0.866025i) q^{25} +6.72423 q^{26} +1.00000 q^{27} +(-1.89374 - 3.28006i) q^{28} -1.86387i q^{29} +(-0.500000 + 0.866025i) q^{30} +8.49606i q^{31} +(-0.866025 - 0.500000i) q^{32} +(1.92019 - 3.32587i) q^{33} +(2.39374 - 4.14609i) q^{34} +(3.28006 - 1.89374i) q^{35} -1.00000 q^{36} +(2.29396 + 5.63363i) q^{37} -5.53266 q^{38} +(-5.82335 + 3.36212i) q^{39} +(0.500000 - 0.866025i) q^{40} +(4.99616 - 8.65360i) q^{41} +(3.28006 + 1.89374i) q^{42} -0.0397760i q^{43} +(-1.92019 + 3.32587i) q^{44} -1.00000i q^{45} +(-4.22814 - 7.32335i) q^{46} +1.04092 q^{47} +1.00000 q^{48} +(-3.67253 - 6.36102i) q^{49} +(0.866025 + 0.500000i) q^{50} +4.78749i q^{51} +(5.82335 - 3.36212i) q^{52} +(-1.60374 - 2.77776i) q^{53} +(0.866025 - 0.500000i) q^{54} +(-3.32587 - 1.92019i) q^{55} +(-3.28006 - 1.89374i) q^{56} +(4.79142 - 2.76633i) q^{57} +(-0.931933 - 1.61416i) q^{58} +(1.56278 - 0.902271i) q^{59} +1.00000i q^{60} +(11.4759 + 6.62563i) q^{61} +(4.24803 + 7.35780i) q^{62} -3.78749 q^{63} -1.00000 q^{64} +(3.36212 + 5.82335i) q^{65} -3.84038i q^{66} +(4.58744 - 7.94568i) q^{67} -4.78749i q^{68} +(7.32335 + 4.22814i) q^{69} +(1.89374 - 3.28006i) q^{70} +(-0.928191 + 1.60767i) q^{71} +(-0.866025 + 0.500000i) q^{72} -11.8343 q^{73} +(4.80344 + 3.73188i) q^{74} -1.00000 q^{75} +(-4.79142 + 2.76633i) q^{76} +(-7.27270 + 12.5967i) q^{77} +(-3.36212 + 5.82335i) q^{78} +(-3.13047 - 1.80738i) q^{79} -1.00000i q^{80} +(-0.500000 + 0.866025i) q^{81} -9.99232i q^{82} +(6.79367 + 11.7670i) q^{83} +3.78749 q^{84} +4.78749 q^{85} +(-0.0198880 - 0.0344471i) q^{86} +(1.61416 + 0.931933i) q^{87} +3.84038i q^{88} +(14.8116 - 8.55149i) q^{89} +(-0.500000 - 0.866025i) q^{90} +(22.0559 - 12.7340i) q^{91} +(-7.32335 - 4.22814i) q^{92} +(-7.35780 - 4.24803i) q^{93} +(0.901463 - 0.520460i) q^{94} +(-2.76633 - 4.79142i) q^{95} +(0.866025 - 0.500000i) q^{96} +6.15065i q^{97} +(-6.36102 - 3.67253i) q^{98} +(1.92019 + 3.32587i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 8q^{3} + 8q^{4} - 2q^{7} - 8q^{9} + O(q^{10}) \) \( 16q - 8q^{3} + 8q^{4} - 2q^{7} - 8q^{9} + 16q^{10} - 8q^{11} + 8q^{12} - 6q^{13} - 8q^{16} + 6q^{17} - 12q^{19} - 2q^{21} + 8q^{25} + 4q^{26} + 16q^{27} + 2q^{28} - 8q^{30} + 4q^{33} + 6q^{34} + 6q^{35} - 16q^{36} + 12q^{37} - 4q^{38} + 6q^{39} + 8q^{40} + 4q^{41} + 6q^{42} - 4q^{44} - 2q^{46} + 68q^{47} + 16q^{48} - 4q^{49} - 6q^{52} - 12q^{53} - 6q^{56} + 12q^{57} - 6q^{58} + 6q^{59} + 12q^{61} + 4q^{62} + 4q^{63} - 16q^{64} + 2q^{65} - 36q^{67} + 18q^{69} - 2q^{70} + 6q^{71} - 16q^{73} + 14q^{74} - 16q^{75} - 12q^{76} + 26q^{77} - 2q^{78} - 24q^{79} - 8q^{81} + 12q^{83} - 4q^{84} + 12q^{85} - 2q^{86} + 24q^{89} - 8q^{90} + 60q^{91} - 18q^{92} - 30q^{93} + 6q^{94} - 2q^{95} - 12q^{98} + 4q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 0.500000i 0.612372 0.353553i
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0.866025 + 0.500000i 0.387298 + 0.223607i
\(6\) 1.00000i 0.408248i
\(7\) 1.89374 3.28006i 0.715768 1.23975i −0.246895 0.969042i \(-0.579410\pi\)
0.962663 0.270704i \(-0.0872565\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 1.00000 0.316228
\(11\) −3.84038 −1.15792 −0.578960 0.815356i \(-0.696541\pi\)
−0.578960 + 0.815356i \(0.696541\pi\)
\(12\) 0.500000 + 0.866025i 0.144338 + 0.250000i
\(13\) 5.82335 + 3.36212i 1.61511 + 0.932483i 0.988161 + 0.153421i \(0.0490290\pi\)
0.626947 + 0.779062i \(0.284304\pi\)
\(14\) 3.78749i 1.01225i
\(15\) −0.866025 + 0.500000i −0.223607 + 0.129099i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 4.14609 2.39374i 1.00557 0.580568i 0.0956811 0.995412i \(-0.469497\pi\)
0.909893 + 0.414844i \(0.136164\pi\)
\(18\) −0.866025 0.500000i −0.204124 0.117851i
\(19\) −4.79142 2.76633i −1.09923 0.634639i −0.163210 0.986591i \(-0.552185\pi\)
−0.936018 + 0.351952i \(0.885518\pi\)
\(20\) 0.866025 0.500000i 0.193649 0.111803i
\(21\) 1.89374 + 3.28006i 0.413249 + 0.715768i
\(22\) −3.32587 + 1.92019i −0.709078 + 0.409386i
\(23\) 8.45628i 1.76326i −0.471945 0.881628i \(-0.656448\pi\)
0.471945 0.881628i \(-0.343552\pi\)
\(24\) 0.866025 + 0.500000i 0.176777 + 0.102062i
\(25\) 0.500000 + 0.866025i 0.100000 + 0.173205i
\(26\) 6.72423 1.31873
\(27\) 1.00000 0.192450
\(28\) −1.89374 3.28006i −0.357884 0.619873i
\(29\) 1.86387i 0.346111i −0.984912 0.173056i \(-0.944636\pi\)
0.984912 0.173056i \(-0.0553640\pi\)
\(30\) −0.500000 + 0.866025i −0.0912871 + 0.158114i
\(31\) 8.49606i 1.52594i 0.646436 + 0.762968i \(0.276259\pi\)
−0.646436 + 0.762968i \(0.723741\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) 1.92019 3.32587i 0.334263 0.578960i
\(34\) 2.39374 4.14609i 0.410524 0.711048i
\(35\) 3.28006 1.89374i 0.554432 0.320101i
\(36\) −1.00000 −0.166667
\(37\) 2.29396 + 5.63363i 0.377125 + 0.926162i
\(38\) −5.53266 −0.897516
\(39\) −5.82335 + 3.36212i −0.932483 + 0.538369i
\(40\) 0.500000 0.866025i 0.0790569 0.136931i
\(41\) 4.99616 8.65360i 0.780269 1.35147i −0.151516 0.988455i \(-0.548416\pi\)
0.931785 0.363011i \(-0.118251\pi\)
\(42\) 3.28006 + 1.89374i 0.506124 + 0.292211i
\(43\) 0.0397760i 0.00606579i −0.999995 0.00303289i \(-0.999035\pi\)
0.999995 0.00303289i \(-0.000965402\pi\)
\(44\) −1.92019 + 3.32587i −0.289480 + 0.501394i
\(45\) 1.00000i 0.149071i
\(46\) −4.22814 7.32335i −0.623405 1.07977i
\(47\) 1.04092 0.151834 0.0759169 0.997114i \(-0.475812\pi\)
0.0759169 + 0.997114i \(0.475812\pi\)
\(48\) 1.00000 0.144338
\(49\) −3.67253 6.36102i −0.524648 0.908717i
\(50\) 0.866025 + 0.500000i 0.122474 + 0.0707107i
\(51\) 4.78749i 0.670382i
\(52\) 5.82335 3.36212i 0.807554 0.466241i
