Properties

Label 1110.2.bb.d.1009.13
Level $1110$
Weight $2$
Character 1110.1009
Analytic conductor $8.863$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $4$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(14\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1009.13
Character \(\chi\) \(=\) 1110.1009
Dual form 1110.2.bb.d.1099.13

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.57341 - 1.58883i) q^{5} +1.00000 q^{6} +(3.59896 - 2.07786i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.57341 - 1.58883i) q^{5} +1.00000 q^{6} +(3.59896 - 2.07786i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.568195 - 2.16267i) q^{10} +3.62754 q^{11} +(0.866025 + 0.500000i) q^{12} +(-1.85017 + 1.06819i) q^{13} +4.15572 q^{14} +(-2.15703 - 0.589266i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.00089 - 0.577862i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-3.73087 - 6.46205i) q^{19} +(0.589266 - 2.15703i) q^{20} +(2.07786 - 3.59896i) q^{21} +(3.14154 + 1.81377i) q^{22} -0.363708i q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.0487778 + 4.99976i) q^{25} -2.13639 q^{26} -1.00000i q^{27} +(3.59896 + 2.07786i) q^{28} -5.15572 q^{29} +(-1.57341 - 1.58883i) q^{30} +3.49115 q^{31} +(-0.866025 + 0.500000i) q^{32} +(3.14154 - 1.81377i) q^{33} +(-0.577862 - 1.00089i) q^{34} +(-8.96401 - 2.44882i) q^{35} +1.00000 q^{36} +(6.08252 - 0.0539383i) q^{37} -7.46174i q^{38} +(-1.06819 + 1.85017i) q^{39} +(1.58883 - 1.57341i) q^{40} +(6.04397 + 10.4685i) q^{41} +(3.59896 - 2.07786i) q^{42} -12.3681i q^{43} +(1.81377 + 3.14154i) q^{44} +(-2.16267 + 0.568195i) q^{45} +(0.181854 - 0.314980i) q^{46} -2.21747i q^{47} +1.00000i q^{48} +(5.13502 - 8.89411i) q^{49} +(-2.54212 + 4.30553i) q^{50} -1.15572 q^{51} +(-1.85017 - 1.06819i) q^{52} +(9.47411 + 5.46988i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-5.70760 - 5.76355i) q^{55} +(2.07786 + 3.59896i) q^{56} +(-6.46205 - 3.73087i) q^{57} +(-4.46499 - 2.57786i) q^{58} +(-4.88507 + 8.46118i) q^{59} +(-0.568195 - 2.16267i) q^{60} +(-3.12535 - 5.41327i) q^{61} +(3.02342 + 1.74558i) q^{62} -4.15572i q^{63} -1.00000 q^{64} +(4.60825 + 1.25890i) q^{65} +3.62754 q^{66} +(13.3985 - 7.73561i) q^{67} -1.15572i q^{68} +(-0.181854 - 0.314980i) q^{69} +(-6.53865 - 6.60275i) q^{70} +(-0.0732348 - 0.126846i) q^{71} +(0.866025 + 0.500000i) q^{72} +9.63375i q^{73} +(5.29459 + 2.99455i) q^{74} +(2.45764 + 4.35431i) q^{75} +(3.73087 - 6.46205i) q^{76} +(13.0554 - 7.53753i) q^{77} +(-1.85017 + 1.06819i) q^{78} +(7.85583 + 13.6067i) q^{79} +(2.16267 - 0.568195i) q^{80} +(-0.500000 - 0.866025i) q^{81} +12.0879i q^{82} +(-11.9781 - 6.91556i) q^{83} +4.15572 q^{84} +(0.656676 + 2.49945i) q^{85} +(6.18403 - 10.7111i) q^{86} +(-4.46499 + 2.57786i) q^{87} +3.62754i q^{88} +(-5.67966 + 9.83745i) q^{89} +(-2.15703 - 0.589266i) q^{90} +(-4.43912 + 7.68878i) q^{91} +(0.314980 - 0.181854i) q^{92} +(3.02342 - 1.74558i) q^{93} +(1.10873 - 1.92038i) q^{94} +(-4.39694 + 16.0952i) q^{95} +(-0.500000 + 0.866025i) q^{96} +11.6594i q^{97} +(8.89411 - 5.13502i) q^{98} +(1.81377 - 3.14154i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 14q^{4} + 2q^{5} + 28q^{6} + 14q^{9} + O(q^{10}) \) \( 28q + 14q^{4} + 2q^{5} + 28q^{6} + 14q^{9} + 4q^{10} - 12q^{11} + 8q^{14} + 2q^{15} - 14q^{16} - 20q^{19} - 2q^{20} + 4q^{21} + 14q^{24} - 8q^{25} - 20q^{26} - 36q^{29} + 2q^{30} + 24q^{31} + 38q^{34} - 2q^{35} + 28q^{36} - 10q^{39} + 2q^{40} - 6q^{44} + 4q^{45} + 8q^{46} + 50q^{49} - 4q^{50} + 76q^{51} + 14q^{54} - 28q^{55} + 4q^{56} - 26q^{59} + 4q^{60} - 28q^{61} - 28q^{64} + 60q^{65} - 12q^{66} - 8q^{69} - 10q^{70} - 64q^{71} + 24q^{74} - 8q^{75} + 20q^{76} + 32q^{79} - 4q^{80} - 14q^{81} + 8q^{84} + 16q^{85} - 8q^{86} + 76q^{89} + 2q^{90} - 8q^{91} - 38q^{94} - 70q^{95} - 14q^{96} - 6q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) 0.866025 0.500000i 0.500000 0.288675i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) −1.57341 1.58883i −0.703649 0.710548i
\(6\) 1.00000 0.408248
\(7\) 3.59896 2.07786i 1.36028 0.785358i 0.370619 0.928785i \(-0.379146\pi\)
0.989661 + 0.143427i \(0.0458123\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) −0.568195 2.16267i −0.179679 0.683897i
\(11\) 3.62754 1.09374 0.546872 0.837216i \(-0.315818\pi\)
0.546872 + 0.837216i \(0.315818\pi\)
\(12\) 0.866025 + 0.500000i 0.250000 + 0.144338i
\(13\) −1.85017 + 1.06819i −0.513144 + 0.296264i −0.734125 0.679014i \(-0.762407\pi\)
0.220981 + 0.975278i \(0.429074\pi\)
\(14\) 4.15572 1.11066
\(15\) −2.15703 0.589266i −0.556942 0.152148i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.00089 0.577862i −0.242750 0.140152i 0.373690 0.927554i \(-0.378092\pi\)
−0.616440 + 0.787402i \(0.711426\pi\)
\(18\) 0.866025 0.500000i 0.204124 0.117851i
\(19\) −3.73087 6.46205i −0.855920 1.48250i −0.875789 0.482694i \(-0.839658\pi\)
0.0198694 0.999803i \(-0.493675\pi\)
\(20\) 0.589266 2.15703i 0.131764 0.482326i
\(21\) 2.07786 3.59896i 0.453427 0.785358i
\(22\) 3.14154 + 1.81377i 0.669779 + 0.386697i
\(23\) 0.363708i 0.0758383i −0.999281 0.0379191i \(-0.987927\pi\)
0.999281 0.0379191i \(-0.0120729\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) −0.0487778 + 4.99976i −0.00975556 + 0.999952i
\(26\) −2.13639 −0.418980
\(27\) 1.00000i 0.192450i
\(28\) 3.59896 + 2.07786i 0.680140 + 0.392679i
\(29\) −5.15572 −0.957394 −0.478697 0.877980i \(-0.658891\pi\)
−0.478697 + 0.877980i \(0.658891\pi\)
\(30\) −1.57341 1.58883i −0.287264 0.290080i
\(31\) 3.49115 0.627029 0.313515 0.949583i \(-0.398494\pi\)
0.313515 + 0.949583i \(0.398494\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) 3.14154 1.81377i 0.546872 0.315737i
\(34\) −0.577862 1.00089i −0.0991025 0.171651i
\(35\) −8.96401 2.44882i −1.51519 0.413927i
\(36\) 1.00000 0.166667
\(37\) 6.08252 0.0539383i 0.999961 0.00886741i
