Properties

Label 490.2.e.i.361.2
Level $490$
Weight $2$
Character 490.361
Analytic conductor $3.913$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 490.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.91266969904\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.2
Root \(-0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 490.361
Dual form 490.2.e.i.471.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.292893 + 0.507306i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -0.585786 q^{6} -1.00000 q^{8} +(1.32843 + 2.30090i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.292893 + 0.507306i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -0.585786 q^{6} -1.00000 q^{8} +(1.32843 + 2.30090i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-2.41421 + 4.18154i) q^{11} +(-0.292893 - 0.507306i) q^{12} +0.828427 q^{13} +0.585786 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.70711 + 4.68885i) q^{17} +(-1.32843 + 2.30090i) q^{18} +(-1.70711 - 2.95680i) q^{19} +1.00000 q^{20} -4.82843 q^{22} +(3.41421 + 5.91359i) q^{23} +(0.292893 - 0.507306i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.414214 + 0.717439i) q^{26} -3.31371 q^{27} +0.828427 q^{29} +(0.292893 + 0.507306i) q^{30} +(-1.41421 + 2.44949i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.41421 - 2.44949i) q^{33} -5.41421 q^{34} -2.65685 q^{36} +(-1.82843 - 3.16693i) q^{37} +(1.70711 - 2.95680i) q^{38} +(-0.242641 + 0.420266i) q^{39} +(0.500000 + 0.866025i) q^{40} +11.0711 q^{41} -3.17157 q^{43} +(-2.41421 - 4.18154i) q^{44} +(1.32843 - 2.30090i) q^{45} +(-3.41421 + 5.91359i) q^{46} +(-5.41421 - 9.37769i) q^{47} +0.585786 q^{48} -1.00000 q^{50} +(-1.58579 - 2.74666i) q^{51} +(-0.414214 + 0.717439i) q^{52} +(5.24264 - 9.08052i) q^{53} +(-1.65685 - 2.86976i) q^{54} +4.82843 q^{55} +2.00000 q^{57} +(0.414214 + 0.717439i) q^{58} +(-5.70711 + 9.88500i) q^{59} +(-0.292893 + 0.507306i) q^{60} +(6.65685 + 11.5300i) q^{61} -2.82843 q^{62} +1.00000 q^{64} +(-0.414214 - 0.717439i) q^{65} +(1.41421 - 2.44949i) q^{66} +(4.82843 - 8.36308i) q^{67} +(-2.70711 - 4.68885i) q^{68} -4.00000 q^{69} +12.4853 q^{71} +(-1.32843 - 2.30090i) q^{72} +(3.29289 - 5.70346i) q^{73} +(1.82843 - 3.16693i) q^{74} +(-0.292893 - 0.507306i) q^{75} +3.41421 q^{76} -0.485281 q^{78} +(0.585786 + 1.01461i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-3.01472 + 5.22165i) q^{81} +(5.53553 + 9.58783i) q^{82} +6.24264 q^{83} +5.41421 q^{85} +(-1.58579 - 2.74666i) q^{86} +(-0.242641 + 0.420266i) q^{87} +(2.41421 - 4.18154i) q^{88} +(6.36396 + 11.0227i) q^{89} +2.65685 q^{90} -6.82843 q^{92} +(-0.828427 - 1.43488i) q^{93} +(5.41421 - 9.37769i) q^{94} +(-1.70711 + 2.95680i) q^{95} +(0.292893 + 0.507306i) q^{96} -16.2426 q^{97} -12.8284 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{2} - 4q^{3} - 2q^{4} - 2q^{5} - 8q^{6} - 4q^{8} - 6q^{9} + O(q^{10}) \) \( 4q + 2q^{2} - 4q^{3} - 2q^{4} - 2q^{5} - 8q^{6} - 4q^{8} - 6q^{9} + 2q^{10} - 4q^{11} - 4q^{12} - 8q^{13} + 8q^{15} - 2q^{16} - 8q^{17} + 6q^{18} - 4q^{19} + 4q^{20} - 8q^{22} + 8q^{23} + 4q^{24} - 2q^{25} - 4q^{26} + 32q^{27} - 8q^{29} + 4q^{30} + 2q^{32} - 16q^{34} + 12q^{36} + 4q^{37} + 4q^{38} + 16q^{39} + 2q^{40} + 16q^{41} - 24q^{43} - 4q^{44} - 6q^{45} - 8q^{46} - 16q^{47} + 8q^{48} - 4q^{50} - 12q^{51} + 4q^{52} + 4q^{53} + 16q^{54} + 8q^{55} + 8q^{57} - 4q^{58} - 20q^{59} - 4q^{60} + 4q^{61} + 4q^{64} + 4q^{65} + 8q^{67} - 8q^{68} - 16q^{69} + 16q^{71} + 6q^{72} + 16q^{73} - 4q^{74} - 4q^{75} + 8q^{76} + 32q^{78} + 8q^{79} - 2q^{80} - 46q^{81} + 8q^{82} + 8q^{83} + 16q^{85} - 12q^{86} + 16q^{87} + 4q^{88} - 12q^{90} - 16q^{92} + 8q^{93} + 16q^{94} - 4q^{95} + 4q^{96} - 48q^{97} - 40q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/490\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) −0.292893 + 0.507306i −0.169102 + 0.292893i −0.938104 0.346353i \(-0.887420\pi\)
0.769002 + 0.639246i \(0.220753\pi\)
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) −0.585786 −0.239146
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) 1.32843 + 2.30090i 0.442809 + 0.766968i
\(10\) 0.500000 0.866025i 0.158114 0.273861i
\(11\) −2.41421 + 4.18154i −0.727913 + 1.26078i 0.229851 + 0.973226i \(0.426176\pi\)
−0.957764 + 0.287556i \(0.907157\pi\)
\(12\) −0.292893 0.507306i −0.0845510 0.146447i
\(13\) 0.828427 0.229764 0.114882 0.993379i \(-0.463351\pi\)
0.114882 + 0.993379i \(0.463351\pi\)
\(14\) 0 0
\(15\) 0.585786 0.151249
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −2.70711 + 4.68885i −0.656570 + 1.13721i 0.324928 + 0.945739i \(0.394660\pi\)
−0.981498 + 0.191474i \(0.938673\pi\)
\(18\) −1.32843 + 2.30090i −0.313113 + 0.542328i
\(19\) −1.70711 2.95680i −0.391637 0.678335i 0.601028 0.799228i \(-0.294758\pi\)
−0.992666 + 0.120892i \(0.961424\pi\)
\(20\) 1.00000 0.223607
\(21\) 0 0
\(22\) −4.82843 −1.02942
\(23\) 3.41421 + 5.91359i 0.711913 + 1.23307i 0.964138 + 0.265401i \(0.0855042\pi\)
−0.252226 + 0.967668i \(0.581162\pi\)
\(24\) 0.292893 0.507306i 0.0597866 0.103553i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 0.414214 + 0.717439i 0.0812340 + 0.140701i
\(27\) −3.31371 −0.637723
\(28\) 0 0
\(29\) 0.828427 0.153835 0.0769175 0.997037i \(-0.475492\pi\)
0.0769175 + 0.997037i \(0.475492\pi\)
\(30\) 0.292893 + 0.507306i 0.0534747 + 0.0926210i