\(53\) −1.60374 2.77776i −0.220291 0.381555i 0.734606 0.678494i \(-0.237367\pi\)
−0.954896 + 0.296940i \(0.904034\pi\)
\(54\) 0.866025 0.500000i 0.117851 0.0680414i
\(55\) −3.32587 1.92019i −0.448460 0.258919i
\(56\) −3.28006 1.89374i −0.438317 0.253062i
\(57\) 4.79142 2.76633i 0.634639 0.366409i
\(58\) −0.931933 1.61416i −0.122369 0.211949i
\(59\) 1.56278 0.902271i 0.203456 0.117466i −0.394810 0.918763i \(-0.629190\pi\)
0.598267 + 0.801297i \(0.295856\pi\)
\(60\) 1.00000i 0.129099i
\(61\) 11.4759 + 6.62563i 1.46934 + 0.848325i 0.999409 0.0343779i \(-0.0109450\pi\)
0.469932 + 0.882702i \(0.344278\pi\)
\(62\) 4.24803 + 7.35780i 0.539500 + 0.934442i
\(63\) −3.78749 −0.477179
\(64\) −1.00000 −0.125000
\(65\) 3.36212 + 5.82335i 0.417019 + 0.722298i
\(66\) 3.84038i 0.472719i
\(67\) 4.58744 7.94568i 0.560445 0.970719i −0.437013 0.899455i \(-0.643964\pi\)
0.997458 0.0712634i \(-0.0227031\pi\)
\(68\) 4.78749i 0.580568i
\(69\) 7.32335 + 4.22814i 0.881628 + 0.509008i
\(70\) 1.89374 3.28006i 0.226346 0.392042i
\(71\) −0.928191 + 1.60767i −0.110156 + 0.190796i −0.915833 0.401559i \(-0.868468\pi\)
0.805677 + 0.592355i \(0.201802\pi\)
\(72\) −0.866025 + 0.500000i −0.102062 + 0.0589256i
\(73\) −11.8343 −1.38510 −0.692550 0.721370i \(-0.743513\pi\)
−0.692550 + 0.721370i \(0.743513\pi\)
\(74\) 4.80344 + 3.73188i 0.558389 + 0.433822i
\(75\) −1.00000 −0.115470
\(76\) −4.79142 + 2.76633i −0.549614 + 0.317320i
\(77\) −7.27270 + 12.5967i −0.828802 + 1.43553i
\(78\) −3.36212 + 5.82335i −0.380685 + 0.659365i
\(79\) −3.13047 1.80738i −0.352205 0.203346i 0.313451 0.949604i \(-0.398515\pi\)
−0.665656 + 0.746259i \(0.731848\pi\)
\(80\) 1.00000i 0.111803i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 9.99232i 1.10347i
\(83\) 6.79367 + 11.7670i 0.745702 + 1.29159i 0.949866 + 0.312657i \(0.101219\pi\)
−0.204164 + 0.978937i \(0.565448\pi\)
\(84\) 3.78749 0.413249
\(85\) 4.78749 0.519276
\(86\) −0.0198880 0.0344471i −0.00214458 0.00371452i
\(87\) 1.61416 + 0.931933i 0.173056 + 0.0999137i
\(88\) 3.84038i 0.409386i
\(89\) 14.8116 8.55149i 1.57003 0.906457i 0.573865 0.818950i \(-0.305443\pi\)
0.996164 0.0875067i \(-0.0278899\pi\)
\(90\) −0.500000 0.866025i −0.0527046 0.0912871i
\(91\) 22.0559 12.7340i 2.31209 1.33488i
\(92\) −7.32335 4.22814i −0.763512 0.440814i
\(93\) −7.35780 4.24803i −0.762968 0.440500i
\(94\) 0.901463 0.520460i 0.0929789 0.0536814i
\(95\) −2.76633 4.79142i −0.283819 0.491590i
\(96\) 0.866025 0.500000i 0.0883883 0.0510310i
\(97\) 6.15065i 0.624504i 0.949999 + 0.312252i \(0.101083\pi\)
−0.949999 + 0.312252i \(0.898917\pi\)
\(98\) −6.36102 3.67253i −0.642560 0.370982i
\(99\) 1.92019 + 3.32587i 0.192987 + 0.334263i
\(100\) 1.00000 0.100000
\(101\) −8.96357 −0.891909 −0.445954 0.895056i \(-0.647136\pi\)
−0.445954 + 0.895056i \(0.647136\pi\)
\(102\) 2.39374 + 4.14609i 0.237016 + 0.410524i
\(103\) 14.7060i 1.44903i 0.689260 + 0.724514i \(0.257936\pi\)
−0.689260 + 0.724514i \(0.742064\pi\)
\(104\) 3.36212 5.82335i 0.329683 0.571027i
\(105\) 3.78749i 0.369621i
\(106\) −2.77776 1.60374i −0.269800 0.155769i
\(107\) −1.95561 + 3.38721i −0.189056 + 0.327454i −0.944936 0.327256i \(-0.893876\pi\)
0.755880 + 0.654710i \(0.227209\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) 3.31422 1.91346i 0.317444 0.183277i −0.332809 0.942994i \(-0.607996\pi\)
0.650253 + 0.759718i \(0.274663\pi\)
\(110\) −3.84038 −0.366166
\(111\) −6.02584 0.830184i −0.571948 0.0787976i
\(112\) −3.78749 −0.357884
\(113\) −14.1231 + 8.15399i −1.32859 + 0.767062i −0.985082 0.172087i \(-0.944949\pi\)
−0.343509 + 0.939149i \(0.611616\pi\)
\(114\) 2.76633 4.79142i 0.259090 0.448758i
\(115\) 4.22814 7.32335i 0.394276 0.682906i
\(116\) −1.61416 0.931933i −0.149871 0.0865278i
\(117\) 6.72423i 0.621655i
\(118\) 0.902271 1.56278i 0.0830607 0.143865i
\(119\) 18.1326i 1.66221i
\(120\) 0.500000 + 0.866025i 0.0456435 + 0.0790569i
\(121\) 3.74855 0.340777
\(122\) 13.2513 1.19971
\(123\) 4.99616 + 8.65360i 0.450488 + 0.780269i
\(124\) 7.35780 + 4.24803i 0.660750 + 0.381484i
\(125\) 1.00000i 0.0894427i
\(126\) −3.28006 + 1.89374i −0.292211 + 0.168708i
\(127\) −5.63891 9.76689i −0.500373 0.866671i −1.00000 0.000430450i \(-0.999863\pi\)
0.499627 0.866241i \(-0.333470\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) 0.0344471 + 0.0198880i 0.00303289 + 0.00175104i
\(130\) 5.82335 + 3.36212i 0.510742 + 0.294877i
\(131\) 7.20809 4.16159i 0.629774 0.363600i −0.150891 0.988550i \(-0.548214\pi\)
0.780664 + 0.624950i \(0.214881\pi\)
\(132\) −1.92019 3.32587i −0.167131 0.289480i
\(133\) −18.1475 + 10.4774i −1.57358 + 0.908509i
\(134\) 9.17488i 0.792589i
\(135\) 0.866025 + 0.500000i 0.0745356 + 0.0430331i
\(136\) −2.39374 4.14609i −0.205262 0.355524i
\(137\) −15.6219 −1.33467 −0.667334 0.744759i \(-0.732565\pi\)
−0.667334 + 0.744759i \(0.732565\pi\)
\(138\) 8.45628 0.719846
\(139\) −1.46820 2.54301i −0.124531 0.215695i 0.797018 0.603955i \(-0.206409\pi\)
−0.921550 + 0.388260i \(0.873076\pi\)
\(140\) 3.78749i 0.320101i
\(141\) −0.520460 + 0.901463i −0.0438307 + 0.0759169i
\(142\) 1.85638i 0.155784i
\(143\) −22.3639 12.9118i −1.87016 1.07974i
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) 0.931933 1.61416i 0.0773928 0.134048i
\(146\) −10.2488 + 5.91715i −0.848197 + 0.489707i
\(147\) 7.34507 0.605811
\(148\) 6.02584 + 0.830184i 0.495321 + 0.0682407i
\(149\) −16.2875 −1.33433 −0.667163 0.744912i \(-0.732492\pi\)
−0.667163 + 0.744912i \(0.732492\pi\)
\(150\) −0.866025 + 0.500000i −0.0707107 + 0.0408248i
\(151\) −10.1392 + 17.5616i −0.825117 + 1.42914i 0.0767136 + 0.997053i \(0.475557\pi\)