\(38\) 7.46174i 1.21045i
\(39\) −1.06819 + 1.85017i −0.171048 + 0.296264i
\(40\) 1.58883 1.57341i 0.251216 0.248778i
\(41\) 6.04397 + 10.4685i 0.943910 + 1.63490i 0.757919 + 0.652349i \(0.226216\pi\)
0.185991 + 0.982551i \(0.440450\pi\)
\(42\) 3.59896 2.07786i 0.555332 0.320621i
\(43\) 12.3681i 1.88611i −0.332634 0.943056i \(-0.607937\pi\)
0.332634 0.943056i \(-0.392063\pi\)
\(44\) 1.81377 + 3.14154i 0.273436 + 0.473605i
\(45\) −2.16267 + 0.568195i −0.322392 + 0.0847014i
\(46\) 0.181854 0.314980i 0.0268129 0.0464413i
\(47\) 2.21747i 0.323451i −0.986836 0.161726i \(-0.948294\pi\)
0.986836 0.161726i \(-0.0517059\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 5.13502 8.89411i 0.733574 1.27059i
\(50\) −2.54212 + 4.30553i −0.359511 + 0.608894i
\(51\) −1.15572 −0.161834
\(52\) −1.85017 1.06819i −0.256572 0.148132i
\(53\) 9.47411 + 5.46988i 1.30137 + 0.751346i 0.980639 0.195825i \(-0.0627385\pi\)
0.320730 + 0.947171i \(0.396072\pi\)
\(54\) 0.500000 0.866025i 0.0680414 0.117851i
\(55\) −5.70760 5.76355i −0.769612 0.777157i
\(56\) 2.07786 + 3.59896i 0.277666 + 0.480932i
\(57\) −6.46205 3.73087i −0.855920 0.494165i
\(58\) −4.46499 2.57786i −0.586282 0.338490i
\(59\) −4.88507 + 8.46118i −0.635982 + 1.10155i 0.350325 + 0.936628i \(0.386071\pi\)
−0.986306 + 0.164924i \(0.947262\pi\)
\(60\) −0.568195 2.16267i −0.0733536 0.279200i
\(61\) −3.12535 5.41327i −0.400160 0.693098i 0.593585 0.804772i \(-0.297712\pi\)
−0.993745 + 0.111674i \(0.964379\pi\)
\(62\) 3.02342 + 1.74558i 0.383975 + 0.221688i
\(63\) 4.15572i 0.523572i
\(64\) −1.00000 −0.125000
\(65\) 4.60825 + 1.25890i 0.571583 + 0.156147i
\(66\) 3.62754 0.446519
\(67\) 13.3985 7.73561i 1.63688 0.945055i 0.654986 0.755641i \(-0.272674\pi\)
0.981897 0.189415i \(-0.0606590\pi\)
\(68\) 1.15572i 0.140152i
\(69\) −0.181854 0.314980i −0.0218926 0.0379191i
\(70\) −6.53865 6.60275i −0.781518 0.789179i
\(71\) −0.0732348 0.126846i −0.00869137 0.0150539i 0.861647 0.507508i \(-0.169433\pi\)
−0.870338 + 0.492454i \(0.836100\pi\)
\(72\) 0.866025 + 0.500000i 0.102062 + 0.0589256i
\(73\) 9.63375i 1.12754i 0.825930 + 0.563772i \(0.190650\pi\)
−0.825930 + 0.563772i \(0.809350\pi\)
\(74\) 5.29459 + 2.99455i 0.615483 + 0.348109i
\(75\) 2.45764 + 4.35431i 0.283784 + 0.502792i
\(76\) 3.73087 6.46205i 0.427960 0.741248i
\(77\) 13.0554 7.53753i 1.48780 0.858981i
\(78\) −1.85017 + 1.06819i −0.209490 + 0.120949i
\(79\) 7.85583 + 13.6067i 0.883850 + 1.53087i 0.847026 + 0.531552i \(0.178391\pi\)
0.0368247 + 0.999322i \(0.488276\pi\)
\(80\) 2.16267 0.568195i 0.241794 0.0635261i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 12.0879i 1.33489i
\(83\) −11.9781 6.91556i −1.31477 0.759082i −0.331886 0.943319i \(-0.607685\pi\)
−0.982882 + 0.184238i \(0.941018\pi\)
\(84\) 4.15572 0.453427
\(85\) 0.656676 + 2.49945i 0.0712265 + 0.271104i
\(86\) 6.18403 10.7111i 0.666841 1.15500i
\(87\) −4.46499 + 2.57786i −0.478697 + 0.276376i
\(88\) 3.62754i 0.386697i
\(89\) −5.67966 + 9.83745i −0.602042 + 1.04277i 0.390469 + 0.920616i \(0.372313\pi\)
−0.992511 + 0.122152i \(0.961021\pi\)
\(90\) −2.15703 0.589266i −0.227371 0.0621140i
\(91\) −4.43912 + 7.68878i −0.465346 + 0.806004i
\(92\) 0.314980 0.181854i 0.0328389 0.0189596i
\(93\) 3.02342 1.74558i 0.313515 0.181008i
\(94\) 1.10873 1.92038i 0.114357 0.198073i
\(95\) −4.39694 + 16.0952i −0.451117 + 1.65133i
\(96\) −0.500000 + 0.866025i −0.0510310 + 0.0883883i
\(97\) 11.6594i 1.18384i 0.805998 + 0.591919i \(0.201629\pi\)
−0.805998 + 0.591919i \(0.798371\pi\)
\(98\) 8.89411 5.13502i 0.898441 0.518715i
\(99\) 1.81377 3.14154i 0.182291 0.315737i
\(100\) −4.35431 + 2.45764i −0.435431 + 0.245764i
\(101\) −10.4486 −1.03968 −0.519838 0.854265i \(-0.674008\pi\)
−0.519838 + 0.854265i \(0.674008\pi\)
\(102\) −1.00089 0.577862i −0.0991025 0.0572168i
\(103\) 9.76260i 0.961938i −0.876738 0.480969i \(-0.840285\pi\)
0.876738 0.480969i \(-0.159715\pi\)
\(104\) −1.06819 1.85017i −0.104745 0.181424i
\(105\) −8.98747 + 2.36126i −0.877087 + 0.230435i
\(106\) 5.46988 + 9.47411i 0.531282 + 0.920207i
\(107\) −1.06082 + 0.612466i −0.102554 + 0.0592093i −0.550400 0.834901i \(-0.685525\pi\)
0.447846 + 0.894111i \(0.352191\pi\)
\(108\) 0.866025 0.500000i 0.0833333 0.0481125i
\(109\) −4.94812 + 8.57040i −0.473944 + 0.820896i −0.999555 0.0298295i \(-0.990504\pi\)
0.525611 + 0.850725i \(0.323837\pi\)
\(110\) −2.06115 7.84518i −0.196523 0.748009i
\(111\) 5.24065 3.08797i 0.497421 0.293097i
\(112\) 4.15572i 0.392679i
\(113\) −7.25569 4.18907i −0.682558 0.394075i 0.118260 0.992983i \(-0.462268\pi\)
−0.800818 + 0.598908i \(0.795602\pi\)
\(114\) −3.73087 6.46205i −0.349428 0.605227i
\(115\) −0.577871 + 0.572260i −0.0538867 + 0.0533636i
\(116\) −2.57786 4.46499i −0.239348 0.414564i
\(117\) 2.13639i 0.197509i
\(118\) −8.46118 + 4.88507i −0.778915 + 0.449707i
\(119\) −4.80287 −0.440278
\(120\) 0.589266 2.15703i 0.0537923 0.196909i
\(121\) 2.15904 0.196276
\(122\) 6.25070i 0.565912i
\(123\) 10.4685 + 6.04397i 0.943910 + 0.544967i
\(124\) 1.74558 + 3.02342i 0.156757 + 0.271512i
\(125\) 8.02053 7.78916i 0.717378 0.696684i
\(126\) 2.07786 3.59896i 0.185111 0.320621i
\(127\) −4.57107 2.63911i −0.405617 0.234183i 0.283288 0.959035i \(-0.408575\pi\)
−0.688905 + 0.724852i \(0.741908\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) −6.18403 10.7111i −0.544474 0.943056i
\(130\) 3.36141 + 3.39436i 0.294815 + 0.297705i
\(131\) −7.60944 + 13.1799i −0.664840 + 1.15154i 0.314489 + 0.949261i \(0.398167\pi\)
−0.979329 + 0.202275i \(0.935167\pi\)
\(132\) 3.14154 + 1.81377i 0.273436 + 0.157868i
\(133\) −26.8545 15.5045i −2.32858 1.34441i
\(134\) 15.4712 1.33651
\(135\) −1.58883 + 1.57341i −0.136745 + 0.135417i
\(136\) 0.577862 1.00089i 0.0495512 0.0858253i
\(137\) 6.94371i 0.593241i 0.954995 + 0.296620i \(0.0958596\pi\)
−0.954995 + 0.296620i \(0.904140\pi\)