\(31\) −1.41421 + 2.44949i −0.254000 + 0.439941i −0.964623 0.263631i \(-0.915080\pi\)
0.710623 + 0.703573i \(0.248413\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) −1.41421 2.44949i −0.246183 0.426401i
\(34\) −5.41421 −0.928530
\(35\) 0 0
\(36\) −2.65685 −0.442809
\(37\) −1.82843 3.16693i −0.300592 0.520640i 0.675679 0.737196i \(-0.263851\pi\)
−0.976270 + 0.216557i \(0.930517\pi\)
\(38\) 1.70711 2.95680i 0.276929 0.479656i
\(39\) −0.242641 + 0.420266i −0.0388536 + 0.0672964i
\(40\) 0.500000 + 0.866025i 0.0790569 + 0.136931i
\(41\) 11.0711 1.72901 0.864505 0.502624i \(-0.167632\pi\)
0.864505 + 0.502624i \(0.167632\pi\)
\(42\) 0 0
\(43\) −3.17157 −0.483660 −0.241830 0.970319i \(-0.577748\pi\)
−0.241830 + 0.970319i \(0.577748\pi\)
\(44\) −2.41421 4.18154i −0.363956 0.630391i
\(45\) 1.32843 2.30090i 0.198030 0.342998i
\(46\) −3.41421 + 5.91359i −0.503398 + 0.871911i
\(47\) −5.41421 9.37769i −0.789744 1.36788i −0.926124 0.377220i \(-0.876880\pi\)
0.136379 0.990657i \(-0.456453\pi\)
\(48\) 0.585786 0.0845510
\(49\) 0 0
\(50\) −1.00000 −0.141421
\(51\) −1.58579 2.74666i −0.222055 0.384610i
\(52\) −0.414214 + 0.717439i −0.0574411 + 0.0994909i
\(53\) 5.24264 9.08052i 0.720132 1.24731i −0.240814 0.970571i \(-0.577415\pi\)
0.960947 0.276734i \(-0.0892521\pi\)
\(54\) −1.65685 2.86976i −0.225469 0.390524i
\(55\) 4.82843 0.651065
\(56\) 0 0
\(57\) 2.00000 0.264906
\(58\) 0.414214 + 0.717439i 0.0543889 + 0.0942043i
\(59\) −5.70711 + 9.88500i −0.743002 + 1.28692i 0.208120 + 0.978103i \(0.433265\pi\)
−0.951122 + 0.308814i \(0.900068\pi\)
\(60\) −0.292893 + 0.507306i −0.0378124 + 0.0654929i
\(61\) 6.65685 + 11.5300i 0.852323 + 1.47627i 0.879107 + 0.476625i \(0.158140\pi\)
−0.0267837 + 0.999641i \(0.508527\pi\)
\(62\) −2.82843 −0.359211
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −0.414214 0.717439i −0.0513769 0.0889873i
\(66\) 1.41421 2.44949i 0.174078 0.301511i
\(67\) 4.82843 8.36308i 0.589886 1.02171i −0.404361 0.914600i \(-0.632506\pi\)
0.994247 0.107113i \(-0.0341608\pi\)
\(68\) −2.70711 4.68885i −0.328285 0.568606i
\(69\) −4.00000 −0.481543
\(70\) 0 0
\(71\) 12.4853 1.48173 0.740865 0.671654i \(-0.234416\pi\)
0.740865 + 0.671654i \(0.234416\pi\)
\(72\) −1.32843 2.30090i −0.156557 0.271164i
\(73\) 3.29289 5.70346i 0.385404 0.667539i −0.606421 0.795144i \(-0.707395\pi\)
0.991825 + 0.127604i \(0.0407288\pi\)
\(74\) 1.82843 3.16693i 0.212550 0.368148i
\(75\) −0.292893 0.507306i −0.0338204 0.0585786i
\(76\) 3.41421 0.391637
\(77\) 0 0
\(78\) −0.485281 −0.0549473
\(79\) 0.585786 + 1.01461i 0.0659061 + 0.114153i 0.897096 0.441837i \(-0.145673\pi\)
−0.831189 + 0.555989i \(0.812340\pi\)
\(80\) −0.500000 + 0.866025i −0.0559017 + 0.0968246i
\(81\) −3.01472 + 5.22165i −0.334969 + 0.580183i
\(82\) 5.53553 + 9.58783i 0.611297 + 1.05880i
\(83\) 6.24264 0.685219 0.342609 0.939478i \(-0.388689\pi\)
0.342609 + 0.939478i \(0.388689\pi\)
\(84\) 0 0
\(85\) 5.41421 0.587254
\(86\) −1.58579 2.74666i −0.171000 0.296180i
\(87\) −0.242641 + 0.420266i −0.0260138 + 0.0450572i
\(88\) 2.41421 4.18154i 0.257356 0.445754i
\(89\) 6.36396 + 11.0227i 0.674579 + 1.16840i 0.976592 + 0.215101i \(0.0690079\pi\)
−0.302013 + 0.953304i \(0.597659\pi\)
\(90\) 2.65685 0.280057
\(91\) 0 0
\(92\) −6.82843 −0.711913
\(93\) −0.828427 1.43488i −0.0859039 0.148790i
\(94\) 5.41421 9.37769i 0.558433 0.967235i
\(95\) −1.70711 + 2.95680i −0.175145 + 0.303361i
\(96\) 0.292893 + 0.507306i 0.0298933 + 0.0517767i
\(97\) −16.2426 −1.64919 −0.824595 0.565723i \(-0.808597\pi\)
−0.824595 + 0.565723i \(0.808597\pi\)
\(98\) 0 0
\(99\) −12.8284 −1.28931
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) 4.65685 8.06591i 0.463374 0.802588i −0.535752 0.844375i \(-0.679972\pi\)
0.999127 + 0.0417874i \(0.0133052\pi\)
\(102\) 1.58579 2.74666i 0.157016 0.271960i
\(103\) 4.58579 + 7.94282i 0.451851 + 0.782629i 0.998501 0.0547323i \(-0.0174305\pi\)
−0.546650 + 0.837361i \(0.684097\pi\)
\(104\) −0.828427 −0.0812340
\(105\) 0 0
\(106\) 10.4853 1.01842
\(107\) 0.828427 + 1.43488i 0.0800871 + 0.138715i 0.903287 0.429036i \(-0.141147\pi\)
−0.823200 + 0.567751i \(0.807813\pi\)
\(108\) 1.65685 2.86976i 0.159431 0.276142i
\(109\) 7.24264 12.5446i 0.693719 1.20156i −0.276891 0.960901i \(-0.589304\pi\)
0.970611 0.240656i \(-0.0773624\pi\)
\(110\) 2.41421 + 4.18154i 0.230186 + 0.398694i
\(111\) 2.14214 0.203323
\(112\) 0 0
\(113\) 7.31371 0.688016 0.344008 0.938967i \(-0.388215\pi\)
0.344008 + 0.938967i \(0.388215\pi\)
\(114\) 1.00000 + 1.73205i 0.0936586 + 0.162221i
\(115\) 3.41421 5.91359i 0.318377 0.551445i
\(116\) −0.414214 + 0.717439i −0.0384588 + 0.0666125i
\(117\) 1.10051 + 1.90613i 0.101742 + 0.176222i
\(118\) −11.4142 −1.05076
\(119\) 0 0
\(120\) −0.585786 −0.0534747
\(121\) −6.15685 10.6640i −0.559714 0.969453i
\(122\) −6.65685 + 11.5300i −0.602683 + 1.04388i
\(123\) −3.24264 + 5.61642i −0.292379 + 0.506415i
\(124\) −1.41421 2.44949i −0.127000 0.219971i
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −2.82843 −0.250982 −0.125491 0.992095i \(-0.540051\pi\)
−0.125491 + 0.992095i \(0.540051\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0.928932 1.60896i 0.0817879 0.141661i
\(130\) 0.414214 0.717439i 0.0363289 0.0629236i
\(131\) −1.12132 1.94218i −0.0979702 0.169689i 0.812874 0.582439i \(-0.197902\pi\)