−0.901830 + 0.432091i \(0.857776\pi\)
\(152\) −2.76633 + 4.79142i −0.224379 + 0.388636i
\(153\) −4.14609 2.39374i −0.335191 0.193523i
\(154\) 14.5454i 1.17210i
\(155\) −4.24803 + 7.35780i −0.341210 + 0.590993i
\(156\) 6.72423i 0.538369i
\(157\) 3.39853 + 5.88642i 0.271232 + 0.469788i 0.969178 0.246363i \(-0.0792356\pi\)
−0.697945 + 0.716151i \(0.745902\pi\)
\(158\) −3.61475 −0.287574
\(159\) 3.20748 0.254370
\(160\) −0.500000 0.866025i −0.0395285 0.0684653i
\(161\) −27.7371 16.0140i −2.18599 1.26208i
\(162\) 1.00000i 0.0785674i
\(163\) −7.74406 + 4.47104i −0.606562 + 0.350199i −0.771619 0.636085i \(-0.780553\pi\)
0.165057 + 0.986284i \(0.447219\pi\)
\(164\) −4.99616 8.65360i −0.390134 0.675733i
\(165\) 3.32587 1.92019i 0.258919 0.149487i
\(166\) 11.7670 + 6.79367i 0.913295 + 0.527291i
\(167\) 2.72208 + 1.57160i 0.210641 + 0.121614i 0.601609 0.798790i \(-0.294526\pi\)
−0.390968 + 0.920404i \(0.627860\pi\)
\(168\) 3.28006 1.89374i 0.253062 0.146106i
\(169\) 16.1076 + 27.8992i 1.23905 + 2.14610i
\(170\) 4.14609 2.39374i 0.317990 0.183592i
\(171\) 5.53266i 0.423093i
\(172\) −0.0344471 0.0198880i −0.00262656 0.00151645i
\(173\) −0.362029 0.627052i −0.0275245 0.0476739i 0.851935 0.523648i \(-0.175429\pi\)
−0.879460 + 0.475974i \(0.842096\pi\)
\(174\) 1.86387 0.141299
\(175\) 3.78749 0.286307
\(176\) 1.92019 + 3.32587i 0.144740 + 0.250697i
\(177\) 1.80454i 0.135638i
\(178\) 8.55149 14.8116i 0.640962 1.11018i
\(179\) 20.9563i 1.56635i 0.621801 + 0.783175i \(0.286401\pi\)
−0.621801 + 0.783175i \(0.713599\pi\)
\(180\) −0.866025 0.500000i −0.0645497 0.0372678i
\(181\) −7.72795 + 13.3852i −0.574414 + 0.994914i 0.421691 + 0.906740i \(0.361437\pi\)
−0.996105 + 0.0881744i \(0.971897\pi\)
\(182\) 12.7340 22.0559i 0.943905 1.63489i
\(183\) −11.4759 + 6.62563i −0.848325 + 0.489780i
\(184\) −8.45628 −0.623405
\(185\) −0.830184 + 6.02584i −0.0610363 + 0.443029i
\(186\) −8.49606 −0.622961
\(187\) −15.9226 + 9.19290i −1.16437 + 0.672251i
\(188\) 0.520460 0.901463i 0.0379585 0.0657460i
\(189\) 1.89374 3.28006i 0.137750 0.238589i
\(190\) −4.79142 2.76633i −0.347606 0.200691i
\(191\) 3.03855i 0.219862i 0.993939 + 0.109931i \(0.0350630\pi\)
−0.993939 + 0.109931i \(0.964937\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) 14.3431i 1.03244i −0.856456 0.516220i \(-0.827339\pi\)
0.856456 0.516220i \(-0.172661\pi\)
\(194\) 3.07533 + 5.32662i 0.220796 + 0.382429i
\(195\) −6.72423 −0.481532
\(196\) −7.34507 −0.524648
\(197\) −0.401713 0.695787i −0.0286209 0.0495728i 0.851360 0.524582i \(-0.175778\pi\)
−0.879981 + 0.475009i \(0.842445\pi\)
\(198\) 3.32587 + 1.92019i 0.236359 + 0.136462i
\(199\) 4.01820i 0.284842i 0.989806 + 0.142421i \(0.0454888\pi\)
−0.989806 + 0.142421i \(0.954511\pi\)
\(200\) 0.866025 0.500000i 0.0612372 0.0353553i
\(201\) 4.58744 + 7.94568i 0.323573 + 0.560445i
\(202\) −7.76268 + 4.48179i −0.546180 + 0.315337i
\(203\) −6.11359 3.52969i −0.429090 0.247735i
\(204\) 4.14609 + 2.39374i 0.290284 + 0.167596i
\(205\) 8.65360 4.99616i 0.604394 0.348947i
\(206\) 7.35302 + 12.7358i 0.512309 + 0.887345i
\(207\) −7.32335 + 4.22814i −0.509008 + 0.293876i
\(208\) 6.72423i 0.466241i
\(209\) 18.4009 + 10.6238i 1.27282 + 0.734861i
\(210\) 1.89374 + 3.28006i 0.130681 + 0.226346i
\(211\) −9.46215 −0.651401 −0.325701 0.945473i \(-0.605600\pi\)
−0.325701 + 0.945473i \(0.605600\pi\)
\(212\) −3.20748 −0.220291
\(213\) −0.928191 1.60767i −0.0635986 0.110156i
\(214\) 3.91122i 0.267365i
\(215\) 0.0198880 0.0344471i 0.00135635 0.00234927i
\(216\) 1.00000i 0.0680414i
\(217\) 27.8676 + 16.0894i 1.89178 + 1.09222i
\(218\) 1.91346 3.31422i 0.129596 0.224467i
\(219\) 5.91715 10.2488i 0.399844 0.692550i
\(220\) −3.32587 + 1.92019i −0.224230 + 0.129459i
\(221\) 32.1922 2.16548
\(222\) −5.63363 + 2.29396i −0.378104 + 0.153961i
\(223\) 11.8558 0.793923 0.396961 0.917835i \(-0.370065\pi\)
0.396961 + 0.917835i \(0.370065\pi\)
\(224\) −3.28006 + 1.89374i −0.219158 + 0.126531i
\(225\) 0.500000 0.866025i 0.0333333 0.0577350i
\(226\) −8.15399 + 14.1231i −0.542395 + 0.939456i
\(227\) 10.7982 + 6.23432i 0.716699 + 0.413786i 0.813537 0.581514i \(-0.197539\pi\)
−0.0968375 + 0.995300i \(0.530873\pi\)
\(228\) 5.53266i 0.366409i
\(229\) −5.00593 + 8.67053i −0.330801 + 0.572965i −0.982669 0.185368i \(-0.940652\pi\)
0.651868 + 0.758332i \(0.273986\pi\)
\(230\) 8.45628i 0.557591i
\(231\) −7.27270 12.5967i −0.478509 0.828802i
\(232\) −1.86387 −0.122369
\(233\) 9.91106 0.649295 0.324648 0.945835i \(-0.394754\pi\)
0.324648 + 0.945835i \(0.394754\pi\)
\(234\) −3.36212 5.82335i −0.219788 0.380685i
\(235\) 0.901463 + 0.520460i 0.0588050 + 0.0339511i
\(236\) 1.80454i 0.117466i
\(237\) 3.13047 1.80738i 0.203346 0.117402i
\(238\) −9.06628 15.7033i −0.587680 1.01789i
\(239\) −13.5328 + 7.81314i −0.875361 + 0.505390i −0.869126 0.494591i \(-0.835318\pi\)
−0.00623501 + 0.999981i \(0.501985\pi\)
\(240\) 0.866025 + 0.500000i 0.0559017 + 0.0322749i
\(241\) −11.0815 6.39792i −0.713824 0.412127i 0.0986513 0.995122i \(-0.468547\pi\)
−0.812475 + 0.582996i \(0.801880\pi\)
\(242\) 3.24634 1.87427i 0.208682 0.120483i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) 11.4759 6.62563i 0.734671 0.424162i
\(245\) 7.34507i 0.469259i
\(246\) 8.65360 + 4.99616i 0.551733 + 0.318543i
\(247\) −18.6014 32.2186i −1.18358 2.05002i
\(248\) 8.49606 0.539500
\(249\) −13.5873 −0.861063
\(250\) 0.500000 + 0.866025i 0.0316228 + 0.0547723i
\(251\) 9.23928i 0.583178i −0.956544 0.291589i \(-0.905816\pi\)
0.956544 0.291589i \(-0.0941840\pi\)
\(252\) −1.89374 + 3.28006i −0.119295 + 0.206624i
\(253\) 32.4754i 2.04171i