\(138\) 0.363708i 0.0309609i
\(139\) −6.89557 + 11.9435i −0.584874 + 1.01303i 0.410017 + 0.912078i \(0.365523\pi\)
−0.994891 + 0.100954i \(0.967811\pi\)
\(140\) −2.36126 8.98747i −0.199563 0.759580i
\(141\) −1.10873 1.92038i −0.0933723 0.161726i
\(142\) 0.146470i 0.0122915i
\(143\) −6.71155 + 3.87492i −0.561248 + 0.324037i
\(144\) 0.500000 + 0.866025i 0.0416667 + 0.0721688i
\(145\) 8.11205 + 8.19158i 0.673669 + 0.680274i
\(146\) −4.81687 + 8.34307i −0.398647 + 0.690477i
\(147\) 10.2700i 0.847058i
\(148\) 3.08797 + 5.24065i 0.253830 + 0.430779i
\(149\) −5.53123 −0.453136 −0.226568 0.973995i \(-0.572751\pi\)
−0.226568 + 0.973995i \(0.572751\pi\)
\(150\) −0.0487778 + 4.99976i −0.00398269 + 0.408229i
\(151\) −11.1149 19.2515i −0.904517 1.56667i −0.821565 0.570115i \(-0.806899\pi\)
−0.0829517 0.996554i \(-0.526435\pi\)
\(152\) 6.46205 3.73087i 0.524142 0.302613i
\(153\) −1.00089 + 0.577862i −0.0809168 + 0.0467174i
\(154\) 15.0751 1.21478
\(155\) −5.49300 5.54685i −0.441209 0.445534i
\(156\) −2.13639 −0.171048
\(157\) 7.34502 + 4.24065i 0.586197 + 0.338441i 0.763592 0.645699i \(-0.223434\pi\)
−0.177396 + 0.984140i \(0.556767\pi\)
\(158\) 15.7117i 1.24995i
\(159\) 10.9398 0.867579
\(160\) 2.15703 + 0.589266i 0.170528 + 0.0465855i
\(161\) −0.755734 1.30897i −0.0595602 0.103161i
\(162\) 1.00000i 0.0785674i
\(163\) 21.4841 + 12.4039i 1.68277 + 0.971546i 0.959810 + 0.280652i \(0.0905507\pi\)
0.722957 + 0.690893i \(0.242783\pi\)
\(164\) −6.04397 + 10.4685i −0.471955 + 0.817450i
\(165\) −7.82470 2.13758i −0.609152 0.166411i
\(166\) −6.91556 11.9781i −0.536752 0.929681i
\(167\) −9.99502 + 5.77063i −0.773438 + 0.446545i −0.834100 0.551614i \(-0.814012\pi\)
0.0606617 + 0.998158i \(0.480679\pi\)
\(168\) 3.59896 + 2.07786i 0.277666 + 0.160311i
\(169\) −4.21792 + 7.30565i −0.324455 + 0.561973i
\(170\) −0.681028 + 2.49293i −0.0522325 + 0.191199i
\(171\) −7.46174 −0.570613
\(172\) 10.7111 6.18403i 0.816711 0.471528i
\(173\) 3.13632 + 1.81075i 0.238450 + 0.137669i 0.614464 0.788945i \(-0.289372\pi\)
−0.376014 + 0.926614i \(0.622706\pi\)
\(174\) −5.15572 −0.390854
\(175\) 10.2133 + 18.0953i 0.772050 + 1.36788i
\(176\) −1.81377 + 3.14154i −0.136718 + 0.236803i
\(177\) 9.77013i 0.734368i
\(178\) −9.83745 + 5.67966i −0.737348 + 0.425708i
\(179\) 12.5453 0.937680 0.468840 0.883283i \(-0.344672\pi\)
0.468840 + 0.883283i \(0.344672\pi\)
\(180\) −1.57341 1.58883i −0.117275 0.118425i
\(181\) −1.46011 2.52899i −0.108529 0.187979i 0.806645 0.591036i \(-0.201281\pi\)
−0.915175 + 0.403057i \(0.867948\pi\)
\(182\) −7.68878 + 4.43912i −0.569931 + 0.329050i
\(183\) −5.41327 3.12535i −0.400160 0.231033i
\(184\) 0.363708 0.0268129
\(185\) −9.65599 9.57924i −0.709922 0.704280i
\(186\) 3.49115 0.255984
\(187\) −3.63075 2.09622i −0.265507 0.153291i
\(188\) 1.92038 1.10873i 0.140058 0.0808628i
\(189\) −2.07786 3.59896i −0.151142 0.261786i
\(190\) −11.8554 + 11.7404i −0.860085 + 0.851735i
\(191\) 20.4211 1.47762 0.738808 0.673916i \(-0.235389\pi\)
0.738808 + 0.673916i \(0.235389\pi\)
\(192\) −0.866025 + 0.500000i −0.0625000 + 0.0360844i
\(193\) 4.78676i 0.344558i 0.985048 + 0.172279i \(0.0551131\pi\)
−0.985048 + 0.172279i \(0.944887\pi\)
\(194\) −5.82972 + 10.0974i −0.418550 + 0.724949i
\(195\) 4.62031 1.21388i 0.330867 0.0869281i
\(196\) 10.2700 0.733574
\(197\) 3.56459 + 2.05802i 0.253967 + 0.146628i 0.621579 0.783351i \(-0.286491\pi\)
−0.367613 + 0.929979i \(0.619825\pi\)
\(198\) 3.14154 1.81377i 0.223260 0.128899i
\(199\) −6.59431 −0.467458 −0.233729 0.972302i \(-0.575093\pi\)
−0.233729 + 0.972302i \(0.575093\pi\)
\(200\) −4.99976 0.0487778i −0.353537 0.00344911i
\(201\) 7.73561 13.3985i 0.545628 0.945055i
\(202\) −9.04876 5.22430i −0.636668 0.367581i
\(203\) −18.5553 + 10.7129i −1.30232 + 0.751897i
\(204\) −0.577862 1.00089i −0.0404584 0.0700760i
\(205\) 7.12301 26.0740i 0.497493 1.82109i
\(206\) 4.88130 8.45466i 0.340096 0.589064i
\(207\) −0.314980 0.181854i −0.0218926 0.0126397i
\(208\) 2.13639i 0.148132i
\(209\) −13.5339 23.4413i −0.936157 1.62147i
\(210\) −8.96401 2.44882i −0.618575 0.168985i
\(211\) −3.49904 −0.240884 −0.120442 0.992720i \(-0.538431\pi\)
−0.120442 + 0.992720i \(0.538431\pi\)
\(212\) 10.9398i 0.751346i
\(213\) −0.126846 0.0732348i −0.00869137 0.00501797i
\(214\) −1.22493 −0.0837346
\(215\) −19.6508 + 19.4600i −1.34017 + 1.32716i
\(216\) 1.00000 0.0680414
\(217\) 12.5645 7.25413i 0.852935 0.492442i
\(218\) −8.57040 + 4.94812i −0.580461 + 0.335129i
\(219\) 4.81687 + 8.34307i 0.325494 + 0.563772i
\(220\) 2.13758 7.82470i 0.144116 0.527541i
\(221\) 2.46908 0.166088
\(222\) 6.08252 0.0539383i 0.408232 0.00362010i
\(223\) 11.9286i 0.798799i −0.916777 0.399400i \(-0.869219\pi\)
0.916777 0.399400i \(-0.130781\pi\)
\(224\) −2.07786 + 3.59896i −0.138833 + 0.240466i
\(225\) 4.30553 + 2.54212i 0.287035 + 0.169475i
\(226\) −4.18907 7.25569i −0.278653 0.482641i
\(227\) 6.93104 4.00164i 0.460030 0.265598i −0.252027 0.967720i \(-0.581097\pi\)
0.712057 + 0.702122i \(0.247764\pi\)
\(228\) 7.46174i 0.494165i
\(229\) −1.64726 2.85314i −0.108854 0.188541i 0.806452 0.591299i \(-0.201385\pi\)
−0.915306 + 0.402759i \(0.868051\pi\)
\(230\) −0.786581 + 0.206657i −0.0518656 + 0.0136265i
\(231\) 7.53753 13.0554i 0.495933 0.858981i
\(232\) 5.15572i 0.338490i
\(233\) 9.21492i 0.603690i 0.953357 + 0.301845i \(0.0976024\pi\)
−0.953357 + 0.301845i \(0.902398\pi\)
\(234\) −1.06819 + 1.85017i −0.0698301 + 0.120949i
\(235\) −3.52319 + 3.48898i −0.229827 + 0.227596i
\(236\) −9.77013 −0.635982
\(237\) 13.6067 + 7.85583i 0.883850 + 0.510291i
\(238\) −4.15940 2.40143i −0.269614 0.155662i
\(239\) 9.36223 16.2159i 0.605592 1.04892i −0.386366 0.922346i \(-0.626270\pi\)
0.991958 0.126570i \(-0.0403970\pi\)
\(240\) 1.58883 1.57341i 0.102559 0.101563i
\(241\) 8.14642 + 14.1100i 0.524757 + 0.908906i 0.999584 + 0.0288271i \(0.00917722\pi\)