−0.910844 + 0.412750i \(0.864568\pi\)
\(132\) 2.82843 0.246183
\(133\) 0 0
\(134\) 9.65685 0.834225
\(135\) 1.65685 + 2.86976i 0.142599 + 0.246989i
\(136\) 2.70711 4.68885i 0.232132 0.402065i
\(137\) 8.00000 13.8564i 0.683486 1.18383i −0.290424 0.956898i \(-0.593796\pi\)
0.973910 0.226935i \(-0.0728704\pi\)
\(138\) −2.00000 3.46410i −0.170251 0.294884i
\(139\) 0.100505 0.00852473 0.00426236 0.999991i \(-0.498643\pi\)
0.00426236 + 0.999991i \(0.498643\pi\)
\(140\) 0 0
\(141\) 6.34315 0.534189
\(142\) 6.24264 + 10.8126i 0.523871 + 0.907371i
\(143\) −2.00000 + 3.46410i −0.167248 + 0.289683i
\(144\) 1.32843 2.30090i 0.110702 0.191742i
\(145\) −0.414214 0.717439i −0.0343986 0.0595801i
\(146\) 6.58579 0.545044
\(147\) 0 0
\(148\) 3.65685 0.300592
\(149\) 3.00000 + 5.19615i 0.245770 + 0.425685i 0.962348 0.271821i \(-0.0876260\pi\)
−0.716578 + 0.697507i \(0.754293\pi\)
\(150\) 0.292893 0.507306i 0.0239146 0.0414214i
\(151\) −5.65685 + 9.79796i −0.460348 + 0.797347i −0.998978 0.0451959i \(-0.985609\pi\)
0.538630 + 0.842542i \(0.318942\pi\)
\(152\) 1.70711 + 2.95680i 0.138465 + 0.239828i
\(153\) −14.3848 −1.16294
\(154\) 0 0
\(155\) 2.82843 0.227185
\(156\) −0.242641 0.420266i −0.0194268 0.0336482i
\(157\) 5.24264 9.08052i 0.418408 0.724704i −0.577371 0.816482i \(-0.695921\pi\)
0.995780 + 0.0917773i \(0.0292548\pi\)
\(158\) −0.585786 + 1.01461i −0.0466027 + 0.0807182i
\(159\) 3.07107 + 5.31925i 0.243552 + 0.421844i
\(160\) −1.00000 −0.0790569
\(161\) 0 0
\(162\) −6.02944 −0.473717
\(163\) −4.07107 7.05130i −0.318871 0.552300i 0.661382 0.750049i \(-0.269970\pi\)
−0.980253 + 0.197749i \(0.936637\pi\)
\(164\) −5.53553 + 9.58783i −0.432253 + 0.748683i
\(165\) −1.41421 + 2.44949i −0.110096 + 0.190693i
\(166\) 3.12132 + 5.40629i 0.242261 + 0.419609i
\(167\) −23.7990 −1.84162 −0.920811 0.390010i \(-0.872471\pi\)
−0.920811 + 0.390010i \(0.872471\pi\)
\(168\) 0 0
\(169\) −12.3137 −0.947208
\(170\) 2.70711 + 4.68885i 0.207626 + 0.359618i
\(171\) 4.53553 7.85578i 0.346841 0.600746i
\(172\) 1.58579 2.74666i 0.120915 0.209431i
\(173\) 1.58579 + 2.74666i 0.120565 + 0.208825i 0.919991 0.391940i \(-0.128196\pi\)
−0.799426 + 0.600765i \(0.794863\pi\)
\(174\) −0.485281 −0.0367891
\(175\) 0 0
\(176\) 4.82843 0.363956
\(177\) −3.34315 5.79050i −0.251286 0.435241i
\(178\) −6.36396 + 11.0227i −0.476999 + 0.826187i
\(179\) −2.00000 + 3.46410i −0.149487 + 0.258919i −0.931038 0.364922i \(-0.881096\pi\)
0.781551 + 0.623841i \(0.214429\pi\)
\(180\) 1.32843 + 2.30090i 0.0990151 + 0.171499i
\(181\) 14.4853 1.07668 0.538341 0.842727i \(-0.319051\pi\)
0.538341 + 0.842727i \(0.319051\pi\)
\(182\) 0 0
\(183\) −7.79899 −0.576518
\(184\) −3.41421 5.91359i −0.251699 0.435956i
\(185\) −1.82843 + 3.16693i −0.134429 + 0.232837i
\(186\) 0.828427 1.43488i 0.0607432 0.105210i
\(187\) −13.0711 22.6398i −0.955851 1.65558i
\(188\) 10.8284 0.789744
\(189\) 0 0
\(190\) −3.41421 −0.247693
\(191\) 9.07107 + 15.7116i 0.656359 + 1.13685i 0.981551 + 0.191200i \(0.0612378\pi\)
−0.325192 + 0.945648i \(0.605429\pi\)
\(192\) −0.292893 + 0.507306i −0.0211377 + 0.0366117i
\(193\) 2.82843 4.89898i 0.203595 0.352636i −0.746089 0.665846i \(-0.768071\pi\)
0.949684 + 0.313210i \(0.101404\pi\)
\(194\) −8.12132 14.0665i −0.583077 1.00992i
\(195\) 0.485281 0.0347517
\(196\) 0 0
\(197\) 13.7990 0.983137 0.491569 0.870839i \(-0.336424\pi\)
0.491569 + 0.870839i \(0.336424\pi\)
\(198\) −6.41421 11.1097i −0.455838 0.789535i
\(199\) 0.242641 0.420266i 0.0172003 0.0297919i −0.857297 0.514822i \(-0.827858\pi\)
0.874497 + 0.485030i \(0.161191\pi\)
\(200\) 0.500000 0.866025i 0.0353553 0.0612372i
\(201\) 2.82843 + 4.89898i 0.199502 + 0.345547i
\(202\) 9.31371 0.655310
\(203\) 0 0
\(204\) 3.17157 0.222055
\(205\) −5.53553 9.58783i −0.386618 0.669643i
\(206\) −4.58579 + 7.94282i −0.319507 + 0.553402i
\(207\) −9.07107 + 15.7116i −0.630483 + 1.09203i
\(208\) −0.414214 0.717439i −0.0287205 0.0497454i
\(209\) 16.4853 1.14031
\(210\) 0 0
\(211\) −26.6274 −1.83311 −0.916553 0.399912i \(-0.869041\pi\)
−0.916553 + 0.399912i \(0.869041\pi\)
\(212\) 5.24264 + 9.08052i 0.360066 + 0.623653i
\(213\) −3.65685 + 6.33386i −0.250564 + 0.433989i
\(214\) −0.828427 + 1.43488i −0.0566301 + 0.0980862i
\(215\) 1.58579 + 2.74666i 0.108150 + 0.187321i
\(216\) 3.31371 0.225469
\(217\) 0 0
\(218\) 14.4853 0.981067
\(219\) 1.92893 + 3.34101i 0.130345 + 0.225764i
\(220\) −2.41421 + 4.18154i −0.162766 + 0.281919i
\(221\) −2.24264 + 3.88437i −0.150856 + 0.261291i
\(222\) 1.07107 + 1.85514i 0.0718854 + 0.124509i
\(223\) 15.3137 1.02548 0.512741 0.858543i \(-0.328630\pi\)
0.512741 + 0.858543i \(0.328630\pi\)
\(224\) 0 0
\(225\) −2.65685 −0.177124
\(226\) 3.65685 + 6.33386i 0.243250 + 0.421322i
\(227\) −4.87868 + 8.45012i −0.323809 + 0.560854i −0.981271 0.192634i \(-0.938297\pi\)
0.657461 + 0.753488i \(0.271630\pi\)
\(228\) −1.00000 + 1.73205i −0.0662266 + 0.114708i
\(229\) −6.07107 10.5154i −0.401187 0.694877i 0.592682 0.805437i \(-0.298069\pi\)
−0.993870 + 0.110559i \(0.964736\pi\)
\(230\) 6.82843 0.450253
\(231\) 0 0
\(232\) −0.828427 −0.0543889
\(233\) −0.343146 0.594346i −0.0224802 0.0389369i 0.854566 0.519342i \(-0.173823\pi\)
−0.877047 + 0.480405i \(0.840490\pi\)
\(234\) −1.10051 + 1.90613i −0.0719423 + 0.124608i
\(235\) −5.41421 + 9.37769i −0.353184 + 0.611733i
\(236\) −5.70711 9.88500i −0.371501 0.643459i