\(254\) −9.76689 5.63891i −0.612829 0.353817i
\(255\) −2.39374 + 4.14609i −0.149902 + 0.259638i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −10.4372 + 6.02592i −0.651055 + 0.375887i −0.788860 0.614573i \(-0.789328\pi\)
0.137805 + 0.990459i \(0.455995\pi\)
\(258\) 0.0397760 0.00247635
\(259\) 22.8228 + 3.14431i 1.41814 + 0.195378i
\(260\) 6.72423 0.417019
\(261\) −1.61416 + 0.931933i −0.0999137 + 0.0576852i
\(262\) 4.16159 7.20809i 0.257104 0.445317i
\(263\) −3.65537 + 6.33128i −0.225400 + 0.390404i −0.956439 0.291931i \(-0.905702\pi\)
0.731040 + 0.682335i \(0.239035\pi\)
\(264\) −3.32587 1.92019i −0.204693 0.118180i
\(265\) 3.20748i 0.197034i
\(266\) −10.4774 + 18.1475i −0.642413 + 1.11269i
\(267\) 17.1030i 1.04669i
\(268\) −4.58744 7.94568i −0.280222 0.485359i
\(269\) −15.1627 −0.924484 −0.462242 0.886754i \(-0.652955\pi\)
−0.462242 + 0.886754i \(0.652955\pi\)
\(270\) 1.00000 0.0608581
\(271\) −5.39620 9.34650i −0.327796 0.567759i 0.654278 0.756254i \(-0.272973\pi\)
−0.982074 + 0.188495i \(0.939639\pi\)
\(272\) −4.14609 2.39374i −0.251393 0.145142i
\(273\) 25.4679i 1.54139i
\(274\) −13.5290 + 7.81094i −0.817314 + 0.471876i
\(275\) −1.92019 3.32587i −0.115792 0.200558i
\(276\) 7.32335 4.22814i 0.440814 0.254504i
\(277\) 6.93540 + 4.00416i 0.416708 + 0.240587i 0.693668 0.720295i \(-0.255994\pi\)
−0.276960 + 0.960882i \(0.589327\pi\)
\(278\) −2.54301 1.46820i −0.152519 0.0880571i
\(279\) 7.35780 4.24803i 0.440500 0.254323i
\(280\) −1.89374 3.28006i −0.113173 0.196021i
\(281\) 21.6964 12.5264i 1.29430 0.747262i 0.314884 0.949130i \(-0.398034\pi\)
0.979413 + 0.201868i \(0.0647011\pi\)
\(282\) 1.04092i 0.0619859i
\(283\) 3.42387 + 1.97677i 0.203528 + 0.117507i 0.598300 0.801272i \(-0.295843\pi\)
−0.394772 + 0.918779i \(0.629176\pi\)
\(284\) 0.928191 + 1.60767i 0.0550780 + 0.0953979i
\(285\) 5.53266 0.327726
\(286\) −25.8236 −1.52698
\(287\) −18.9229 32.7754i −1.11698 1.93467i
\(288\) 1.00000i 0.0589256i
\(289\) 2.96002 5.12691i 0.174119 0.301583i
\(290\) 1.86387i 0.109450i
\(291\) −5.32662 3.07533i −0.312252 0.180279i
\(292\) −5.91715 + 10.2488i −0.346275 + 0.599766i
\(293\) −6.27495 + 10.8685i −0.366586 + 0.634946i −0.989029 0.147719i \(-0.952807\pi\)
0.622443 + 0.782665i \(0.286140\pi\)
\(294\) 6.36102 3.67253i 0.370982 0.214187i
\(295\) 1.80454 0.105064
\(296\) 5.63363 2.29396i 0.327448 0.133334i
\(297\) −3.84038 −0.222842
\(298\) −14.1054 + 8.14376i −0.817105 + 0.471756i
\(299\) 28.4310 49.2439i 1.64421 2.84785i
\(300\) −0.500000 + 0.866025i −0.0288675 + 0.0500000i
\(301\) −0.130468 0.0753256i −0.00752004 0.00434170i
\(302\) 20.2784i 1.16689i
\(303\) 4.48179 7.76268i 0.257472 0.445954i
\(304\) 5.53266i 0.317320i
\(305\) 6.62563 + 11.4759i 0.379382 + 0.657109i
\(306\) −4.78749 −0.273682
\(307\) −2.35294 −0.134289 −0.0671446 0.997743i \(-0.521389\pi\)
−0.0671446 + 0.997743i \(0.521389\pi\)
\(308\) 7.27270 + 12.5967i 0.414401 + 0.717763i
\(309\) −12.7358 7.35302i −0.724514 0.418298i
\(310\) 8.49606i 0.482544i
\(311\) −19.5888 + 11.3096i −1.11078 + 0.641309i −0.939031 0.343832i \(-0.888275\pi\)
−0.171748 + 0.985141i \(0.554942\pi\)
\(312\) 3.36212 + 5.82335i 0.190342 + 0.329683i
\(313\) 13.5051 7.79719i 0.763355 0.440723i −0.0671443 0.997743i \(-0.521389\pi\)
0.830499 + 0.557020i \(0.188055\pi\)
\(314\) 5.88642 + 3.39853i 0.332190 + 0.191790i
\(315\) −3.28006 1.89374i −0.184811 0.106700i
\(316\) −3.13047 + 1.80738i −0.176103 + 0.101673i
\(317\) 12.3149 + 21.3299i 0.691671 + 1.19801i 0.971290 + 0.237898i \(0.0764585\pi\)
−0.279619 + 0.960111i \(0.590208\pi\)
\(318\) 2.77776 1.60374i 0.155769 0.0899333i
\(319\) 7.15796i 0.400769i
\(320\) −0.866025 0.500000i −0.0484123 0.0279508i
\(321\) −1.95561 3.38721i −0.109151 0.189056i
\(322\) −32.0281 −1.78485
\(323\) −26.4875 −1.47381
\(324\) 0.500000 + 0.866025i 0.0277778 + 0.0481125i
\(325\) 6.72423i 0.372993i
\(326\) −4.47104 + 7.74406i −0.247628 + 0.428904i
\(327\) 3.82693i 0.211630i
\(328\) −8.65360 4.99616i −0.477815 0.275867i
\(329\) 1.97124 3.41428i 0.108678 0.188235i
\(330\) 1.92019 3.32587i 0.105703 0.183083i
\(331\) 7.39622 4.27021i 0.406533 0.234712i −0.282766 0.959189i \(-0.591252\pi\)
0.689299 + 0.724477i \(0.257919\pi\)
\(332\) 13.5873 0.745702
\(333\) 3.73188 4.80344i 0.204506 0.263227i
\(334\) 3.14319 0.171988
\(335\) 7.94568 4.58744i 0.434119 0.250638i
\(336\) 1.89374 3.28006i 0.103312 0.178942i
\(337\) 6.00674 10.4040i 0.327208 0.566741i −0.654749 0.755847i \(-0.727226\pi\)
0.981957 + 0.189106i \(0.0605589\pi\)
\(338\) 27.8992 + 16.1076i 1.51752 + 0.876140i
\(339\) 16.3080i 0.885727i
\(340\) 2.39374 4.14609i 0.129819 0.224853i
\(341\) 32.6281i 1.76691i
\(342\) 2.76633 + 4.79142i 0.149586 + 0.259090i
\(343\) −1.30694 −0.0705683
\(344\) −0.0397760 −0.00214458
\(345\) 4.22814 + 7.32335i 0.227635 + 0.394276i
\(346\) −0.627052 0.362029i −0.0337105 0.0194628i
\(347\) 5.81798i 0.312325i −0.987731 0.156163i \(-0.950088\pi\)
0.987731 0.156163i \(-0.0499124\pi\)
\(348\) 1.61416 0.931933i 0.0865278 0.0499569i
\(349\) 14.8951 + 25.7991i 0.797318 + 1.38099i 0.921357 + 0.388717i \(0.127082\pi\)
−0.124039 + 0.992277i \(0.539585\pi\)
\(350\) 3.28006 1.89374i 0.175327 0.101225i
\(351\) 5.82335 + 3.36212i 0.310828 + 0.179456i
\(352\) 3.32587 + 1.92019i 0.177269 + 0.102347i
\(353\) −13.6952 + 7.90695i −0.728924 + 0.420845i −0.818029 0.575178i \(-0.804933\pi\)
0.0891041 + 0.996022i \(0.471600\pi\)
\(354\) 0.902271 + 1.56278i 0.0479551 + 0.0830607i
\(355\) −1.60767 + 0.928191i −0.0853265 + 0.0492633i
\(356\) 17.1030i 0.906457i
\(357\) 15.7033 + 9.06628i 0.831104 + 0.479838i