−0.474827 + 0.880079i \(0.657489\pi\)
\(242\) 1.86978 + 1.07952i 0.120194 + 0.0693942i
\(243\) −0.866025 0.500000i −0.0555556 0.0320750i
\(244\) 3.12535 5.41327i 0.200080 0.346549i
\(245\) −22.2107 + 5.83538i −1.41899 + 0.372809i
\(246\) 6.04397 + 10.4685i 0.385350 + 0.667445i
\(247\) 13.8055 + 7.97059i 0.878420 + 0.507156i
\(248\) 3.49115i 0.221688i
\(249\) −13.8311 −0.876512
\(250\) 10.8406 2.73535i 0.685618 0.172999i
\(251\) 16.7386 1.05653 0.528264 0.849080i \(-0.322843\pi\)
0.528264 + 0.849080i \(0.322843\pi\)
\(252\) 3.59896 2.07786i 0.226713 0.130893i
\(253\) 1.31936i 0.0829477i
\(254\) −2.63911 4.57107i −0.165592 0.286814i
\(255\) 1.81842 + 1.83625i 0.113874 + 0.114991i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −6.15672 3.55458i −0.384046 0.221729i 0.295531 0.955333i \(-0.404503\pi\)
−0.679577 + 0.733604i \(0.737837\pi\)
\(258\) 12.3681i 0.770002i
\(259\) 21.7787 12.8328i 1.35326 0.797389i
\(260\) 1.21388 + 4.62031i 0.0752819 + 0.286540i
\(261\) −2.57786 + 4.46499i −0.159566 + 0.276376i
\(262\) −13.1799 + 7.60944i −0.814259 + 0.470113i
\(263\) −6.83430 + 3.94578i −0.421421 + 0.243307i −0.695685 0.718347i \(-0.744899\pi\)
0.274264 + 0.961654i \(0.411566\pi\)
\(264\) 1.81377 + 3.14154i 0.111630 + 0.193348i
\(265\) −6.21591 23.6591i −0.381840 1.45337i
\(266\) −15.5045 26.8545i −0.950639 1.64656i
\(267\) 11.3593i 0.695179i
\(268\) 13.3985 + 7.73561i 0.818442 + 0.472528i
\(269\) −0.806147 −0.0491516 −0.0245758 0.999698i \(-0.507824\pi\)
−0.0245758 + 0.999698i \(0.507824\pi\)
\(270\) −2.16267 + 0.568195i −0.131616 + 0.0345792i
\(271\) −4.63125 + 8.02156i −0.281329 + 0.487275i −0.971712 0.236168i \(-0.924108\pi\)
0.690384 + 0.723443i \(0.257442\pi\)
\(272\) 1.00089 0.577862i 0.0606876 0.0350380i
\(273\) 8.87824i 0.537336i
\(274\) −3.47185 + 6.01343i −0.209742 + 0.363284i
\(275\) −0.176943 + 18.1368i −0.0106701 + 1.09369i
\(276\) 0.181854 0.314980i 0.0109463 0.0189596i
\(277\) 5.54699 3.20256i 0.333287 0.192423i −0.324013 0.946053i \(-0.605032\pi\)
0.657299 + 0.753630i \(0.271699\pi\)
\(278\) −11.9435 + 6.89557i −0.716322 + 0.413569i
\(279\) 1.74558 3.02342i 0.104505 0.181008i
\(280\) 2.44882 8.96401i 0.146345 0.535702i
\(281\) −4.39344 + 7.60967i −0.262091 + 0.453955i −0.966797 0.255544i \(-0.917745\pi\)
0.704706 + 0.709499i \(0.251079\pi\)
\(282\) 2.21747i 0.132048i
\(283\) 8.33863 4.81431i 0.495680 0.286181i −0.231248 0.972895i \(-0.574281\pi\)
0.726928 + 0.686714i \(0.240947\pi\)
\(284\) 0.0732348 0.126846i 0.00434569 0.00752695i
\(285\) 4.23972 + 16.1373i 0.251139 + 0.955891i
\(286\) −7.74984 −0.458257
\(287\) 43.5041 + 25.1171i 2.56796 + 1.48261i
\(288\) 1.00000i 0.0589256i
\(289\) −7.83215 13.5657i −0.460715 0.797981i
\(290\) 2.92945 + 11.1501i 0.172023 + 0.654759i
\(291\) 5.82972 + 10.0974i 0.341744 + 0.591919i
\(292\) −8.34307 + 4.81687i −0.488241 + 0.281886i
\(293\) −15.0103 + 8.66622i −0.876913 + 0.506286i −0.869639 0.493687i \(-0.835649\pi\)
−0.00727385 + 0.999974i \(0.502315\pi\)
\(294\) 5.13502 8.89411i 0.299480 0.518715i
\(295\) 21.1296 5.55134i 1.23021 0.323211i
\(296\) 0.0539383 + 6.08252i 0.00313510 + 0.353539i
\(297\) 3.62754i 0.210491i
\(298\) −4.79019 2.76562i −0.277488 0.160208i
\(299\) 0.388511 + 0.672920i 0.0224681 + 0.0389160i
\(300\) −2.54212 + 4.30553i −0.146770 + 0.248580i
\(301\) −25.6991 44.5122i −1.48127 2.56564i
\(302\) 22.2298i 1.27918i
\(303\) −9.04876 + 5.22430i −0.519838 + 0.300128i
\(304\) 7.46174 0.427960
\(305\) −3.68332 + 13.4829i −0.210907 + 0.772031i
\(306\) −1.15572 −0.0660683
\(307\) 28.2983i 1.61507i 0.589820 + 0.807535i \(0.299199\pi\)
−0.589820 + 0.807535i \(0.700801\pi\)
\(308\) 13.0554 + 7.53753i 0.743899 + 0.429490i
\(309\) −4.88130 8.45466i −0.277687 0.480969i
\(310\) −1.98365 7.55022i −0.112664 0.428823i
\(311\) −1.26886 + 2.19774i −0.0719506 + 0.124622i −0.899756 0.436393i \(-0.856256\pi\)
0.827806 + 0.561015i \(0.189589\pi\)
\(312\) −1.85017 1.06819i −0.104745 0.0604746i
\(313\) −9.42952 5.44413i −0.532988 0.307721i 0.209245 0.977863i \(-0.432900\pi\)
−0.742232 + 0.670143i \(0.766233\pi\)
\(314\) 4.24065 + 7.34502i 0.239314 + 0.414504i
\(315\) −6.60275 + 6.53865i −0.372023 + 0.368411i
\(316\) −7.85583 + 13.6067i −0.441925 + 0.765437i
\(317\) −0.878780 0.507364i −0.0493572 0.0284964i 0.475118 0.879922i \(-0.342405\pi\)
−0.524476 + 0.851426i \(0.675739\pi\)
\(318\) 9.47411 + 5.46988i 0.531282 + 0.306736i
\(319\) −18.7026 −1.04714
\(320\) 1.57341 + 1.58883i 0.0879562 + 0.0888184i
\(321\) −0.612466 + 1.06082i −0.0341845 + 0.0592093i
\(322\) 1.51147i 0.0842308i
\(323\) 8.62370i 0.479836i
\(324\) 0.500000 0.866025i 0.0277778 0.0481125i
\(325\) −5.25047 9.30250i −0.291244 0.516010i
\(326\) 12.4039 + 21.4841i 0.686986 + 1.18990i
\(327\) 9.89625i 0.547264i
\(328\) −10.4685 + 6.04397i −0.578025 + 0.333723i
\(329\) −4.60760 7.98059i −0.254025 0.439984i
\(330\) −5.70760 5.76355i −0.314193 0.317273i
\(331\) −4.88646 + 8.46359i −0.268584 + 0.465201i −0.968496 0.249028i \(-0.919889\pi\)
0.699912 + 0.714229i \(0.253222\pi\)
\(332\) 13.8311i 0.759082i
\(333\) 2.99455 5.29459i 0.164100 0.290142i
\(334\) −11.5413 −0.631509
\(335\) −33.3718 9.11666i −1.82330 0.498096i
\(336\) 2.07786 + 3.59896i 0.113357 + 0.196339i
\(337\) −8.78297 + 5.07085i −0.478439 + 0.276227i −0.719766 0.694217i \(-0.755751\pi\)
0.241327 + 0.970444i \(0.422417\pi\)
\(338\) −7.30565 + 4.21792i −0.397375 + 0.229425i
\(339\) −8.37815 −0.455038
\(340\) −1.83625 + 1.81842i −0.0995847 + 0.0986179i
\(341\) 12.6643 0.685809
\(342\) −6.46205 3.73087i −0.349428 0.201742i
\(343\) 13.5894i 0.733757i
\(344\) 12.3681 0.666841
\(345\) −0.214320 + 0.784527i −0.0115386 + 0.0422375i
\(346\) 1.81075 + 3.13632i 0.0973468 + 0.168610i
\(347\) 16.3722i 0.878906i 0.898266 + 0.439453i \(0.144828\pi\)
−0.898266 + 0.439453i \(0.855172\pi\)