\(237\) −0.686292 −0.0445794
\(238\) 0 0
\(239\) −9.65685 −0.624650 −0.312325 0.949975i \(-0.601108\pi\)
−0.312325 + 0.949975i \(0.601108\pi\)
\(240\) −0.292893 0.507306i −0.0189062 0.0327465i
\(241\) 5.29289 9.16756i 0.340945 0.590534i −0.643663 0.765309i \(-0.722586\pi\)
0.984609 + 0.174774i \(0.0559196\pi\)
\(242\) 6.15685 10.6640i 0.395778 0.685507i
\(243\) −6.73654 11.6680i −0.432150 0.748505i
\(244\) −13.3137 −0.852323
\(245\) 0 0
\(246\) −6.48528 −0.413486
\(247\) −1.41421 2.44949i −0.0899843 0.155857i
\(248\) 1.41421 2.44949i 0.0898027 0.155543i
\(249\) −1.82843 + 3.16693i −0.115872 + 0.200696i
\(250\) 0.500000 + 0.866025i 0.0316228 + 0.0547723i
\(251\) 3.41421 0.215503 0.107752 0.994178i \(-0.465635\pi\)
0.107752 + 0.994178i \(0.465635\pi\)
\(252\) 0 0
\(253\) −32.9706 −2.07284
\(254\) −1.41421 2.44949i −0.0887357 0.153695i
\(255\) −1.58579 + 2.74666i −0.0993058 + 0.172003i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −4.94975 8.57321i −0.308757 0.534782i 0.669334 0.742962i \(-0.266580\pi\)
−0.978091 + 0.208179i \(0.933246\pi\)
\(258\) 1.85786 0.115666
\(259\) 0 0
\(260\) 0.828427 0.0513769
\(261\) 1.10051 + 1.90613i 0.0681196 + 0.117987i
\(262\) 1.12132 1.94218i 0.0692754 0.119989i
\(263\) −14.0000 + 24.2487i −0.863277 + 1.49524i 0.00547092 + 0.999985i \(0.498259\pi\)
−0.868748 + 0.495255i \(0.835075\pi\)
\(264\) 1.41421 + 2.44949i 0.0870388 + 0.150756i
\(265\) −10.4853 −0.644106
\(266\) 0 0
\(267\) −7.45584 −0.456290
\(268\) 4.82843 + 8.36308i 0.294943 + 0.510856i
\(269\) −0.757359 + 1.31178i −0.0461770 + 0.0799809i −0.888190 0.459476i \(-0.848037\pi\)
0.842013 + 0.539457i \(0.181370\pi\)
\(270\) −1.65685 + 2.86976i −0.100833 + 0.174648i
\(271\) −6.00000 10.3923i −0.364474 0.631288i 0.624218 0.781251i \(-0.285418\pi\)
−0.988692 + 0.149963i \(0.952085\pi\)
\(272\) 5.41421 0.328285
\(273\) 0 0
\(274\) 16.0000 0.966595
\(275\) −2.41421 4.18154i −0.145583 0.252156i
\(276\) 2.00000 3.46410i 0.120386 0.208514i
\(277\) −10.0711 + 17.4436i −0.605112 + 1.04808i 0.386922 + 0.922112i \(0.373538\pi\)
−0.992034 + 0.125972i \(0.959795\pi\)
\(278\) 0.0502525 + 0.0870399i 0.00301395 + 0.00522031i
\(279\) −7.51472 −0.449894
\(280\) 0 0
\(281\) 8.00000 0.477240 0.238620 0.971113i \(-0.423305\pi\)
0.238620 + 0.971113i \(0.423305\pi\)
\(282\) 3.17157 + 5.49333i 0.188864 + 0.327123i
\(283\) −3.12132 + 5.40629i −0.185543 + 0.321370i −0.943759 0.330633i \(-0.892738\pi\)
0.758216 + 0.652003i \(0.226071\pi\)
\(284\) −6.24264 + 10.8126i −0.370433 + 0.641608i
\(285\) −1.00000 1.73205i −0.0592349 0.102598i
\(286\) −4.00000 −0.236525
\(287\) 0 0
\(288\) 2.65685 0.156557
\(289\) −6.15685 10.6640i −0.362168 0.627293i
\(290\) 0.414214 0.717439i 0.0243235 0.0421295i
\(291\) 4.75736 8.23999i 0.278881 0.483037i
\(292\) 3.29289 + 5.70346i 0.192702 + 0.333770i
\(293\) −19.6569 −1.14837 −0.574183 0.818727i \(-0.694680\pi\)
−0.574183 + 0.818727i \(0.694680\pi\)
\(294\) 0 0
\(295\) 11.4142 0.664561
\(296\) 1.82843 + 3.16693i 0.106275 + 0.184074i
\(297\) 8.00000 13.8564i 0.464207 0.804030i
\(298\) −3.00000 + 5.19615i −0.173785 + 0.301005i
\(299\) 2.82843 + 4.89898i 0.163572 + 0.283315i
\(300\) 0.585786 0.0338204
\(301\) 0 0
\(302\) −11.3137 −0.651031
\(303\) 2.72792 + 4.72490i 0.156715 + 0.271438i
\(304\) −1.70711 + 2.95680i −0.0979093 + 0.169584i
\(305\) 6.65685 11.5300i 0.381170 0.660206i
\(306\) −7.19239 12.4576i −0.411161 0.712153i
\(307\) 29.0711 1.65917 0.829587 0.558378i \(-0.188576\pi\)
0.829587 + 0.558378i \(0.188576\pi\)
\(308\) 0 0
\(309\) −5.37258 −0.305636
\(310\) 1.41421 + 2.44949i 0.0803219 + 0.139122i
\(311\) −2.00000 + 3.46410i −0.113410 + 0.196431i −0.917143 0.398559i \(-0.869511\pi\)
0.803733 + 0.594990i \(0.202844\pi\)
\(312\) 0.242641 0.420266i 0.0137368 0.0237929i
\(313\) 11.1924 + 19.3858i 0.632631 + 1.09575i 0.987012 + 0.160648i \(0.0513584\pi\)
−0.354381 + 0.935101i \(0.615308\pi\)
\(314\) 10.4853 0.591719
\(315\) 0 0
\(316\) −1.17157 −0.0659061
\(317\) 3.24264 + 5.61642i 0.182125 + 0.315449i 0.942604 0.333913i \(-0.108369\pi\)
−0.760479 + 0.649362i \(0.775036\pi\)
\(318\) −3.07107 + 5.31925i −0.172217 + 0.298288i
\(319\) −2.00000 + 3.46410i −0.111979 + 0.193952i
\(320\) −0.500000 0.866025i −0.0279508 0.0484123i
\(321\) −0.970563 −0.0541715
\(322\) 0 0
\(323\) 18.4853 1.02855
\(324\) −3.01472 5.22165i −0.167484 0.290091i
\(325\) −0.414214 + 0.717439i −0.0229764 + 0.0397964i
\(326\) 4.07107 7.05130i 0.225476 0.390535i
\(327\) 4.24264 + 7.34847i 0.234619 + 0.406371i
\(328\) −11.0711 −0.611297
\(329\) 0 0
\(330\) −2.82843 −0.155700
\(331\) 2.89949 + 5.02207i 0.159371 + 0.276038i 0.934642 0.355590i \(-0.115720\pi\)
−0.775271 + 0.631628i \(0.782387\pi\)
\(332\) −3.12132 + 5.40629i −0.171305 + 0.296708i
\(333\) 4.85786 8.41407i 0.266209 0.461088i
\(334\) −11.8995 20.6105i −0.651111 1.12776i
\(335\) −9.65685 −0.527610
\(336\) 0 0
\(337\) 6.00000 0.326841 0.163420 0.986557i \(-0.447747\pi\)
0.163420 + 0.986557i \(0.447747\pi\)
\(338\) −6.15685 10.6640i −0.334889 0.580044i
\(339\) −2.14214 + 3.71029i −0.116345 + 0.201515i
\(340\) −2.70711 + 4.68885i −0.146813 + 0.254288i
\(341\) −6.82843 11.8272i −0.369780 0.640478i
\(342\) 9.07107 0.490507
\(343\) 0 0
\(344\) 3.17157 0.171000
\(345\) 2.00000 + 3.46410i 0.107676 + 0.186501i
\(346\) −1.58579 + 2.74666i −0.0852524 + 0.147662i