\(358\) 10.4782 + 18.1487i 0.553788 + 0.959190i
\(359\) 20.8727 1.10162 0.550809 0.834631i \(-0.314319\pi\)
0.550809 + 0.834631i \(0.314319\pi\)
\(360\) −1.00000 −0.0527046
\(361\) 5.80516 + 10.0548i 0.305534 + 0.529201i
\(362\) 15.4559i 0.812344i
\(363\) −1.87427 + 3.24634i −0.0983739 + 0.170389i
\(364\) 25.4679i 1.33488i
\(365\) −10.2488 5.91715i −0.536447 0.309718i
\(366\) −6.62563 + 11.4759i −0.346327 + 0.599856i
\(367\) 12.5188 21.6833i 0.653478 1.13186i −0.328795 0.944401i \(-0.606643\pi\)
0.982273 0.187456i \(-0.0600242\pi\)
\(368\) −7.32335 + 4.22814i −0.381756 + 0.220407i
\(369\) −9.99232 −0.520179
\(370\) 2.29396 + 5.63363i 0.119257 + 0.292878i
\(371\) −12.1483 −0.630708
\(372\) −7.35780 + 4.24803i −0.381484 + 0.220250i
\(373\) 8.34468 14.4534i 0.432071 0.748369i −0.564980 0.825104i \(-0.691116\pi\)
0.997052 + 0.0767350i \(0.0244495\pi\)
\(374\) −9.19290 + 15.9226i −0.475353 + 0.823336i
\(375\) −0.866025 0.500000i −0.0447214 0.0258199i
\(376\) 1.04092i 0.0536814i
\(377\) 6.26653 10.8540i 0.322743 0.559007i
\(378\) 3.78749i 0.194807i
\(379\) 12.4760 + 21.6091i 0.640849 + 1.10998i 0.985244 + 0.171158i \(0.0547509\pi\)
−0.344394 + 0.938825i \(0.611916\pi\)
\(380\) −5.53266 −0.283819
\(381\) 11.2778 0.577781
\(382\) 1.51928 + 2.63146i 0.0777329 + 0.134637i
\(383\) −8.07527 4.66226i −0.412627 0.238230i 0.279291 0.960207i \(-0.409901\pi\)
−0.691918 + 0.721976i \(0.743234\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) −12.5967 + 7.27270i −0.641987 + 0.370651i
\(386\) −7.17156 12.4215i −0.365023 0.632238i
\(387\) −0.0344471 + 0.0198880i −0.00175104 + 0.00101096i
\(388\) 5.32662 + 3.07533i 0.270418 + 0.156126i
\(389\) 18.8460 + 10.8808i 0.955532 + 0.551677i 0.894795 0.446477i \(-0.147322\pi\)
0.0607371 + 0.998154i \(0.480655\pi\)
\(390\) −5.82335 + 3.36212i −0.294877 + 0.170247i
\(391\) −20.2422 35.0605i −1.02369 1.77308i
\(392\) −6.36102 + 3.67253i −0.321280 + 0.185491i
\(393\) 8.32318i 0.419849i
\(394\) −0.695787 0.401713i −0.0350533 0.0202380i
\(395\) −1.80738 3.13047i −0.0909390 0.157511i
\(396\) 3.84038 0.192987
\(397\) −4.30813 −0.216219 −0.108109 0.994139i \(-0.534480\pi\)
−0.108109 + 0.994139i \(0.534480\pi\)
\(398\) 2.00910 + 3.47986i 0.100707 + 0.174430i
\(399\) 20.9549i 1.04906i
\(400\) 0.500000 0.866025i 0.0250000 0.0433013i
\(401\) 15.7601i 0.787021i −0.919320 0.393510i \(-0.871261\pi\)
0.919320 0.393510i \(-0.128739\pi\)
\(402\) 7.94568 + 4.58744i 0.396294 + 0.228801i
\(403\) −28.5647 + 49.4755i −1.42291 + 2.46455i
\(404\) −4.48179 + 7.76268i −0.222977 + 0.386208i
\(405\) −0.866025 + 0.500000i −0.0430331 + 0.0248452i
\(406\) −7.05937 −0.350351
\(407\) −8.80969 21.6353i −0.436680 1.07242i
\(408\) 4.78749 0.237016
\(409\) 25.1445 14.5172i 1.24331 0.717828i 0.273547 0.961859i \(-0.411803\pi\)
0.969768 + 0.244030i \(0.0784697\pi\)
\(410\) 4.99616 8.65360i 0.246743 0.427371i
\(411\) 7.81094 13.5290i 0.385285 0.667334i
\(412\) 12.7358 + 7.35302i 0.627448 + 0.362257i
\(413\) 6.83468i 0.336313i
\(414\) −4.22814 + 7.32335i −0.207802 + 0.359923i
\(415\) 13.5873i 0.666976i
\(416\) −3.36212 5.82335i −0.164841 0.285513i
\(417\) 2.93641 0.143797
\(418\) 21.2475 1.03925
\(419\) −14.1287 24.4716i −0.690230 1.19551i −0.971762 0.235962i \(-0.924176\pi\)
0.281532 0.959552i \(-0.409157\pi\)
\(420\) 3.28006 + 1.89374i 0.160051 + 0.0924053i
\(421\) 3.46274i 0.168763i 0.996434 + 0.0843817i \(0.0268915\pi\)
−0.996434 + 0.0843817i \(0.973108\pi\)
\(422\) −8.19446 + 4.73108i −0.398900 + 0.230305i
\(423\) −0.520460 0.901463i −0.0253056 0.0438307i
\(424\) −2.77776 + 1.60374i −0.134900 + 0.0778845i
\(425\) 4.14609 + 2.39374i 0.201115 + 0.116114i
\(426\) −1.60767 0.928191i −0.0778921 0.0449710i
\(427\) 43.4649 25.0945i 2.10341 1.21441i
\(428\) 1.95561 + 3.38721i 0.0945279 + 0.163727i
\(429\) 22.3639 12.9118i 1.07974 0.623388i
\(430\) 0.0397760i 0.00191817i
\(431\) 1.54704 + 0.893186i 0.0745185 + 0.0430233i 0.536796 0.843712i \(-0.319634\pi\)
−0.462278 + 0.886735i \(0.652968\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) −33.6257 −1.61595 −0.807974 0.589218i \(-0.799436\pi\)
−0.807974 + 0.589218i \(0.799436\pi\)
\(434\) 32.1787 1.54463
\(435\) 0.931933 + 1.61416i 0.0446828 + 0.0773928i
\(436\) 3.82693i 0.183277i
\(437\) −23.3929 + 40.5176i −1.11903 + 1.93822i
\(438\) 11.8343i 0.565465i
\(439\) 10.2005 + 5.88926i 0.486843 + 0.281079i 0.723264 0.690572i \(-0.242641\pi\)
−0.236421 + 0.971651i \(0.575974\pi\)
\(440\) −1.92019 + 3.32587i −0.0915416 + 0.158555i
\(441\) −3.67253 + 6.36102i −0.174883 + 0.302906i
\(442\) 27.8792 16.0961i 1.32608 0.765613i
\(443\) −26.7397 −1.27044 −0.635220 0.772331i \(-0.719091\pi\)
−0.635220 + 0.772331i \(0.719091\pi\)
\(444\) −3.73188 + 4.80344i −0.177107 + 0.227961i
\(445\) 17.1030 0.810759
\(446\) 10.2674 5.92790i 0.486176 0.280694i
\(447\) 8.14376 14.1054i 0.385187 0.667163i
\(448\) −1.89374 + 3.28006i −0.0894710 + 0.154968i
\(449\) 12.1655 + 7.02375i 0.574125 + 0.331471i 0.758795 0.651329i \(-0.225788\pi\)
−0.184670 + 0.982801i \(0.559122\pi\)
\(450\) 1.00000i 0.0471405i
\(451\) −19.1872 + 33.2331i −0.903488 + 1.56489i
\(452\) 16.3080i 0.767062i
\(453\) −10.1392 17.5616i −0.476381 0.825117i
\(454\) 12.4686 0.585182
\(455\) 25.4679 1.19396
\(456\) −2.76633 4.79142i −0.129545 0.224379i
\(457\) 10.5277 + 6.07816i 0.492464 + 0.284324i 0.725596 0.688121i \(-0.241564\pi\)
−0.233132 + 0.972445i \(0.574897\pi\)
\(458\) 10.0119i 0.467824i
\(459\) 4.14609 2.39374i 0.193523 0.111730i
\(460\) −4.22814 7.32335i −0.197138 0.341453i
\(461\) 28.6410 16.5359i 1.33395 0.770154i 0.348044 0.937478i \(-0.386846\pi\)