\(348\) −4.46499 2.57786i −0.239348 0.138188i
\(349\) 7.28289 12.6143i 0.389844 0.675230i −0.602584 0.798055i \(-0.705862\pi\)
0.992428 + 0.122826i \(0.0391956\pi\)
\(350\) −0.202707 + 20.7776i −0.0108351 + 1.11061i
\(351\) 1.06819 + 1.85017i 0.0570160 + 0.0987546i
\(352\) −3.14154 + 1.81377i −0.167445 + 0.0966742i
\(353\) −20.7462 11.9778i −1.10421 0.637516i −0.166887 0.985976i \(-0.553371\pi\)
−0.937324 + 0.348460i \(0.886705\pi\)
\(354\) −4.88507 + 8.46118i −0.259638 + 0.449707i
\(355\) −0.0863095 + 0.315939i −0.00458083 + 0.0167683i
\(356\) −11.3593 −0.602042
\(357\) −4.15940 + 2.40143i −0.220139 + 0.127097i
\(358\) 10.8646 + 6.27265i 0.574210 + 0.331520i
\(359\) −31.6699 −1.67147 −0.835736 0.549132i \(-0.814958\pi\)
−0.835736 + 0.549132i \(0.814958\pi\)
\(360\) −0.568195 2.16267i −0.0299465 0.113983i
\(361\) −18.3387 + 31.7636i −0.965197 + 1.67177i
\(362\) 2.92023i 0.153484i
\(363\) 1.86978 1.07952i 0.0981382 0.0566601i
\(364\) −8.87824 −0.465346
\(365\) 15.3064 15.1578i 0.801174 0.793396i
\(366\) −3.12535 5.41327i −0.163365 0.282956i
\(367\) 18.6346 10.7587i 0.972720 0.561600i 0.0726556 0.997357i \(-0.476853\pi\)
0.900064 + 0.435757i \(0.143519\pi\)
\(368\) 0.314980 + 0.181854i 0.0164195 + 0.00947979i
\(369\) 12.0879 0.629273
\(370\) −3.57271 13.1239i −0.185736 0.682277i
\(371\) 45.4626 2.36030
\(372\) 3.02342 + 1.74558i 0.156757 + 0.0905039i
\(373\) 8.45399 4.88092i 0.437731 0.252724i −0.264904 0.964275i \(-0.585340\pi\)
0.702635 + 0.711551i \(0.252007\pi\)
\(374\) −2.09622 3.63075i −0.108393 0.187742i
\(375\) 3.05140 10.7559i 0.157574 0.555431i
\(376\) 2.21747 0.114357
\(377\) 9.53895 5.50732i 0.491281 0.283641i
\(378\) 4.15572i 0.213747i
\(379\) 11.7727 20.3909i 0.604722 1.04741i −0.387374 0.921923i \(-0.626618\pi\)
0.992095 0.125486i \(-0.0400489\pi\)
\(380\) −16.1373 + 4.23972i −0.827826 + 0.217493i
\(381\) −5.27821 −0.270411
\(382\) 17.6852 + 10.2105i 0.904851 + 0.522416i
\(383\) 5.85258 3.37899i 0.299053 0.172658i −0.342965 0.939348i \(-0.611431\pi\)
0.642017 + 0.766690i \(0.278098\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −32.5173 8.88321i −1.65723 0.452730i
\(386\) −2.39338 + 4.14545i −0.121820 + 0.210998i
\(387\) −10.7111 6.18403i −0.544474 0.314352i
\(388\) −10.0974 + 5.82972i −0.512617 + 0.295959i
\(389\) 2.80650 + 4.86100i 0.142295 + 0.246462i 0.928361 0.371681i \(-0.121218\pi\)
−0.786065 + 0.618143i \(0.787885\pi\)
\(390\) 4.60825 + 1.25890i 0.233348 + 0.0637469i
\(391\) −0.210173 + 0.364030i −0.0106289 + 0.0184098i
\(392\) 8.89411 + 5.13502i 0.449221 + 0.259358i
\(393\) 15.2189i 0.767691i
\(394\) 2.05802 + 3.56459i 0.103681 + 0.179581i
\(395\) 9.25835 33.8905i 0.465838 1.70522i
\(396\) 3.62754 0.182291
\(397\) 24.5689i 1.23308i −0.787324 0.616540i \(-0.788534\pi\)
0.787324 0.616540i \(-0.211466\pi\)
\(398\) −5.71084 3.29715i −0.286258 0.165271i
\(399\) −31.0089 −1.55239
\(400\) −4.30553 2.54212i −0.215277 0.127106i
\(401\) 33.1745 1.65665 0.828327 0.560245i \(-0.189293\pi\)
0.828327 + 0.560245i \(0.189293\pi\)
\(402\) 13.3985 7.73561i 0.668255 0.385817i
\(403\) −6.45921 + 3.72923i −0.321756 + 0.185766i
\(404\) −5.22430 9.04876i −0.259919 0.450193i
\(405\) −0.589266 + 2.15703i −0.0292808 + 0.107184i
\(406\) −21.4258 −1.06334
\(407\) 22.0646 0.195663i 1.09370 0.00969867i
\(408\) 1.15572i 0.0572168i
\(409\) −13.1498 + 22.7761i −0.650215 + 1.12621i 0.332855 + 0.942978i \(0.391988\pi\)
−0.983070 + 0.183228i \(0.941345\pi\)
\(410\) 19.2057 19.0193i 0.948503 0.939295i
\(411\) 3.47185 + 6.01343i 0.171254 + 0.296620i
\(412\) 8.45466 4.88130i 0.416531 0.240484i
\(413\) 40.6020i 1.99789i
\(414\) −0.181854 0.314980i −0.00893763 0.0154804i
\(415\) 7.85877 + 29.9122i 0.385772 + 1.46833i
\(416\) 1.06819 1.85017i 0.0523725 0.0907119i
\(417\) 13.7911i 0.675355i
\(418\) 27.0677i 1.32393i
\(419\) −16.1912 + 28.0440i −0.790991 + 1.37004i 0.134363 + 0.990932i \(0.457101\pi\)
−0.925354 + 0.379105i \(0.876232\pi\)
\(420\) −6.53865 6.60275i −0.319053 0.322181i
\(421\) 7.22310 0.352032 0.176016 0.984387i \(-0.443679\pi\)
0.176016 + 0.984387i \(0.443679\pi\)
\(422\) −3.03026 1.74952i −0.147511 0.0851652i
\(423\) −1.92038 1.10873i −0.0933723 0.0539085i
\(424\) −5.46988 + 9.47411i −0.265641 + 0.460103i
\(425\) 2.93799 4.97600i 0.142514 0.241372i
\(426\) −0.0732348 0.126846i −0.00354824 0.00614573i
\(427\) −22.4960 12.9881i −1.08866 0.628538i
\(428\) −1.06082 0.612466i −0.0512768 0.0296046i
\(429\) −3.87492 + 6.71155i −0.187083 + 0.324037i
\(430\) −26.7481 + 7.02747i −1.28991 + 0.338895i
\(431\) −2.04698 3.54547i −0.0985995 0.170779i 0.812506 0.582953i \(-0.198103\pi\)
−0.911105 + 0.412174i \(0.864770\pi\)
\(432\) 0.866025 + 0.500000i 0.0416667 + 0.0240563i
\(433\) 1.11862i 0.0537574i 0.999639 + 0.0268787i \(0.00855678\pi\)
−0.999639 + 0.0268787i \(0.991443\pi\)
\(434\) 14.5083 0.696419
\(435\) 11.1210 + 3.03809i 0.533213 + 0.145665i
\(436\) −9.89625 −0.473944
\(437\) −2.35030 + 1.35695i −0.112430 + 0.0649115i
\(438\) 9.63375i 0.460318i
\(439\) −2.98041 5.16221i −0.142247 0.246379i 0.786095 0.618105i \(-0.212099\pi\)
−0.928342 + 0.371726i \(0.878766\pi\)
\(440\) 5.76355 5.70760i 0.274767 0.272099i
\(441\) −5.13502 8.89411i −0.244525 0.423529i
\(442\) 2.13828 + 1.23454i 0.101708 + 0.0587210i
\(443\) 10.0305i 0.476563i −0.971196 0.238282i \(-0.923416\pi\)
0.971196 0.238282i \(-0.0765841\pi\)
\(444\) 5.29459 + 2.99455i 0.251270 + 0.142115i
\(445\) 24.5665 6.45430i 1.16456 0.305963i
\(446\) 5.96431 10.3305i 0.282418 0.489163i
\(447\) −4.79019 + 2.76562i −0.226568 + 0.130809i
\(448\) −3.59896 + 2.07786i −0.170035 + 0.0981697i
\(449\) 7.09889 + 12.2956i 0.335017 + 0.580267i 0.983488 0.180972i \(-0.0579245\pi\)
−0.648471 + 0.761239i \(0.724591\pi\)
\(450\) 2.45764 + 4.35431i 0.115854 + 0.205264i
\(451\) 21.9248 + 37.9748i 1.03240 + 1.78816i
\(452\) 8.37815i 0.394075i