\(347\) 4.41421 7.64564i 0.236967 0.410440i −0.722875 0.690979i \(-0.757180\pi\)
0.959843 + 0.280539i \(0.0905132\pi\)
\(348\) −0.242641 0.420266i −0.0130069 0.0225286i
\(349\) −14.4853 −0.775379 −0.387690 0.921790i \(-0.626727\pi\)
−0.387690 + 0.921790i \(0.626727\pi\)
\(350\) 0 0
\(351\) −2.74517 −0.146526
\(352\) 2.41421 + 4.18154i 0.128678 + 0.222877i
\(353\) −17.1924 + 29.7781i −0.915058 + 1.58493i −0.108243 + 0.994124i \(0.534522\pi\)
−0.806816 + 0.590803i \(0.798811\pi\)
\(354\) 3.34315 5.79050i 0.177686 0.307762i
\(355\) −6.24264 10.8126i −0.331325 0.573872i
\(356\) −12.7279 −0.674579
\(357\) 0 0
\(358\) −4.00000 −0.211407
\(359\) 14.1421 + 24.4949i 0.746393 + 1.29279i 0.949541 + 0.313643i \(0.101550\pi\)
−0.203148 + 0.979148i \(0.565117\pi\)
\(360\) −1.32843 + 2.30090i −0.0700143 + 0.121268i
\(361\) 3.67157 6.35935i 0.193241 0.334703i
\(362\) 7.24264 + 12.5446i 0.380665 + 0.659331i
\(363\) 7.21320 0.378595
\(364\) 0 0
\(365\) −6.58579 −0.344716
\(366\) −3.89949 6.75412i −0.203830 0.353044i
\(367\) 4.48528 7.76874i 0.234130 0.405525i −0.724890 0.688865i \(-0.758109\pi\)
0.959019 + 0.283340i \(0.0914426\pi\)
\(368\) 3.41421 5.91359i 0.177978 0.308267i
\(369\) 14.7071 + 25.4735i 0.765621 + 1.32610i
\(370\) −3.65685 −0.190111
\(371\) 0 0
\(372\) 1.65685 0.0859039
\(373\) 6.75736 + 11.7041i 0.349883 + 0.606015i 0.986228 0.165389i \(-0.0528881\pi\)
−0.636346 + 0.771404i \(0.719555\pi\)
\(374\) 13.0711 22.6398i 0.675889 1.17067i
\(375\) −0.292893 + 0.507306i −0.0151249 + 0.0261972i
\(376\) 5.41421 + 9.37769i 0.279217 + 0.483618i
\(377\) 0.686292 0.0353458
\(378\) 0 0
\(379\) 17.5147 0.899671 0.449835 0.893112i \(-0.351483\pi\)
0.449835 + 0.893112i \(0.351483\pi\)
\(380\) −1.70711 2.95680i −0.0875727 0.151680i
\(381\) 0.828427 1.43488i 0.0424416 0.0735110i
\(382\) −9.07107 + 15.7116i −0.464116 + 0.803873i
\(383\) 7.75736 + 13.4361i 0.396383 + 0.686555i 0.993277 0.115765i \(-0.0369321\pi\)
−0.596894 + 0.802320i \(0.703599\pi\)
\(384\) −0.585786 −0.0298933
\(385\) 0 0
\(386\) 5.65685 0.287926
\(387\) −4.21320 7.29748i −0.214169 0.370952i
\(388\) 8.12132 14.0665i 0.412298 0.714120i
\(389\) 0.0710678 0.123093i 0.00360328 0.00624107i −0.864218 0.503117i \(-0.832186\pi\)
0.867821 + 0.496876i \(0.165520\pi\)
\(390\) 0.242641 + 0.420266i 0.0122866 + 0.0212810i
\(391\) −36.9706 −1.86968
\(392\) 0 0
\(393\) 1.31371 0.0662678
\(394\) 6.89949 + 11.9503i 0.347592 + 0.602046i
\(395\) 0.585786 1.01461i 0.0294741 0.0510507i
\(396\) 6.41421 11.1097i 0.322326 0.558286i
\(397\) 2.89949 + 5.02207i 0.145521 + 0.252051i 0.929567 0.368652i \(-0.120181\pi\)
−0.784046 + 0.620703i \(0.786847\pi\)
\(398\) 0.485281 0.0243250
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) 3.00000 + 5.19615i 0.149813 + 0.259483i 0.931158 0.364615i \(-0.118800\pi\)
−0.781345 + 0.624099i \(0.785466\pi\)
\(402\) −2.82843 + 4.89898i −0.141069 + 0.244339i
\(403\) −1.17157 + 2.02922i −0.0583602 + 0.101083i
\(404\) 4.65685 + 8.06591i 0.231687 + 0.401294i
\(405\) 6.02944 0.299605
\(406\) 0 0
\(407\) 17.6569 0.875218
\(408\) 1.58579 + 2.74666i 0.0785081 + 0.135980i
\(409\) 6.70711 11.6170i 0.331645 0.574426i −0.651189 0.758915i \(-0.725730\pi\)
0.982835 + 0.184489i \(0.0590630\pi\)
\(410\) 5.53553 9.58783i 0.273381 0.473509i
\(411\) 4.68629 + 8.11689i 0.231158 + 0.400377i
\(412\) −9.17157 −0.451851
\(413\) 0 0
\(414\) −18.1421 −0.891637
\(415\) −3.12132 5.40629i −0.153220 0.265384i
\(416\) 0.414214 0.717439i 0.0203085 0.0351753i
\(417\) −0.0294373 + 0.0509868i −0.00144155 + 0.00249684i
\(418\) 8.24264 + 14.2767i 0.403161 + 0.698295i
\(419\) 32.8701 1.60581 0.802904 0.596109i \(-0.203287\pi\)
0.802904 + 0.596109i \(0.203287\pi\)
\(420\) 0 0
\(421\) −5.31371 −0.258974 −0.129487 0.991581i \(-0.541333\pi\)
−0.129487 + 0.991581i \(0.541333\pi\)
\(422\) −13.3137 23.0600i −0.648101 1.12254i
\(423\) 14.3848 24.9152i 0.699412 1.21142i
\(424\) −5.24264 + 9.08052i −0.254605 + 0.440989i
\(425\) −2.70711 4.68885i −0.131314 0.227442i
\(426\) −7.31371 −0.354350
\(427\) 0 0
\(428\) −1.65685 −0.0800871
\(429\) −1.17157 2.02922i −0.0565641 0.0979718i
\(430\) −1.58579 + 2.74666i −0.0764734 + 0.132456i
\(431\) 16.8284 29.1477i 0.810597 1.40399i −0.101850 0.994800i \(-0.532476\pi\)
0.912447 0.409195i \(-0.134190\pi\)
\(432\) 1.65685 + 2.86976i 0.0797154 + 0.138071i
\(433\) 13.4142 0.644646 0.322323 0.946630i \(-0.395536\pi\)
0.322323 + 0.946630i \(0.395536\pi\)
\(434\) 0 0
\(435\) 0.485281 0.0232675
\(436\) 7.24264 + 12.5446i 0.346860 + 0.600778i
\(437\) 11.6569 20.1903i 0.557623 0.965831i
\(438\) −1.92893 + 3.34101i −0.0921679 + 0.159640i
\(439\) −4.48528 7.76874i −0.214071 0.370782i 0.738914 0.673800i \(-0.235339\pi\)
−0.952985 + 0.303018i \(0.902006\pi\)
\(440\) −4.82843 −0.230186
\(441\) 0 0
\(442\) −4.48528 −0.213343
\(443\) −18.4853 32.0174i −0.878262 1.52119i −0.853247 0.521508i \(-0.825370\pi\)
−0.0250157 0.999687i \(-0.507964\pi\)
\(444\) −1.07107 + 1.85514i −0.0508306 + 0.0880412i
\(445\) 6.36396 11.0227i 0.301681 0.522526i
\(446\) 7.65685 + 13.2621i 0.362563 + 0.627977i
\(447\) −3.51472 −0.166240
\(448\) 0 0
\(449\) 28.6274 1.35101 0.675506 0.737355i \(-0.263925\pi\)
0.675506 + 0.737355i \(0.263925\pi\)
\(450\) −1.32843 2.30090i −0.0626227 0.108466i
\(451\) −26.7279 + 46.2941i −1.25857 + 2.17990i