0.985902 + 0.167324i \(0.0535127\pi\)
\(462\) −12.5967 7.27270i −0.586051 0.338357i
\(463\) 32.8685 + 18.9767i 1.52753 + 0.881920i 0.999465 + 0.0327173i \(0.0104161\pi\)
0.528066 + 0.849203i \(0.322917\pi\)
\(464\) −1.61416 + 0.931933i −0.0749353 + 0.0432639i
\(465\) −4.24803 7.35780i −0.196998 0.341210i
\(466\) 8.58323 4.95553i 0.397610 0.229561i
\(467\) 13.0633i 0.604500i 0.953229 + 0.302250i \(0.0977377\pi\)
−0.953229 + 0.302250i \(0.902262\pi\)
\(468\) −5.82335 3.36212i −0.269185 0.155414i
\(469\) −17.3749 30.0942i −0.802297 1.38962i
\(470\) 1.04092 0.0480141
\(471\) −6.79706 −0.313192
\(472\) −0.902271 1.56278i −0.0415304 0.0719327i
\(473\) 0.152755i 0.00702369i
\(474\) 1.80738 3.13047i 0.0830155 0.143787i
\(475\) 5.53266i 0.253856i
\(476\) −15.7033 9.06628i −0.719758 0.415552i
\(477\) −1.60374 + 2.77776i −0.0734302 + 0.127185i
\(478\) −7.81314 + 13.5328i −0.357365 + 0.618974i
\(479\) −3.55432 + 2.05209i −0.162401 + 0.0937623i −0.578998 0.815329i \(-0.696556\pi\)
0.416597 + 0.909091i \(0.363223\pi\)
\(480\) 1.00000 0.0456435
\(481\) −5.58235 + 40.5192i −0.254533 + 1.84751i
\(482\) −12.7958 −0.582835
\(483\) 27.7371 16.0140i 1.26208 0.728664i
\(484\) 1.87427 3.24634i 0.0851943 0.147561i
\(485\) −3.07533 + 5.32662i −0.139643 + 0.241869i
\(486\) −0.866025 0.500000i −0.0392837 0.0226805i
\(487\) 32.1531i 1.45699i −0.685049 0.728497i \(-0.740219\pi\)
0.685049 0.728497i \(-0.259781\pi\)
\(488\) 6.62563 11.4759i 0.299928 0.519491i
\(489\) 8.94207i 0.404375i
\(490\) −3.67253 6.36102i −0.165908 0.287361i
\(491\) 31.3238 1.41362 0.706812 0.707402i \(-0.250133\pi\)
0.706812 + 0.707402i \(0.250133\pi\)
\(492\) 9.99232 0.450488
\(493\) −4.46162 7.72775i −0.200941 0.348040i
\(494\) −32.2186 18.6014i −1.44958 0.836918i
\(495\) 3.84038i 0.172612i
\(496\) 7.35780 4.24803i 0.330375 0.190742i
\(497\) 3.51551 + 6.08905i 0.157692 + 0.273131i
\(498\) −11.7670 + 6.79367i −0.527291 + 0.304432i
\(499\) −24.8514 14.3480i −1.11250 0.642303i −0.173025 0.984917i \(-0.555354\pi\)
−0.939476 + 0.342615i \(0.888687\pi\)
\(500\) 0.866025 + 0.500000i 0.0387298 + 0.0223607i
\(501\) −2.72208 + 1.57160i −0.121614 + 0.0702137i
\(502\) −4.61964 8.00145i −0.206185 0.357122i
\(503\) −17.4569 + 10.0787i −0.778364 + 0.449389i −0.835850 0.548957i \(-0.815025\pi\)
0.0574859 + 0.998346i \(0.481692\pi\)
\(504\) 3.78749i 0.168708i
\(505\) −7.76268 4.48179i −0.345435 0.199437i
\(506\) 16.2377 + 28.1245i 0.721853 + 1.25029i
\(507\) −32.2153 −1.43073
\(508\) −11.2778 −0.500373
\(509\) −16.5772 28.7126i −0.734772 1.27266i −0.954823 0.297174i \(-0.903956\pi\)
0.220052 0.975488i \(-0.429377\pi\)
\(510\) 4.78749i 0.211994i
\(511\) −22.4111 + 38.8172i −0.991410 + 1.71717i
\(512\) 1.00000i 0.0441942i
\(513\) −4.79142 2.76633i −0.211546 0.122136i
\(514\) −6.02592 + 10.4372i −0.265792 + 0.460365i
\(515\) −7.35302 + 12.7358i −0.324013 + 0.561206i
\(516\) 0.0344471 0.0198880i 0.00151645 0.000875521i
\(517\) −3.99753 −0.175811
\(518\) 21.3373 8.68835i 0.937507 0.381744i
\(519\) 0.724057 0.0317826
\(520\) 5.82335 3.36212i 0.255371 0.147438i
\(521\) −12.7108 + 22.0158i −0.556870 + 0.964528i 0.440885 + 0.897564i \(0.354665\pi\)
−0.997755 + 0.0669640i \(0.978669\pi\)
\(522\) −0.931933 + 1.61416i −0.0407896 + 0.0706497i
\(523\) 15.7552 + 9.09627i 0.688927 + 0.397752i 0.803210 0.595696i \(-0.203124\pi\)
−0.114283 + 0.993448i \(0.536457\pi\)
\(524\) 8.32318i 0.363600i
\(525\) −1.89374 + 3.28006i −0.0826498 + 0.143154i
\(526\) 7.31074i 0.318763i
\(527\) 20.3374 + 35.2254i 0.885910 + 1.53444i
\(528\) −3.84038 −0.167131
\(529\) −48.5087 −2.10907
\(530\) −1.60374 2.77776i −0.0696620 0.120658i
\(531\) −1.56278 0.902271i −0.0678188 0.0391552i
\(532\) 20.9549i 0.908509i
\(533\) 58.1888 33.5953i 2.52044 1.45517i
\(534\) 8.55149 + 14.8116i 0.370059 + 0.640962i
\(535\) −3.38721 + 1.95561i −0.146442 + 0.0845483i
\(536\) −7.94568 4.58744i −0.343201 0.198147i
\(537\) −18.1487 10.4782i −0.783175 0.452166i
\(538\) −13.1312 + 7.58133i −0.566128 + 0.326854i
\(539\) 14.1039 + 24.4287i 0.607500 + 1.05222i
\(540\) 0.866025 0.500000i 0.0372678 0.0215166i
\(541\) 32.6823i 1.40512i −0.711624 0.702560i \(-0.752040\pi\)
0.711624 0.702560i \(-0.247960\pi\)
\(542\) −9.34650 5.39620i −0.401466 0.231787i
\(543\) −7.72795 13.3852i −0.331638 0.574414i
\(544\) −4.78749 −0.205262
\(545\) 3.82693 0.163928
\(546\) 12.7340 + 22.0559i 0.544964 + 0.943905i
\(547\) 21.1126i 0.902711i −0.892344 0.451355i \(-0.850941\pi\)
0.892344 0.451355i \(-0.149059\pi\)
\(548\) −7.81094 + 13.5290i −0.333667 + 0.577928i
\(549\) 13.2513i 0.565550i
\(550\) −3.32587 1.92019i −0.141816 0.0818773i
\(551\) −5.15607 + 8.93057i −0.219656 + 0.380455i
\(552\) 4.22814 7.32335i 0.179962 0.311703i
\(553\) −11.8566 + 6.84542i −0.504194 + 0.291097i
\(554\) 8.00832 0.340241
\(555\) −4.80344 3.73188i −0.203895 0.158410i
\(556\) −2.93641 −0.124531
\(557\) −14.5555 + 8.40363i −0.616737 + 0.356073i −0.775598 0.631228i \(-0.782551\pi\)
0.158860 + 0.987301i \(0.449218\pi\)
\(558\) 4.24803 7.35780i 0.179833 0.311481i
\(559\) 0.133732 0.231630i 0.00565624 0.00979690i
\(560\) −3.28006 1.89374i −0.138608 0.0800253i
\(561\) 18.3858i 0.776249i
\(562\) 12.5264 21.6964i 0.528394 0.915206i
\(563\) 5.35688i 0.225766i 0.993608 + 0.112883i \(0.0360085\pi\)
−0.993608 + 0.112883i \(0.963992\pi\)
\(564\) 0.520460 + 0.901463i 0.0219153 + 0.0379585i
\(565\) −16.3080 −0.686082
\(566\) 3.95355 0.166180
\(567\) 1.89374 + 3.28006i 0.0795298 + 0.137750i
\(568\) 1.60767 + 0.928191i 0.0674565 + 0.0389460i
\(569\) 8.95342i 0.375347i 0.982231 + 0.187673i \(0.0600947\pi\)