\(453\) −19.2515 11.1149i −0.904517 0.522223i
\(454\) 8.00328 0.375613
\(455\) 19.2007 5.04457i 0.900144 0.236493i
\(456\) 3.73087 6.46205i 0.174714 0.302613i
\(457\) −9.49114 + 5.47971i −0.443977 + 0.256330i −0.705283 0.708926i \(-0.749180\pi\)
0.261306 + 0.965256i \(0.415847\pi\)
\(458\) 3.29452i 0.153943i
\(459\) −0.577862 + 1.00089i −0.0269723 + 0.0467174i
\(460\) −0.784527 0.214320i −0.0365788 0.00999274i
\(461\) 13.1296 22.7411i 0.611506 1.05916i −0.379481 0.925199i \(-0.623897\pi\)
0.990987 0.133959i \(-0.0427692\pi\)
\(462\) 13.0554 7.53753i 0.607391 0.350677i
\(463\) −21.8170 + 12.5961i −1.01392 + 0.585388i −0.912338 0.409439i \(-0.865725\pi\)
−0.101584 + 0.994827i \(0.532391\pi\)
\(464\) 2.57786 4.46499i 0.119674 0.207282i
\(465\) −7.53051 2.05721i −0.349219 0.0954011i
\(466\) −4.60746 + 7.98036i −0.213437 + 0.369683i
\(467\) 22.8651i 1.05807i −0.848600 0.529035i \(-0.822554\pi\)
0.848600 0.529035i \(-0.177446\pi\)
\(468\) −1.85017 + 1.06819i −0.0855240 + 0.0493773i
\(469\) 32.1471 55.6803i 1.48441 2.57108i
\(470\) −4.79566 + 1.25995i −0.221207 + 0.0581174i
\(471\) 8.48130 0.390798
\(472\) −8.46118 4.88507i −0.389458 0.224853i
\(473\) 44.8656i 2.06292i
\(474\) 7.85583 + 13.6067i 0.360830 + 0.624977i
\(475\) 32.4907 18.3382i 1.49078 0.841416i
\(476\) −2.40143 4.15940i −0.110070 0.190646i
\(477\) 9.47411 5.46988i 0.433790 0.250449i
\(478\) 16.2159 9.36223i 0.741696 0.428218i
\(479\) 12.4085 21.4922i 0.566960 0.982004i −0.429904 0.902874i \(-0.641453\pi\)
0.996864 0.0791292i \(-0.0252140\pi\)
\(480\) 2.16267 0.568195i 0.0987121 0.0259344i
\(481\) −11.1961 + 6.59711i −0.510497 + 0.300802i
\(482\) 16.2928i 0.742119i
\(483\) −1.30897 0.755734i −0.0595602 0.0343871i
\(484\) 1.07952 + 1.86978i 0.0490691 + 0.0849902i
\(485\) 18.5249 18.3451i 0.841173 0.833006i
\(486\) −0.500000 0.866025i −0.0226805 0.0392837i
\(487\) 12.1033i 0.548454i −0.961665 0.274227i \(-0.911578\pi\)
0.961665 0.274227i \(-0.0884220\pi\)
\(488\) 5.41327 3.12535i 0.245047 0.141478i
\(489\) 24.8077 1.12184
\(490\) −22.1527 6.05178i −1.00076 0.273392i
\(491\) −33.2720 −1.50154 −0.750772 0.660562i \(-0.770318\pi\)
−0.750772 + 0.660562i \(0.770318\pi\)
\(492\) 12.0879i 0.544967i
\(493\) 5.16029 + 2.97930i 0.232408 + 0.134181i
\(494\) 7.97059 + 13.8055i 0.358614 + 0.621137i
\(495\) −7.84518 + 2.06115i −0.352615 + 0.0926417i
\(496\) −1.74558 + 3.02342i −0.0783786 + 0.135756i
\(497\) −0.527139 0.304344i −0.0236454 0.0136517i
\(498\) −11.9781 6.91556i −0.536752 0.309894i
\(499\) −9.98553 17.2955i −0.447014 0.774251i 0.551176 0.834389i \(-0.314179\pi\)
−0.998190 + 0.0601381i \(0.980846\pi\)
\(500\) 10.7559 + 3.05140i 0.481018 + 0.136463i
\(501\) −5.77063 + 9.99502i −0.257813 + 0.446545i
\(502\) 14.4960 + 8.36928i 0.646989 + 0.373539i
\(503\) −2.50589 1.44678i −0.111732 0.0645086i 0.443092 0.896476i \(-0.353881\pi\)
−0.554825 + 0.831967i \(0.687215\pi\)
\(504\) 4.15572 0.185111
\(505\) 16.4399 + 16.6011i 0.731567 + 0.738739i
\(506\) 0.659682 1.14260i 0.0293264 0.0507949i
\(507\) 8.43584i 0.374649i
\(508\) 5.27821i 0.234183i
\(509\) −6.90016 + 11.9514i −0.305844 + 0.529738i −0.977449 0.211172i \(-0.932272\pi\)
0.671605 + 0.740910i \(0.265605\pi\)
\(510\) 0.656676 + 2.49945i 0.0290781 + 0.110678i
\(511\) 20.0176 + 34.6715i 0.885526 + 1.53378i
\(512\) 1.00000i 0.0441942i
\(513\) −6.46205 + 3.73087i −0.285307 + 0.164722i
\(514\) −3.55458 6.15672i −0.156786 0.271561i
\(515\) −15.5111 + 15.3605i −0.683502 + 0.676867i
\(516\) 6.18403 10.7111i 0.272237 0.471528i
\(517\) 8.04396i 0.353773i
\(518\) 25.2773 0.224153i 1.11062 0.00984871i
\(519\) 3.62151 0.158967
\(520\) −1.25890 + 4.60825i −0.0552064 + 0.202085i
\(521\) −4.95593 8.58393i −0.217123 0.376069i 0.736804 0.676106i \(-0.236334\pi\)
−0.953927 + 0.300038i \(0.903001\pi\)
\(522\) −4.46499 + 2.57786i −0.195427 + 0.112830i
\(523\) 34.6236 19.9900i 1.51399 0.874100i 0.514120 0.857718i \(-0.328118\pi\)
0.999866 0.0163822i \(-0.00521485\pi\)
\(524\) −15.2189 −0.664840
\(525\) 17.8926 + 10.5644i 0.780897 + 0.461067i
\(526\) −7.89156 −0.344089
\(527\) −3.49424 2.01740i −0.152212 0.0878794i
\(528\) 3.62754i 0.157868i
\(529\) 22.8677 0.994249
\(530\) 6.44642 23.5974i 0.280015 1.02500i
\(531\) 4.88507 + 8.46118i 0.211994 + 0.367184i
\(532\) 31.0089i 1.34441i
\(533\) −22.3647 12.9123i −0.968724 0.559293i
\(534\) −5.67966 + 9.83745i −0.245783 + 0.425708i
\(535\) 2.64221 + 0.721810i 0.114233 + 0.0312066i
\(536\) 7.73561 + 13.3985i 0.334127 + 0.578726i
\(537\) 10.8646 6.27265i 0.468840 0.270685i
\(538\) −0.698143 0.403073i −0.0300991 0.0173777i
\(539\) 18.6275 32.2637i 0.802342 1.38970i
\(540\) −2.15703 0.589266i −0.0928237 0.0253580i
\(541\) −7.11266 −0.305797 −0.152899 0.988242i \(-0.548861\pi\)
−0.152899 + 0.988242i \(0.548861\pi\)
\(542\) −8.02156 + 4.63125i −0.344556 + 0.198929i
\(543\) −2.52899 1.46011i −0.108529 0.0626595i
\(544\) 1.15572 0.0495512
\(545\) 21.4024 5.62300i 0.916776 0.240863i
\(546\) −4.43912 + 7.68878i −0.189977 + 0.329050i
\(547\) 10.4605i 0.447260i −0.974674 0.223630i \(-0.928209\pi\)
0.974674 0.223630i \(-0.0717907\pi\)
\(548\) −6.01343 + 3.47185i −0.256881 + 0.148310i
\(549\) −6.25070 −0.266774
\(550\) −9.22165 + 15.6185i −0.393213 + 0.665975i
\(551\) 19.2353 + 33.3166i 0.819452 + 1.41933i
\(552\) 0.314980 0.181854i 0.0134064 0.00774021i
\(553\) 56.5457 + 32.6467i 2.40457 + 1.38828i
\(554\) 6.40512 0.272127
\(555\) −13.1520 3.46788i −0.558269 0.147203i
\(556\) −13.7911 −0.584874
\(557\) 11.6439 + 6.72259i 0.493367 + 0.284845i 0.725970 0.687726i \(-0.241391\pi\)
−0.232603 + 0.972572i \(0.574724\pi\)
\(558\) 3.02342 1.74558i 0.127992 0.0738961i
\(559\) 13.2115 + 22.8830i 0.558787 + 0.967847i
\(560\) 6.60275 6.53865i 0.279017 0.276308i
\(561\) −4.19243 −0.177005
\(562\) −7.60967 + 4.39344i −0.320994 + 0.185326i
\(563\) 7.95921i 0.335441i 0.985835 + 0.167720i \(0.0536406\pi\)