\(452\) −3.65685 + 6.33386i −0.172004 + 0.297920i
\(453\) −3.31371 5.73951i −0.155692 0.269666i
\(454\) −9.75736 −0.457936
\(455\) 0 0
\(456\) −2.00000 −0.0936586
\(457\) −5.17157 8.95743i −0.241916 0.419011i 0.719344 0.694654i \(-0.244443\pi\)
−0.961260 + 0.275643i \(0.911109\pi\)
\(458\) 6.07107 10.5154i 0.283682 0.491352i
\(459\) 8.97056 15.5375i 0.418710 0.725227i
\(460\) 3.41421 + 5.91359i 0.159189 + 0.275723i
\(461\) −7.17157 −0.334013 −0.167007 0.985956i \(-0.553410\pi\)
−0.167007 + 0.985956i \(0.553410\pi\)
\(462\) 0 0
\(463\) 16.9706 0.788689 0.394344 0.918963i \(-0.370972\pi\)
0.394344 + 0.918963i \(0.370972\pi\)
\(464\) −0.414214 0.717439i −0.0192294 0.0333063i
\(465\) −0.828427 + 1.43488i −0.0384174 + 0.0665409i
\(466\) 0.343146 0.594346i 0.0158959 0.0275325i
\(467\) −1.94975 3.37706i −0.0902236 0.156272i 0.817382 0.576097i \(-0.195425\pi\)
−0.907605 + 0.419825i \(0.862091\pi\)
\(468\) −2.20101 −0.101742
\(469\) 0 0
\(470\) −10.8284 −0.499478
\(471\) 3.07107 + 5.31925i 0.141507 + 0.245098i
\(472\) 5.70711 9.88500i 0.262691 0.454994i
\(473\) 7.65685 13.2621i 0.352063 0.609790i
\(474\) −0.343146 0.594346i −0.0157612 0.0272992i
\(475\) 3.41421 0.156655
\(476\) 0 0
\(477\) 27.8579 1.27552
\(478\) −4.82843 8.36308i −0.220847 0.382518i
\(479\) 11.4142 19.7700i 0.521529 0.903314i −0.478158 0.878274i \(-0.658695\pi\)
0.999686 0.0250403i \(-0.00797140\pi\)
\(480\) 0.292893 0.507306i 0.0133687 0.0231552i
\(481\) −1.51472 2.62357i −0.0690652 0.119624i
\(482\) 10.5858 0.482169
\(483\) 0 0
\(484\) 12.3137 0.559714
\(485\) 8.12132 + 14.0665i 0.368770 + 0.638729i
\(486\) 6.73654 11.6680i 0.305576 0.529273i
\(487\) 3.89949 6.75412i 0.176703 0.306059i −0.764046 0.645161i \(-0.776790\pi\)
0.940749 + 0.339103i \(0.110123\pi\)
\(488\) −6.65685 11.5300i −0.301342 0.521939i
\(489\) 4.76955 0.215687
\(490\) 0 0
\(491\) −24.2843 −1.09593 −0.547967 0.836500i \(-0.684598\pi\)
−0.547967 + 0.836500i \(0.684598\pi\)
\(492\) −3.24264 5.61642i −0.146190 0.253208i
\(493\) −2.24264 + 3.88437i −0.101003 + 0.174943i
\(494\) 1.41421 2.44949i 0.0636285 0.110208i
\(495\) 6.41421 + 11.1097i 0.288297 + 0.499346i
\(496\) 2.82843 0.127000
\(497\) 0 0
\(498\) −3.65685 −0.163868
\(499\) −20.8284 36.0759i −0.932408 1.61498i −0.779191 0.626786i \(-0.784370\pi\)
−0.153217 0.988193i \(-0.548963\pi\)
\(500\) −0.500000 + 0.866025i −0.0223607 + 0.0387298i
\(501\) 6.97056 12.0734i 0.311422 0.539398i
\(502\) 1.70711 + 2.95680i 0.0761919 + 0.131968i
\(503\) 6.34315 0.282827 0.141413 0.989951i \(-0.454835\pi\)
0.141413 + 0.989951i \(0.454835\pi\)
\(504\) 0 0
\(505\) −9.31371 −0.414455
\(506\) −16.4853 28.5533i −0.732860 1.26935i
\(507\) 3.60660 6.24682i 0.160175 0.277431i
\(508\) 1.41421 2.44949i 0.0627456 0.108679i
\(509\) 16.8995 + 29.2708i 0.749057 + 1.29740i 0.948275 + 0.317450i \(0.102826\pi\)
−0.199218 + 0.979955i \(0.563840\pi\)
\(510\) −3.17157 −0.140440
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 5.65685 + 9.79796i 0.249756 + 0.432590i
\(514\) 4.94975 8.57321i 0.218324 0.378148i
\(515\) 4.58579 7.94282i 0.202074 0.350002i
\(516\) 0.928932 + 1.60896i 0.0408940 + 0.0708304i
\(517\) 52.2843 2.29946
\(518\) 0 0
\(519\) −1.85786 −0.0815512
\(520\) 0.414214 + 0.717439i 0.0181645 + 0.0314618i
\(521\) −2.46447 + 4.26858i −0.107970 + 0.187010i −0.914948 0.403572i \(-0.867768\pi\)
0.806978 + 0.590582i \(0.201102\pi\)
\(522\) −1.10051 + 1.90613i −0.0481678 + 0.0834291i
\(523\) −2.05025 3.55114i −0.0896513 0.155281i 0.817712 0.575627i \(-0.195242\pi\)
−0.907364 + 0.420346i \(0.861909\pi\)
\(524\) 2.24264 0.0979702
\(525\) 0 0
\(526\) −28.0000 −1.22086
\(527\) −7.65685 13.2621i −0.333538 0.577704i
\(528\) −1.41421 + 2.44949i −0.0615457 + 0.106600i
\(529\) −11.8137 + 20.4619i −0.513639 + 0.889650i
\(530\) −5.24264 9.08052i −0.227726 0.394433i
\(531\) −30.3259 −1.31603
\(532\) 0 0
\(533\) 9.17157 0.397265
\(534\) −3.72792 6.45695i −0.161323 0.279420i
\(535\) 0.828427 1.43488i 0.0358160 0.0620352i
\(536\) −4.82843 + 8.36308i −0.208556 + 0.361230i
\(537\) −1.17157 2.02922i −0.0505571 0.0875675i
\(538\) −1.51472 −0.0653042
\(539\) 0 0
\(540\) −3.31371 −0.142599
\(541\) −9.48528 16.4290i −0.407804 0.706337i 0.586839 0.809703i \(-0.300372\pi\)
−0.994643 + 0.103366i \(0.967039\pi\)
\(542\) 6.00000 10.3923i 0.257722 0.446388i
\(543\) −4.24264 + 7.34847i −0.182069 + 0.315353i
\(544\) 2.70711 + 4.68885i 0.116066 + 0.201033i
\(545\) −14.4853 −0.620481
\(546\) 0 0
\(547\) 6.48528 0.277291 0.138645 0.990342i \(-0.455725\pi\)
0.138645 + 0.990342i \(0.455725\pi\)
\(548\) 8.00000 + 13.8564i 0.341743 + 0.591916i
\(549\) −17.6863 + 30.6336i −0.754833 + 1.30741i
\(550\) 2.41421 4.18154i 0.102942 0.178301i
\(551\) −1.41421 2.44949i −0.0602475 0.104352i
\(552\) 4.00000 0.170251
\(553\) 0 0
\(554\) −20.1421 −0.855757
\(555\) −1.07107 1.85514i −0.0454643 0.0787465i
\(556\) −0.0502525 + 0.0870399i −0.00213118 + 0.00369132i
\(557\) −10.4142 + 18.0379i −0.441264 + 0.764292i −0.997784 0.0665424i \(-0.978803\pi\)
0.556519 + 0.830835i \(0.312137\pi\)
\(558\) −3.75736 6.50794i −0.159062 0.275503i
\(559\) −2.62742 −0.111128
\(560\) 0 0
\(561\) 15.3137 0.646545
\(562\) 4.00000 + 6.92820i 0.168730 + 0.292249i
\(563\) 19.7071 34.1337i 0.830556 1.43856i −0.0670428 0.997750i \(-0.521356\pi\)
0.897598 0.440814i \(-0.145310\pi\)