−0.982231 + 0.187673i \(0.939905\pi\)
\(570\) 4.79142 2.76633i 0.200691 0.115869i
\(571\) −18.6922 32.3758i −0.782242 1.35488i −0.930633 0.365955i \(-0.880743\pi\)
0.148390 0.988929i \(-0.452591\pi\)
\(572\) −22.3639 + 12.9118i −0.935082 + 0.539870i
\(573\) −2.63146 1.51928i −0.109931 0.0634686i
\(574\) −32.7754 18.9229i −1.36802 0.789826i
\(575\) 7.32335 4.22814i 0.305405 0.176326i
\(576\) 0.500000 + 0.866025i 0.0208333 + 0.0360844i
\(577\) 3.18442 1.83852i 0.132569 0.0765387i −0.432249 0.901754i \(-0.642280\pi\)
0.564818 + 0.825216i \(0.308946\pi\)
\(578\) 5.92005i 0.246241i
\(579\) 12.4215 + 7.17156i 0.516220 + 0.298040i
\(580\) −0.931933 1.61416i −0.0386964 0.0670242i
\(581\) 51.4619 2.13500
\(582\) −6.15065 −0.254953
\(583\) 6.15898 + 10.6677i 0.255079 + 0.441809i
\(584\) 11.8343i 0.489707i
\(585\) 3.36212 5.82335i 0.139006 0.240766i
\(586\) 12.5499i 0.518431i
\(587\) −33.6978 19.4555i −1.39086 0.803013i −0.397448 0.917625i \(-0.630104\pi\)
−0.993410 + 0.114612i \(0.963438\pi\)
\(588\) 3.67253 6.36102i 0.151453 0.262324i
\(589\) 23.5029 40.7082i 0.968420 1.67735i
\(590\) 1.56278 0.902271i 0.0643386 0.0371459i
\(591\) 0.803426 0.0330485
\(592\) 3.73188 4.80344i 0.153379 0.197420i
\(593\) 2.91438 0.119679 0.0598397 0.998208i \(-0.480941\pi\)
0.0598397 + 0.998208i \(0.480941\pi\)
\(594\) −3.32587 + 1.92019i −0.136462 + 0.0787864i
\(595\) 9.06628 15.7033i 0.371681 0.643771i
\(596\) −8.14376 + 14.1054i −0.333582 + 0.577780i
\(597\) −3.47986 2.00910i −0.142421 0.0822269i
\(598\) 56.8620i 2.32526i
\(599\) −1.93950 + 3.35931i −0.0792458 + 0.137258i −0.902925 0.429799i \(-0.858585\pi\)
0.823679 + 0.567056i \(0.191918\pi\)
\(600\) 1.00000i 0.0408248i
\(601\) −20.7686 35.9723i −0.847170 1.46734i −0.883723 0.468010i \(-0.844971\pi\)
0.0365530 0.999332i \(-0.488362\pi\)
\(602\) −0.150651 −0.00614009
\(603\) −9.17488 −0.373630
\(604\) 10.1392 + 17.5616i 0.412558 + 0.714572i
\(605\) 3.24634 + 1.87427i 0.131982 + 0.0762001i
\(606\) 8.96357i 0.364120i
\(607\) −10.3055 + 5.94986i −0.418286 + 0.241497i −0.694344 0.719644i \(-0.744305\pi\)
0.276058 + 0.961141i \(0.410972\pi\)
\(608\) 2.76633 + 4.79142i 0.112189 + 0.194318i
\(609\) 6.11359 3.52969i 0.247735 0.143030i
\(610\) 11.4759 + 6.62563i 0.464646 + 0.268264i
\(611\) 6.06165 + 3.49969i 0.245228 + 0.141582i
\(612\) −4.14609 + 2.39374i −0.167596 + 0.0967614i
\(613\) −4.99067 8.64409i −0.201571 0.349132i 0.747464 0.664303i \(-0.231271\pi\)
−0.949035 + 0.315171i \(0.897938\pi\)
\(614\) −2.03770 + 1.17647i −0.0822350 + 0.0474784i
\(615\) 9.99232i 0.402929i
\(616\) 12.5967 + 7.27270i 0.507535 + 0.293026i
\(617\) −9.78398 16.9464i −0.393888 0.682234i 0.599070 0.800696i \(-0.295537\pi\)
−0.992959 + 0.118462i \(0.962204\pi\)
\(618\) −14.7060 −0.591563
\(619\) 27.2882 1.09680 0.548402 0.836215i \(-0.315236\pi\)
0.548402 + 0.836215i \(0.315236\pi\)
\(620\) 4.24803 + 7.35780i 0.170605 + 0.295496i
\(621\) 8.45628i 0.339339i
\(622\) −11.3096 + 19.5888i −0.453474 + 0.785439i
\(623\) 64.7774i 2.59525i
\(624\) 5.82335 + 3.36212i 0.233121 + 0.134592i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 7.79719 13.5051i 0.311638 0.539773i
\(627\) −18.4009 + 10.6238i −0.734861 + 0.424272i
\(628\) 6.79706 0.271232
\(629\) 22.9964 + 17.8663i 0.916927 + 0.712378i
\(630\) −3.78749 −0.150897
\(631\) 17.1937 9.92680i 0.684471 0.395180i −0.117066 0.993124i \(-0.537349\pi\)
0.801538 + 0.597945i \(0.204016\pi\)
\(632\) −1.80738 + 3.13047i −0.0718936 + 0.124523i
\(633\) 4.73108 8.19446i 0.188043 0.325701i
\(634\) 21.3299 + 12.3149i 0.847120 + 0.489085i
\(635\) 11.2778i 0.447547i
\(636\) 1.60374 2.77776i 0.0635924 0.110145i
\(637\) 49.3899i 1.95690i
\(638\) 3.57898 + 6.19898i 0.141693 + 0.245420i
\(639\) 1.85638 0.0734374
\(640\) −1.00000 −0.0395285
\(641\) 4.37909 + 7.58480i 0.172964 + 0.299582i 0.939455 0.342673i \(-0.111332\pi\)
−0.766491 + 0.642255i \(0.777999\pi\)
\(642\) −3.38721 1.95561i −0.133683 0.0771817i
\(643\) 23.7722i 0.937485i 0.883335 + 0.468742i \(0.155293\pi\)
−0.883335 + 0.468742i \(0.844707\pi\)
\(644\) −27.7371 + 16.0140i −1.09300 + 0.631041i
\(645\) 0.0198880 + 0.0344471i 0.000783090 + 0.00135635i
\(646\) −22.9389 + 13.2438i −0.902518 + 0.521069i
\(647\) 14.1817 + 8.18780i 0.557539 + 0.321896i 0.752157 0.658984i \(-0.229013\pi\)
−0.194618 + 0.980879i \(0.562347\pi\)
\(648\) 0.866025 + 0.500000i 0.0340207 + 0.0196419i
\(649\) −6.00167 + 3.46507i −0.235586 + 0.136016i
\(650\) 3.36212 + 5.82335i 0.131873 + 0.228411i
\(651\) −27.8676 + 16.0894i −1.09222 + 0.630592i
\(652\) 8.94207i 0.350199i
\(653\) 19.1663 + 11.0657i 0.750034 + 0.433032i 0.825706 0.564100i \(-0.190777\pi\)
−0.0756720 + 0.997133i \(0.524110\pi\)
\(654\) 1.91346 + 3.31422i 0.0748223 + 0.129596i
\(655\) 8.32318 0.325214
\(656\) −9.99232 −0.390134
\(657\) 5.91715 + 10.2488i 0.230850 + 0.399844i
\(658\) 3.94247i 0.153694i
\(659\) −1.48559 + 2.57312i −0.0578705 + 0.100235i −0.893509 0.449045i \(-0.851764\pi\)
0.835639 + 0.549279i \(0.185098\pi\)
\(660\) 3.84038i 0.149487i
\(661\) −7.65152 4.41761i −0.297609 0.171825i 0.343759 0.939058i \(-0.388300\pi\)
−0.641368 + 0.767233i \(0.721633\pi\)
\(662\) 4.27021 7.39622i 0.165966 0.287462i
\(663\) −16.0961 + 27.8792i −0.625120 + 1.08274i
\(664\) 11.7670 6.79367i 0.456647 0.263645i
\(665\) −20.9549 −0.812595
\(666\) 0.830184 6.02584i 0.0321690 0.233497i
\(667\) −15.7614 −0.610283
\(668\) 2.72208 1.57160i 0.105321 0.0608069i
\(669\) −5.92790 + 10.2674i −0.229186 + 0.396961i
\(670\) 4.58744 7.94568i 0.177228 0.306968i
\(671\) −44.0719 25.4449i −1.70138 0.982291i