−0.985835 + 0.167720i \(0.946359\pi\)
\(564\) 1.10873 1.92038i 0.0466862 0.0808628i
\(565\) 4.76042 + 18.1192i 0.200272 + 0.762280i
\(566\) 9.62862 0.404721
\(567\) −3.59896 2.07786i −0.151142 0.0872620i
\(568\) 0.126846 0.0732348i 0.00532236 0.00307287i
\(569\) −6.60381 −0.276846 −0.138423 0.990373i \(-0.544203\pi\)
−0.138423 + 0.990373i \(0.544203\pi\)
\(570\) −4.39694 + 16.0952i −0.184168 + 0.674152i
\(571\) 8.02353 13.8972i 0.335774 0.581578i −0.647859 0.761760i \(-0.724335\pi\)
0.983633 + 0.180182i \(0.0576687\pi\)
\(572\) −6.71155 3.87492i −0.280624 0.162018i
\(573\) 17.6852 10.2105i 0.738808 0.426551i
\(574\) 25.1171 + 43.5041i 1.04837 + 1.81582i
\(575\) 1.81845 + 0.0177409i 0.0758347 + 0.000739845i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −21.9490 12.6723i −0.913749 0.527553i −0.0321136 0.999484i \(-0.510224\pi\)
−0.881636 + 0.471931i \(0.843557\pi\)
\(578\) 15.6643i 0.651549i
\(579\) 2.39338 + 4.14545i 0.0994654 + 0.172279i
\(580\) −3.03809 + 11.1210i −0.126150 + 0.461776i
\(581\) −57.4783 −2.38460
\(582\) 11.6594i 0.483300i
\(583\) 34.3677 + 19.8422i 1.42336 + 0.821780i
\(584\) −9.63375 −0.398647
\(585\) 3.39436 3.36141i 0.140340 0.138977i
\(586\) −17.3324 −0.715997
\(587\) 1.63238 0.942454i 0.0673754 0.0388992i −0.465934 0.884820i \(-0.654282\pi\)
0.533309 + 0.845920i \(0.320948\pi\)
\(588\) 8.89411 5.13502i 0.366787 0.211765i
\(589\) −13.0250 22.5600i −0.536687 0.929568i
\(590\) 21.0744 + 5.75720i 0.867621 + 0.237020i
\(591\) 4.11603 0.169311
\(592\) −2.99455 + 5.29459i −0.123075 + 0.217606i
\(593\) 5.11792i 0.210168i −0.994463 0.105084i \(-0.966489\pi\)
0.994463 0.105084i \(-0.0335111\pi\)
\(594\) 1.81377 3.14154i 0.0744199 0.128899i
\(595\) 7.55687 + 7.63095i 0.309801 + 0.312839i
\(596\) −2.76562 4.79019i −0.113284 0.196214i
\(597\) −5.71084 + 3.29715i −0.233729 + 0.134943i
\(598\) 0.777021i 0.0317748i
\(599\) −1.84896 3.20250i −0.0755466 0.130851i 0.825777 0.563996i \(-0.190737\pi\)
−0.901324 + 0.433146i \(0.857404\pi\)
\(600\) −4.35431 + 2.45764i −0.177764 + 0.100333i
\(601\) −12.3196 + 21.3383i −0.502529 + 0.870406i 0.497467 + 0.867483i \(0.334264\pi\)
−0.999996 + 0.00292268i \(0.999070\pi\)
\(602\) 51.3983i 2.09484i
\(603\) 15.4712i 0.630037i
\(604\) 11.1149 19.2515i 0.452258 0.783334i
\(605\) −3.39705 3.43036i −0.138110 0.139464i
\(606\) −10.4486 −0.424446
\(607\) 25.1410 + 14.5152i 1.02044 + 0.589153i 0.914232 0.405190i \(-0.132795\pi\)
0.106211 + 0.994344i \(0.466128\pi\)
\(608\) 6.46205 + 3.73087i 0.262071 + 0.151307i
\(609\) −10.7129 + 18.5553i −0.434108 + 0.751897i
\(610\) −9.93132 + 9.83490i −0.402107 + 0.398204i
\(611\) 2.36869 + 4.10269i 0.0958269 + 0.165977i
\(612\) −1.00089 0.577862i −0.0404584 0.0233587i
\(613\) −7.41060 4.27851i −0.299311 0.172807i 0.342822 0.939400i \(-0.388617\pi\)
−0.642133 + 0.766593i \(0.721950\pi\)
\(614\) −14.1491 + 24.5070i −0.571013 + 0.989024i
\(615\) −6.86831 26.1423i −0.276957 1.05416i
\(616\) 7.53753 + 13.0554i 0.303696 + 0.526016i
\(617\) 18.6337 + 10.7581i 0.750163 + 0.433107i 0.825753 0.564032i \(-0.190751\pi\)
−0.0755901 + 0.997139i \(0.524084\pi\)
\(618\) 9.76260i 0.392709i
\(619\) 0.00690520 0.000277543 0.000138772 1.00000i \(-0.499956\pi\)
0.000138772 1.00000i \(0.499956\pi\)
\(620\) 2.05721 7.53051i 0.0826197 0.302432i
\(621\) −0.363708 −0.0145951
\(622\) −2.19774 + 1.26886i −0.0881212 + 0.0508768i
\(623\) 47.2062i 1.89127i
\(624\) −1.06819 1.85017i −0.0427620 0.0740660i
\(625\) −24.9952 0.487755i −0.999810 0.0195102i
\(626\) −5.44413 9.42952i −0.217591 0.376879i
\(627\) −23.4413 13.5339i −0.936157 0.540491i
\(628\) 8.48130i 0.338441i
\(629\) −6.11908 3.46087i −0.243984 0.137994i
\(630\) −8.98747 + 2.36126i −0.358069 + 0.0940748i
\(631\) −8.60323 + 14.9012i −0.342489 + 0.593209i −0.984894 0.173157i \(-0.944603\pi\)
0.642405 + 0.766365i \(0.277937\pi\)
\(632\) −13.6067 + 7.85583i −0.541246 + 0.312488i
\(633\) −3.03026 + 1.74952i −0.120442 + 0.0695371i
\(634\) −0.507364 0.878780i −0.0201500 0.0349008i
\(635\) 2.99905 + 11.4150i 0.119014 + 0.452992i
\(636\) 5.46988 + 9.47411i 0.216895 + 0.375673i
\(637\) 21.9408i 0.869326i
\(638\) −16.1969 9.35129i −0.641242 0.370221i
\(639\) −0.146470 −0.00579425
\(640\) 0.568195 + 2.16267i 0.0224599 + 0.0854872i
\(641\) 9.46037 16.3858i 0.373662 0.647202i −0.616464 0.787383i \(-0.711435\pi\)
0.990126 + 0.140182i \(0.0447686\pi\)
\(642\) −1.06082 + 0.612466i −0.0418673 + 0.0241721i
\(643\) 42.2666i 1.66683i −0.552647 0.833415i \(-0.686382\pi\)
0.552647 0.833415i \(-0.313618\pi\)
\(644\) 0.755734 1.30897i 0.0297801 0.0515806i
\(645\) −7.28808 + 26.6783i −0.286968 + 1.05046i
\(646\) −4.31185 + 7.46835i −0.169648 + 0.293838i
\(647\) 36.1233 20.8558i 1.42015 0.819926i 0.423841 0.905736i \(-0.360681\pi\)
0.996311 + 0.0858109i \(0.0273481\pi\)
\(648\) 0.866025 0.500000i 0.0340207 0.0196419i
\(649\) −17.7208 + 30.6933i −0.695601 + 1.20482i
\(650\) 0.104208 10.6814i 0.00408739 0.418960i
\(651\) 7.25413 12.5645i 0.284312 0.492442i
\(652\) 24.8077i 0.971546i
\(653\) 27.3064 15.7653i 1.06858 0.616946i 0.140788 0.990040i \(-0.455036\pi\)
0.927793 + 0.373094i \(0.121703\pi\)
\(654\) −4.94812 + 8.57040i −0.193487 + 0.335129i
\(655\) 32.9134 8.64728i 1.28603 0.337877i
\(656\) −12.0879 −0.471955
\(657\) 8.34307 + 4.81687i 0.325494 + 0.187924i
\(658\) 9.21519i 0.359246i
\(659\) −23.8572 41.3218i −0.929343 1.60967i −0.784423 0.620226i \(-0.787041\pi\)
−0.144919 0.989443i \(-0.546292\pi\)
\(660\) −2.06115 7.84518i −0.0802301 0.305373i
\(661\) −18.8385 32.6293i −0.732733 1.26913i −0.955711 0.294307i \(-0.904911\pi\)
0.222978 0.974824i \(-0.428422\pi\)
\(662\) −8.46359 + 4.88646i −0.328947 + 0.189918i
\(663\) 2.13828 1.23454i 0.0830440 0.0479455i
\(664\) 6.91556 11.9781i 0.268376 0.464841i
\(665\) 17.6191 + 67.0621i 0.683239 + 2.60056i