\(564\) −3.17157 + 5.49333i −0.133547 + 0.231311i
\(565\) −3.65685 6.33386i −0.153845 0.266467i
\(566\) −6.24264 −0.262398
\(567\) 0 0
\(568\) −12.4853 −0.523871
\(569\) 3.34315 + 5.79050i 0.140152 + 0.242750i 0.927554 0.373690i \(-0.121908\pi\)
−0.787402 + 0.616440i \(0.788574\pi\)
\(570\) 1.00000 1.73205i 0.0418854 0.0725476i
\(571\) 20.8995 36.1990i 0.874617 1.51488i 0.0174461 0.999848i \(-0.494446\pi\)
0.857171 0.515033i \(-0.172220\pi\)
\(572\) −2.00000 3.46410i −0.0836242 0.144841i
\(573\) −10.6274 −0.443967
\(574\) 0 0
\(575\) −6.82843 −0.284765
\(576\) 1.32843 + 2.30090i 0.0553511 + 0.0958710i
\(577\) −12.9497 + 22.4296i −0.539105 + 0.933757i 0.459847 + 0.887998i \(0.347904\pi\)
−0.998952 + 0.0457594i \(0.985429\pi\)
\(578\) 6.15685 10.6640i 0.256091 0.443563i
\(579\) 1.65685 + 2.86976i 0.0688565 + 0.119263i
\(580\) 0.828427 0.0343986
\(581\) 0 0
\(582\) 9.51472 0.394398
\(583\) 25.3137 + 43.8446i 1.04839 + 1.81586i
\(584\) −3.29289 + 5.70346i −0.136261 + 0.236011i
\(585\) 1.10051 1.90613i 0.0455003 0.0788088i
\(586\) −9.82843 17.0233i −0.406009 0.703227i
\(587\) 2.92893 0.120890 0.0604450 0.998172i \(-0.480748\pi\)
0.0604450 + 0.998172i \(0.480748\pi\)
\(588\) 0 0
\(589\) 9.65685 0.397904
\(590\) 5.70711 + 9.88500i 0.234958 + 0.406959i
\(591\) −4.04163 + 7.00031i −0.166250 + 0.287954i
\(592\) −1.82843 + 3.16693i −0.0751479 + 0.130160i
\(593\) −14.3640 24.8791i −0.589857 1.02166i −0.994251 0.107078i \(-0.965851\pi\)
0.404393 0.914585i \(-0.367483\pi\)
\(594\) 16.0000 0.656488
\(595\) 0 0
\(596\) −6.00000 −0.245770
\(597\) 0.142136 + 0.246186i 0.00581722 + 0.0100757i
\(598\) −2.82843 + 4.89898i −0.115663 + 0.200334i
\(599\) 2.58579 4.47871i 0.105652 0.182995i −0.808352 0.588699i \(-0.799640\pi\)
0.914005 + 0.405704i \(0.132974\pi\)
\(600\) 0.292893 + 0.507306i 0.0119573 + 0.0207107i
\(601\) 9.41421 0.384014 0.192007 0.981394i \(-0.438500\pi\)
0.192007 + 0.981394i \(0.438500\pi\)
\(602\) 0 0
\(603\) 25.6569 1.04483
\(604\) −5.65685 9.79796i −0.230174 0.398673i
\(605\) −6.15685 + 10.6640i −0.250312 + 0.433553i
\(606\) −2.72792 + 4.72490i −0.110814 + 0.191936i
\(607\) 20.1421 + 34.8872i 0.817544 + 1.41603i 0.907487 + 0.420081i \(0.137998\pi\)
−0.0899426 + 0.995947i \(0.528668\pi\)
\(608\) −3.41421 −0.138465
\(609\) 0 0
\(610\) 13.3137 0.539056
\(611\) −4.48528 7.76874i −0.181455 0.314289i
\(612\) 7.19239 12.4576i 0.290735 0.503568i
\(613\) 11.8284 20.4874i 0.477746 0.827480i −0.521929 0.852989i \(-0.674787\pi\)
0.999675 + 0.0255092i \(0.00812071\pi\)
\(614\) 14.5355 + 25.1763i 0.586606 + 1.01603i
\(615\) 6.48528 0.261512
\(616\) 0 0
\(617\) −10.6863 −0.430214 −0.215107 0.976590i \(-0.569010\pi\)
−0.215107 + 0.976590i \(0.569010\pi\)
\(618\) −2.68629 4.65279i −0.108058 0.187163i
\(619\) −7.46447 + 12.9288i −0.300022 + 0.519654i −0.976141 0.217139i \(-0.930327\pi\)
0.676118 + 0.736793i \(0.263661\pi\)
\(620\) −1.41421 + 2.44949i −0.0567962 + 0.0983739i
\(621\) −11.3137 19.5959i −0.454003 0.786357i
\(622\) −4.00000 −0.160385
\(623\) 0 0
\(624\) 0.485281 0.0194268
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) −11.1924 + 19.3858i −0.447338 + 0.774812i
\(627\) −4.82843 + 8.36308i −0.192829 + 0.333989i
\(628\) 5.24264 + 9.08052i 0.209204 + 0.362352i
\(629\) 19.7990 0.789437
\(630\) 0 0
\(631\) 4.48528 0.178556 0.0892781 0.996007i \(-0.471544\pi\)
0.0892781 + 0.996007i \(0.471544\pi\)
\(632\) −0.585786 1.01461i −0.0233013 0.0403591i
\(633\) 7.79899 13.5082i 0.309982 0.536905i
\(634\) −3.24264 + 5.61642i −0.128782 + 0.223056i
\(635\) 1.41421 + 2.44949i 0.0561214 + 0.0972050i
\(636\) −6.14214 −0.243552
\(637\) 0 0
\(638\) −4.00000 −0.158362
\(639\) 16.5858 + 28.7274i 0.656124 + 1.13644i
\(640\) 0.500000 0.866025i 0.0197642 0.0342327i
\(641\) −10.3137 + 17.8639i −0.407367 + 0.705580i −0.994594 0.103842i \(-0.966886\pi\)
0.587227 + 0.809422i \(0.300220\pi\)
\(642\) −0.485281 0.840532i −0.0191525 0.0331732i
\(643\) 47.2132 1.86191 0.930953 0.365138i \(-0.118978\pi\)
0.930953 + 0.365138i \(0.118978\pi\)
\(644\) 0 0
\(645\) −1.85786 −0.0731533
\(646\) 9.24264 + 16.0087i 0.363647 + 0.629855i
\(647\) −19.5563 + 33.8726i −0.768839 + 1.33167i 0.169353 + 0.985555i \(0.445832\pi\)
−0.938193 + 0.346114i \(0.887501\pi\)
\(648\) 3.01472 5.22165i 0.118429 0.205126i
\(649\) −27.5563 47.7290i −1.08168 1.87353i
\(650\) −0.828427 −0.0324936
\(651\) 0 0
\(652\) 8.14214 0.318871
\(653\) −7.82843 13.5592i −0.306350 0.530614i 0.671211 0.741266i \(-0.265774\pi\)
−0.977561 + 0.210653i \(0.932441\pi\)
\(654\) −4.24264 + 7.34847i −0.165900 + 0.287348i
\(655\) −1.12132 + 1.94218i −0.0438136 + 0.0758874i
\(656\) −5.53553 9.58783i −0.216126 0.374342i
\(657\) 17.4975 0.682642
\(658\) 0 0
\(659\) −32.8284 −1.27881 −0.639407 0.768868i \(-0.720820\pi\)
−0.639407 + 0.768868i \(0.720820\pi\)
\(660\) −1.41421 2.44949i −0.0550482 0.0953463i
\(661\) −9.14214 + 15.8346i −0.355588 + 0.615896i −0.987218 0.159373i \(-0.949053\pi\)
0.631631 + 0.775270i \(0.282386\pi\)
\(662\) −2.89949 + 5.02207i −0.112692 + 0.195188i
\(663\) −1.31371 2.27541i −0.0510202 0.0883696i
\(664\) −6.24264 −0.242261
\(665\) 0 0
\(666\) 9.71573 0.376477
\(667\) 2.82843 + 4.89898i 0.109517 + 0.189689i
\(668\) 11.8995 20.6105i 0.460405 0.797445i
\(669\) −4.48528 + 7.76874i −0.173411 + 0.300357i
\(670\) −4.82843 8.36308i −0.186538 0.323094i