\(672\) 3.78749i 0.146106i
\(673\) 13.7552 23.8248i 0.530226 0.918378i −0.469152 0.883117i \(-0.655440\pi\)
0.999378 0.0352608i \(-0.0112262\pi\)
\(674\) 12.0135i 0.462742i
\(675\) 0.500000 + 0.866025i 0.0192450 + 0.0333333i
\(676\) 32.2153 1.23905
\(677\) −6.30629 −0.242370 −0.121185 0.992630i \(-0.538669\pi\)
−0.121185 + 0.992630i \(0.538669\pi\)
\(678\) −8.15399 14.1231i −0.313152 0.542395i
\(679\) 20.1745 + 11.6478i 0.774227 + 0.447000i
\(680\) 4.78749i 0.183592i
\(681\) −10.7982 + 6.23432i −0.413786 + 0.238900i
\(682\) −16.3141 28.2568i −0.624698 1.08201i
\(683\) −32.6161 + 18.8309i −1.24802 + 0.720544i −0.970714 0.240238i \(-0.922774\pi\)
−0.277305 + 0.960782i \(0.589441\pi\)
\(684\) 4.79142 + 2.76633i 0.183205 + 0.105773i
\(685\) −13.5290 7.81094i −0.516915 0.298441i
\(686\) −1.13185 + 0.653472i −0.0432141 + 0.0249497i
\(687\) −5.00593 8.67053i −0.190988 0.330801i
\(688\) −0.0344471 + 0.0198880i −0.00131328 + 0.000758223i
\(689\) 21.5678i 0.821669i
\(690\) 7.32335 + 4.22814i 0.278795 + 0.160963i
\(691\) 10.7311 + 18.5868i 0.408230 + 0.707075i 0.994692 0.102902i \(-0.0328128\pi\)
−0.586461 + 0.809977i \(0.699479\pi\)
\(692\) −0.724057 −0.0275245
\(693\) 14.5454 0.552534
\(694\) −2.90899 5.03851i −0.110424 0.191259i
\(695\) 2.93641i 0.111384i
\(696\) 0.931933 1.61416i 0.0353248 0.0611844i
\(697\) 47.8381i 1.81200i
\(698\) 25.7991 + 14.8951i 0.976511 + 0.563789i
\(699\) −4.95553 + 8.58323i −0.187435 + 0.324648i
\(700\) 1.89374 3.28006i 0.0715768 0.123975i
\(701\) 36.0348 20.8047i 1.36102 0.785783i 0.371257 0.928530i \(-0.378927\pi\)
0.989759 + 0.142747i \(0.0455934\pi\)
\(702\) 6.72423 0.253790
\(703\) 4.59312 33.3389i 0.173233 1.25740i
\(704\) 3.84038 0.144740
\(705\) −0.901463 + 0.520460i −0.0339511 + 0.0196017i
\(706\) −7.90695 + 13.6952i −0.297582 + 0.515427i
\(707\) −16.9747 + 29.4011i −0.638400 + 1.10574i
\(708\) 1.56278 + 0.902271i 0.0587328 + 0.0339094i
\(709\) 40.2595i 1.51198i 0.654584 + 0.755989i \(0.272844\pi\)
−0.654584 + 0.755989i \(0.727156\pi\)
\(710\) −0.928191 + 1.60767i −0.0348344 + 0.0603349i
\(711\) 3.61475i 0.135564i
\(712\) −8.55149 14.8116i −0.320481 0.555089i
\(713\) 71.8450 2.69062
\(714\) 18.1326 0.678594
\(715\) −12.9118 22.3639i −0.482874 0.836363i
\(716\) 18.1487 + 10.4782i 0.678249 + 0.391587i
\(717\) 15.6263i 0.583574i
\(718\) 18.0763 10.4363i 0.674601 0.389481i
\(719\) 16.2180 + 28.0903i 0.604828 + 1.04759i 0.992079 + 0.125618i \(0.0400914\pi\)
−0.387251 + 0.921974i \(0.626575\pi\)
\(720\) −0.866025 + 0.500000i −0.0322749 + 0.0186339i
\(721\) 48.2367 + 27.8495i 1.79643 + 1.03717i
\(722\) 10.0548 + 5.80516i 0.374202 + 0.216046i
\(723\) 11.0815 6.39792i 0.412127 0.237941i
\(724\) 7.72795 + 13.3852i 0.287207 + 0.497457i
\(725\) 1.61416 0.931933i 0.0599482 0.0346111i
\(726\) 3.74855i 0.139122i
\(727\) −5.34178 3.08408i −0.198116 0.114382i 0.397661 0.917533i \(-0.369822\pi\)
−0.595776 + 0.803150i \(0.703155\pi\)
\(728\) −12.7340 22.0559i −0.471952 0.817446i
\(729\) 1.00000 0.0370370
\(730\) −11.8343 −0.438007
\(731\) −0.0952136 0.164915i −0.00352160 0.00609960i
\(732\) 13.2513i 0.489780i
\(733\) −5.59909 + 9.69791i −0.206807 + 0.358201i −0.950707 0.310091i \(-0.899641\pi\)
0.743900 + 0.668291i \(0.232974\pi\)
\(734\) 25.0377i 0.924158i
\(735\) 6.36102 + 3.67253i 0.234630 + 0.135463i
\(736\) −4.22814 + 7.32335i −0.155851 + 0.269942i
\(737\) −17.6175 + 30.5144i −0.648950 + 1.12401i
\(738\) −8.65360 + 4.99616i −0.318543 + 0.183911i
\(739\) 47.1766 1.73542 0.867709 0.497073i \(-0.165592\pi\)
0.867709 + 0.497073i \(0.165592\pi\)
\(740\) 4.80344 + 3.73188i 0.176578 + 0.137187i
\(741\) 37.2029 1.36668
\(742\) −10.5207 + 6.07415i −0.386228 + 0.222989i
\(743\) 7.62157 13.2009i 0.279608 0.484296i −0.691679 0.722205i \(-0.743129\pi\)
0.971287 + 0.237909i \(0.0764621\pi\)
\(744\) −4.24803 + 7.35780i −0.155740 + 0.269750i
\(745\) −14.1054 8.14376i −0.516782 0.298364i
\(746\) 16.6894i 0.611041i
\(747\) 6.79367 11.7670i 0.248567 0.430531i
\(748\) 18.3858i 0.672251i
\(749\) 7.40684 + 12.8290i 0.270640 + 0.468762i
\(750\) −1.00000 −0.0365148
\(751\) 43.2557 1.57842 0.789212 0.614120i \(-0.210489\pi\)
0.789212 + 0.614120i \(0.210489\pi\)
\(752\) −0.520460 0.901463i −0.0189792 0.0328730i
\(753\) 8.00145 + 4.61964i 0.291589 + 0.168349i
\(754\) 12.5331i 0.456427i
\(755\) −17.5616 + 10.1392i −0.639133 + 0.369003i
\(756\) −1.89374 3.28006i −0.0688748 0.119295i
\(757\) −9.03971 + 5.21908i −0.328554 + 0.189691i −0.655199 0.755456i \(-0.727415\pi\)
0.326645 + 0.945147i \(0.394082\pi\)
\(758\) 21.6091 + 12.4760i 0.784877 + 0.453149i
\(759\) −28.1245 16.2377i −1.02085 0.589391i
\(760\) −4.79142 + 2.76633i −0.173803 + 0.100345i
\(761\) −25.3188 43.8534i −0.917805 1.58969i −0.802742 0.596327i \(-0.796626\pi\)
−0.115064 0.993358i \(-0.536707\pi\)
\(762\) 9.76689 5.63891i 0.353817 0.204276i
\(763\) 14.4944i 0.524734i
\(764\) 2.63146 + 1.51928i 0.0952030 + 0.0549655i
\(765\) −2.39374 4.14609i −0.0865460 0.149902i
\(766\) −9.32452 −0.336909
\(767\) 12.1341 0.438139
\(768\) −0.500000 0.866025i −0.0180422 0.0312500i
\(769\) 49.0740i 1.76965i 0.465920 + 0.884827i \(0.345724\pi\)
−0.465920 + 0.884827i \(0.654276\pi\)
\(770\) −7.27270 + 12.5967i −0.262090 + 0.453953i
\(771\) 12.0518i 0.434036i
\(772\) −12.4215 7.17156i −0.447060 0.258110i
\(773\) −16.7780 + 29.0604i −0.603464 + 1.04523i 0.388828 + 0.921310i \(0.372880\pi\)
−0.992292 + 0.123920i \(0.960453\pi\)
\(774\) −0.0198880 + 0.0344471i −0.000714860 + 0.00123817i
\(775\) −7.35780 + 4.24803i −0.264300 + 0.152594i
\(776\) 6.15065 0.220796
\(777\) −14.1345