\(666\) 5.24065 3.08797i 0.203071 0.119657i
\(667\) 1.87518i 0.0726071i
\(668\) −9.99502 5.77063i −0.386719 0.223272i
\(669\) −5.96431 10.3305i −0.230593 0.399400i
\(670\) −24.3425 24.5812i −0.940434 0.949654i
\(671\) −11.3373 19.6368i −0.437673 0.758072i
\(672\) 4.15572i 0.160311i
\(673\) 25.4131 14.6723i 0.979603 0.565574i 0.0774530 0.996996i \(-0.475321\pi\)
0.902150 + 0.431422i \(0.141988\pi\)
\(674\) −10.1417 −0.390644
\(675\) 4.99976 + 0.0487778i 0.192441 + 0.00187746i
\(676\) −8.43584 −0.324455
\(677\) 20.0254i 0.769639i 0.922992 + 0.384820i \(0.125736\pi\)
−0.922992 + 0.384820i \(0.874264\pi\)
\(678\) −7.25569 4.18907i −0.278653 0.160880i
\(679\) 24.2267 + 41.9619i 0.929736 + 1.61035i
\(680\) −2.49945 + 0.656676i −0.0958496 + 0.0251824i
\(681\) 4.00164 6.93104i 0.153343 0.265598i
\(682\) 10.9676 + 6.33214i 0.419971 + 0.242470i
\(683\) 22.8200 + 13.1751i 0.873183 + 0.504133i 0.868405 0.495856i \(-0.165146\pi\)
0.00477842 + 0.999989i \(0.498479\pi\)
\(684\) −3.73087 6.46205i −0.142653 0.247083i
\(685\) 11.0324 10.9253i 0.421526 0.417434i
\(686\) 6.79469 11.7687i 0.259422 0.449333i
\(687\) −2.85314 1.64726i −0.108854 0.0628469i
\(688\) 10.7111 + 6.18403i 0.408355 + 0.235764i
\(689\) −23.3716 −0.890386
\(690\) −0.577871 + 0.572260i −0.0219992 + 0.0217856i
\(691\) −16.1086 + 27.9009i −0.612801 + 1.06140i 0.377965 + 0.925820i \(0.376624\pi\)
−0.990766 + 0.135582i \(0.956709\pi\)
\(692\) 3.62151i 0.137669i
\(693\) 15.0751i 0.572654i
\(694\) −8.18610 + 14.1787i −0.310740 + 0.538218i
\(695\) 29.8257 7.83605i 1.13135 0.297238i
\(696\) −2.57786 4.46499i −0.0977136 0.169245i
\(697\) 13.9703i 0.529164i
\(698\) 12.6143 7.28289i 0.477459 0.275661i
\(699\) 4.60746 + 7.98036i 0.174270 + 0.301845i
\(700\) −10.5644 + 17.8926i −0.399295 + 0.676277i
\(701\) 19.8955 34.4600i 0.751442 1.30154i −0.195682 0.980667i \(-0.562692\pi\)
0.947124 0.320868i \(-0.103975\pi\)
\(702\) 2.13639i 0.0806328i
\(703\) −23.0416 39.1043i −0.869032 1.47485i
\(704\) −3.62754 −0.136718
\(705\) −1.30668 + 4.78314i −0.0492124 + 0.180144i
\(706\) −11.9778 20.7462i −0.450792 0.780795i
\(707\) −37.6041 + 21.7108i −1.41425 + 0.816517i
\(708\) −8.46118 + 4.88507i −0.317991 + 0.183592i
\(709\) −38.2518 −1.43658 −0.718288 0.695746i \(-0.755074\pi\)
−0.718288 + 0.695746i \(0.755074\pi\)
\(710\) −0.232716 + 0.230456i −0.00873367 + 0.00864888i
\(711\) 15.7117 0.589234
\(712\) −9.83745 5.67966i −0.368674 0.212854i
\(713\) 1.26976i 0.0475528i
\(714\) −4.80287 −0.179743
\(715\) 16.7166 + 4.56671i 0.625166 + 0.170785i
\(716\) 6.27265 + 10.8646i 0.234420 + 0.406027i
\(717\) 18.7245i 0.699277i
\(718\) −27.4269 15.8349i −1.02356 0.590954i
\(719\) −14.0689 + 24.3681i −0.524681 + 0.908775i 0.474906 + 0.880037i \(0.342482\pi\)
−0.999587 + 0.0287381i \(0.990851\pi\)
\(720\) 0.589266 2.15703i 0.0219606 0.0803877i
\(721\) −20.2853 35.1352i −0.755465 1.30850i
\(722\) −31.7636 + 18.3387i −1.18212 + 0.682497i
\(723\) 14.1100 + 8.14642i 0.524757 + 0.302969i
\(724\) 1.46011 2.52899i 0.0542647 0.0939893i
\(725\) 0.251485 25.7774i 0.00933991 0.957348i
\(726\) 2.15904 0.0801295
\(727\) 8.63854 4.98746i 0.320386 0.184975i −0.331179 0.943568i \(-0.607446\pi\)
0.651564 + 0.758593i \(0.274113\pi\)
\(728\) −7.68878 4.43912i −0.284965 0.164525i
\(729\) −1.00000 −0.0370370
\(730\) 20.8346 5.47384i 0.771125 0.202596i
\(731\) −7.14703 + 12.3790i −0.264343 + 0.457855i
\(732\) 6.25070i 0.231033i
\(733\) −8.08570 + 4.66828i −0.298652 + 0.172427i −0.641837 0.766841i \(-0.721828\pi\)
0.343185 + 0.939268i \(0.388494\pi\)
\(734\) 21.5174 0.794223
\(735\) −16.3174 + 16.1590i −0.601875 + 0.596032i
\(736\) 0.181854 + 0.314980i 0.00670322 + 0.0116103i
\(737\) 48.6035 28.0612i 1.79033 1.03365i
\(738\) 10.4685 + 6.04397i 0.385350 + 0.222482i
\(739\) 34.3088 1.26207 0.631035 0.775754i \(-0.282630\pi\)
0.631035 + 0.775754i \(0.282630\pi\)
\(740\) 3.46788 13.1520i 0.127482 0.483475i
\(741\) 15.9412 0.585614
\(742\) 39.3718 + 22.7313i 1.44538 + 0.834492i
\(743\) −6.05632 + 3.49662i −0.222185 + 0.128278i −0.606962 0.794731i \(-0.707612\pi\)
0.384777 + 0.923010i \(0.374278\pi\)
\(744\) 1.74558 + 3.02342i 0.0639959 + 0.110844i
\(745\) 8.70288 + 8.78820i 0.318849 + 0.321975i
\(746\) 9.76183 0.357406
\(747\) −11.9781 + 6.91556i −0.438256 + 0.253027i
\(748\) 4.19243i 0.153291i
\(749\) −2.54524 + 4.40848i −0.0930010 + 0.161082i
\(750\) 8.02053 7.78916i 0.292868 0.284420i
\(751\) −3.07125 −0.112071 −0.0560357 0.998429i \(-0.517846\pi\)
−0.0560357 + 0.998429i \(0.517846\pi\)
\(752\) 1.92038 + 1.10873i 0.0700292 + 0.0404314i
\(753\) 14.4960 8.36928i 0.528264 0.304994i
\(754\) 11.0146 0.401129
\(755\) −13.0992 + 47.9502i −0.476730 + 1.74509i
\(756\) 2.07786 3.59896i 0.0755711 0.130893i
\(757\) −26.9227 15.5438i −0.978523 0.564950i −0.0766990 0.997054i \(-0.524438\pi\)
−0.901824 + 0.432104i \(0.857771\pi\)
\(758\) 20.3909 11.7727i 0.740630 0.427603i
\(759\) −0.659682 1.14260i −0.0239449 0.0414738i
\(760\) −16.0952 4.39694i −0.583833 0.159494i
\(761\) 16.6558 28.8487i 0.603772 1.04576i −0.388472 0.921461i \(-0.626997\pi\)
0.992244 0.124304i \(-0.0396698\pi\)
\(762\) −4.57107 2.63911i −0.165592 0.0956047i
\(763\) 41.1261i 1.48886i
\(764\) 10.2105 + 17.6852i 0.369404 + 0.639826i
\(765\) 2.49293 + 0.681028i 0.0901320 + 0.0246226i
\(766\) 6.75798 0.244176
\(767\) 20.8728i 0.753673i
\(768\) −0.866025 0.500000i −0.0312500 0.0180422i
\(769\) 33.0922 1.19333 0.596667 0.802489i \(-0.296491\pi\)
0.596667 + 0.802489i \(0.296491\pi\)
\(770\) −23.7192 23.9517i −0.854781 0.863160i
\(771\) −7.10917 −0.256030
\(772\) −4.14545 + 2.39338i −0.149198 + 0.0861396i
\(773\) 23.9790 13.8443i 0.862464 0.497944i −0.00237240 0.999997i \(-0.500755\pi\)
0.864837 + 0.502053i \(0.167422\pi\)
\(774\) −6.18403 10.7111i −0.222280 0.385001i
\(775\) −0.170291 + 17.4549i −0.00611702 + 0.626999i
\(776\) −11.6594 −0.418550