\(671\) −64.2843 −2.48167
\(672\) 0 0
\(673\) −48.0000 −1.85026 −0.925132 0.379646i \(-0.876046\pi\)
−0.925132 + 0.379646i \(0.876046\pi\)
\(674\) 3.00000 + 5.19615i 0.115556 + 0.200148i
\(675\) 1.65685 2.86976i 0.0637723 0.110457i
\(676\) 6.15685 10.6640i 0.236802 0.410153i
\(677\) 5.72792 + 9.92105i 0.220142 + 0.381297i 0.954851 0.297085i \(-0.0960146\pi\)
−0.734709 + 0.678382i \(0.762681\pi\)
\(678\) −4.28427 −0.164536
\(679\) 0 0
\(680\) −5.41421 −0.207626
\(681\) −2.85786 4.94997i −0.109514 0.189683i
\(682\) 6.82843 11.8272i 0.261474 0.452886i
\(683\) −11.1716 + 19.3497i −0.427468 + 0.740397i −0.996647 0.0818167i \(-0.973928\pi\)
0.569179 + 0.822214i \(0.307261\pi\)
\(684\) 4.53553 + 7.85578i 0.173420 + 0.300373i
\(685\) −16.0000 −0.611329
\(686\) 0 0
\(687\) 7.11270 0.271366
\(688\) 1.58579 + 2.74666i 0.0604575 + 0.104716i
\(689\) 4.34315 7.52255i 0.165461 0.286586i
\(690\) −2.00000 + 3.46410i −0.0761387 + 0.131876i
\(691\) −5.12132 8.87039i −0.194824 0.337445i 0.752019 0.659142i \(-0.229080\pi\)
−0.946843 + 0.321696i \(0.895747\pi\)
\(692\) −3.17157 −0.120565
\(693\) 0 0
\(694\) 8.82843 0.335123
\(695\) −0.0502525 0.0870399i −0.00190619 0.00330161i
\(696\) 0.242641 0.420266i 0.00919727 0.0159301i
\(697\) −29.9706 + 51.9105i −1.13522 + 1.96625i
\(698\) −7.24264 12.5446i −0.274138 0.474821i
\(699\) 0.402020 0.0152058
\(700\) 0 0
\(701\) −14.4853 −0.547102 −0.273551 0.961858i \(-0.588198\pi\)
−0.273551 + 0.961858i \(0.588198\pi\)
\(702\) −1.37258 2.37738i −0.0518048 0.0897286i
\(703\) −6.24264 + 10.8126i −0.235446 + 0.407804i
\(704\) −2.41421 + 4.18154i −0.0909891 + 0.157598i
\(705\) −3.17157 5.49333i −0.119448 0.206891i
\(706\) −34.3848 −1.29409
\(707\) 0 0
\(708\) 6.68629 0.251286
\(709\) 8.55635 + 14.8200i 0.321340 + 0.556578i 0.980765 0.195193i \(-0.0625333\pi\)
−0.659424 + 0.751771i \(0.729200\pi\)
\(710\) 6.24264 10.8126i 0.234282 0.405789i
\(711\) −1.55635 + 2.69568i −0.0583677 + 0.101096i
\(712\) −6.36396 11.0227i −0.238500 0.413093i
\(713\) −19.3137 −0.723304
\(714\) 0 0
\(715\) 4.00000 0.149592
\(716\) −2.00000 3.46410i −0.0747435 0.129460i
\(717\) 2.82843 4.89898i 0.105630 0.182956i
\(718\) −14.1421 + 24.4949i −0.527780 + 0.914141i
\(719\) 4.72792 + 8.18900i 0.176322 + 0.305398i 0.940618 0.339467i \(-0.110247\pi\)
−0.764296 + 0.644865i \(0.776913\pi\)
\(720\) −2.65685 −0.0990151
\(721\) 0 0
\(722\) 7.34315 0.273284
\(723\) 3.10051 + 5.37023i 0.115309 + 0.199721i
\(724\) −7.24264 + 12.5446i −0.269171 + 0.466217i
\(725\) −0.414214 + 0.717439i −0.0153835 + 0.0266450i
\(726\) 3.60660 + 6.24682i 0.133854 + 0.231841i
\(727\) −20.4853 −0.759757 −0.379879 0.925036i \(-0.624034\pi\)
−0.379879 + 0.925036i \(0.624034\pi\)
\(728\) 0 0
\(729\) −10.1960 −0.377628
\(730\) −3.29289 5.70346i −0.121875 0.211094i
\(731\) 8.58579 14.8710i 0.317557 0.550024i
\(732\) 3.89949 6.75412i 0.144129 0.249640i
\(733\) −17.0000 29.4449i −0.627909 1.08757i −0.987971 0.154642i \(-0.950578\pi\)
0.360061 0.932929i \(-0.382756\pi\)
\(734\) 8.97056 0.331110
\(735\) 0 0
\(736\) 6.82843 0.251699
\(737\) 23.3137 + 40.3805i 0.858771 + 1.48744i
\(738\) −14.7071 + 25.4735i −0.541376 + 0.937691i
\(739\) −4.41421 + 7.64564i −0.162379 + 0.281249i −0.935722 0.352739i \(-0.885250\pi\)
0.773342 + 0.633989i \(0.218584\pi\)
\(740\) −1.82843 3.16693i −0.0672143 0.116419i
\(741\) 1.65685 0.0608661
\(742\) 0 0
\(743\) 12.2010 0.447612 0.223806 0.974634i \(-0.428152\pi\)
0.223806 + 0.974634i \(0.428152\pi\)
\(744\) 0.828427 + 1.43488i 0.0303716 + 0.0526052i
\(745\) 3.00000 5.19615i 0.109911 0.190372i
\(746\) −6.75736 + 11.7041i −0.247405 + 0.428517i
\(747\) 8.29289 + 14.3637i 0.303421 + 0.525541i
\(748\) 26.1421 0.955851
\(749\) 0 0
\(750\) −0.585786 −0.0213899
\(751\) 8.34315 + 14.4508i 0.304446 + 0.527315i 0.977138 0.212607i \(-0.0681954\pi\)
−0.672692 + 0.739923i \(0.734862\pi\)
\(752\) −5.41421 + 9.37769i −0.197436 + 0.341969i
\(753\) −1.00000 + 1.73205i −0.0364420 + 0.0631194i
\(754\) 0.343146 + 0.594346i 0.0124966 + 0.0216448i
\(755\) 11.3137 0.411748
\(756\) 0 0
\(757\) −7.65685 −0.278293 −0.139147 0.990272i \(-0.544436\pi\)
−0.139147 + 0.990272i \(0.544436\pi\)
\(758\) 8.75736 + 15.1682i 0.318082 + 0.550934i
\(759\) 9.65685 16.7262i 0.350522 0.607121i
\(760\) 1.70711 2.95680i 0.0619233 0.107254i
\(761\) 7.19239 + 12.4576i 0.260724 + 0.451587i 0.966434 0.256913i \(-0.0827055\pi\)
−0.705711 + 0.708500i \(0.749372\pi\)
\(762\) 1.65685 0.0600215
\(763\) 0 0
\(764\) −18.1421 −0.656359
\(765\) 7.19239 + 12.4576i 0.260041 + 0.450405i
\(766\) −7.75736 + 13.4361i −0.280285 + 0.485467i
\(767\) −4.72792 + 8.18900i −0.170715 + 0.295688i
\(768\) −0.292893 0.507306i −0.0105689 0.0183058i
\(769\) −11.5563 −0.416733 −0.208366 0.978051i \(-0.566815\pi\)
−0.208366 + 0.978051i \(0.566815\pi\)
\(770\) 0 0
\(771\) 5.79899 0.208846
\(772\) 2.82843 + 4.89898i 0.101797 + 0.176318i
\(773\) 1.00000 1.73205i 0.0359675 0.0622975i −0.847481 0.530825i \(-0.821882\pi\)
0.883449 + 0.468528i \(0.155215\pi\)
\(774\) 4.21320 7.29748i 0.151440 0.262303i
\(775\) −1.41421 2.44949i −0.0508001 0.0879883i
\(776\) 16.2426 0.583077
\(777\) 0 0
\(778\) 0.142136 0.00509581
\(779\) −18.8995 32.7349i −0.677145 1.17285i
\(780\) −0.242641 + 0.420266i −0.00868793 + 0.0150479i
\(781\) −30.1421 + 52.2077i −1.07857 + 1.86814i
\(782\) −18.4853 32.0174i −0.661032