Properties

Label 1078.2.e.m.67.1
Level $1078$
Weight $2$
Character 1078.67
Analytic conductor $8.608$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1078.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.60787333789\)
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: no (minimal twist has level 154)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.1
Root \(-0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 1078.67
Dual form 1078.2.e.m.177.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-1.20711 + 2.09077i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.292893 - 0.507306i) q^{5} +2.41421 q^{6} +1.00000 q^{8} +(-1.41421 - 2.44949i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-1.20711 + 2.09077i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.292893 - 0.507306i) q^{5} +2.41421 q^{6} +1.00000 q^{8} +(-1.41421 - 2.44949i) q^{9} +(-0.292893 + 0.507306i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-1.20711 - 2.09077i) q^{12} +3.82843 q^{13} +1.41421 q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.82843 - 3.16693i) q^{17} +(-1.41421 + 2.44949i) q^{18} +(-0.292893 - 0.507306i) q^{19} +0.585786 q^{20} +1.00000 q^{22} +(3.12132 + 5.40629i) q^{23} +(-1.20711 + 2.09077i) q^{24} +(2.32843 - 4.03295i) q^{25} +(-1.91421 - 3.31552i) q^{26} -0.414214 q^{27} +2.65685 q^{29} +(-0.707107 - 1.22474i) q^{30} +(-2.00000 + 3.46410i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.20711 - 2.09077i) q^{33} -3.65685 q^{34} +2.82843 q^{36} +(4.70711 + 8.15295i) q^{37} +(-0.292893 + 0.507306i) q^{38} +(-4.62132 + 8.00436i) q^{39} +(-0.292893 - 0.507306i) q^{40} +5.41421 q^{41} -5.65685 q^{43} +(-0.500000 - 0.866025i) q^{44} +(-0.828427 + 1.43488i) q^{45} +(3.12132 - 5.40629i) q^{46} +(-5.24264 - 9.08052i) q^{47} +2.41421 q^{48} -4.65685 q^{50} +(4.41421 + 7.64564i) q^{51} +(-1.91421 + 3.31552i) q^{52} +(-3.94975 + 6.84116i) q^{53} +(0.207107 + 0.358719i) q^{54} +0.585786 q^{55} +1.41421 q^{57} +(-1.32843 - 2.30090i) q^{58} +(-2.79289 + 4.83743i) q^{59} +(-0.707107 + 1.22474i) q^{60} +(5.91421 + 10.2437i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(-1.12132 - 1.94218i) q^{65} +(-1.20711 + 2.09077i) q^{66} +(-1.37868 + 2.38794i) q^{67} +(1.82843 + 3.16693i) q^{68} -15.0711 q^{69} -11.0711 q^{71} +(-1.41421 - 2.44949i) q^{72} +(-4.70711 + 8.15295i) q^{73} +(4.70711 - 8.15295i) q^{74} +(5.62132 + 9.73641i) q^{75} +0.585786 q^{76} +9.24264 q^{78} +(6.62132 + 11.4685i) q^{79} +(-0.292893 + 0.507306i) q^{80} +(4.74264 - 8.21449i) q^{81} +(-2.70711 - 4.68885i) q^{82} +12.1421 q^{83} -2.14214 q^{85} +(2.82843 + 4.89898i) q^{86} +(-3.20711 + 5.55487i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(6.24264 + 10.8126i) q^{89} +1.65685 q^{90} -6.24264 q^{92} +(-4.82843 - 8.36308i) q^{93} +(-5.24264 + 9.08052i) q^{94} +(-0.171573 + 0.297173i) q^{95} +(-1.20711 - 2.09077i) q^{96} +3.82843 q^{97} +2.82843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} - 2q^{3} - 2q^{4} - 4q^{5} + 4q^{6} + 4q^{8} + O(q^{10}) \) \( 4q - 2q^{2} - 2q^{3} - 2q^{4} - 4q^{5} + 4q^{6} + 4q^{8} - 4q^{10} - 2q^{11} - 2q^{12} + 4q^{13} - 2q^{16} - 4q^{17} - 4q^{19} + 8q^{20} + 4q^{22} + 4q^{23} - 2q^{24} - 2q^{25} - 2q^{26} + 4q^{27} - 12q^{29} - 8q^{31} - 2q^{32} - 2q^{33} + 8q^{34} + 16q^{37} - 4q^{38} - 10q^{39} - 4q^{40} + 16q^{41} - 2q^{44} + 8q^{45} + 4q^{46} - 4q^{47} + 4q^{48} + 4q^{50} + 12q^{51} - 2q^{52} + 4q^{53} - 2q^{54} + 8q^{55} + 6q^{58} - 14q^{59} + 18q^{61} + 16q^{62} + 4q^{64} + 4q^{65} - 2q^{66} - 14q^{67} - 4q^{68} - 32q^{69} - 16q^{71} - 16q^{73} + 16q^{74} + 14q^{75} + 8q^{76} + 20q^{78} + 18q^{79} - 4q^{80} + 2q^{81} - 8q^{82} - 8q^{83} + 48q^{85} - 10q^{87} - 2q^{88} + 8q^{89} - 16q^{90} - 8q^{92} - 8q^{93} - 4q^{94} - 12q^{95} - 2q^{96} + 4q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(981\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(3\) −1.20711 + 2.09077i −0.696923 + 1.20711i 0.272605 + 0.962126i \(0.412115\pi\)
−0.969528 + 0.244981i \(0.921218\pi\)
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −0.292893 0.507306i −0.130986 0.226874i 0.793071 0.609129i \(-0.208481\pi\)
−0.924057 + 0.382255i \(0.875148\pi\)
\(6\) 2.41421 0.985599
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) −1.41421 2.44949i −0.471405 0.816497i
\(10\) −0.292893 + 0.507306i −0.0926210 + 0.160424i
\(11\) −0.500000 + 0.866025i −0.150756 + 0.261116i
\(12\) −1.20711 2.09077i −0.348462 0.603553i
\(13\) 3.82843 1.06181 0.530907 0.847430i \(-0.321851\pi\)
0.530907 + 0.847430i \(0.321851\pi\)
\(14\) 0 0
\(15\) 1.41421 0.365148
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 1.82843 3.16693i 0.443459 0.768093i −0.554485 0.832194i \(-0.687085\pi\)
0.997943 + 0.0641009i \(0.0204179\pi\)
\(18\) −1.41421 + 2.44949i −0.333333 + 0.577350i
\(19\) −0.292893 0.507306i −0.0671943 0.116384i 0.830471 0.557062i \(-0.188071\pi\)
−0.897665 + 0.440678i \(0.854738\pi\)
\(20\) 0.585786 0.130986
\(21\) 0 0
\(22\) 1.00000 0.213201
\(23\) 3.12132 + 5.40629i 0.650840 + 1.12729i 0.982919 + 0.184037i \(0.0589166\pi\)
−0.332079 + 0.943252i \(0.607750\pi\)
\(24\) −1.20711 + 2.09077i −0.246400 + 0.426777i
\(25\) 2.32843 4.03295i 0.465685 0.806591i
\(26\) −1.91421 3.31552i −0.375408 0.650226i
\(27\) −0.414214 −0.0797154
\(28\) 0 0
\(29\) 2.65685 0.493365 0.246683 0.969096i \(-0.420659\pi\)
0.246683 + 0.969096i \(0.420659\pi\)
\(30\) −0.707107 1.22474i −0.129099 0.223607i
\(31\) −2.00000 + 3.46410i −0.359211 + 0.622171i −0.987829 0.155543i \(-0.950287\pi\)
0.628619 + 0.777714i \(0.283621\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) −1.20711 2.09077i −0.210130 0.363956i
\(34\) −3.65685 −0.627145
\(35\) 0 0
\(36\) 2.82843 0.471405
\(37\) 4.70711 + 8.15295i 0.773844 + 1.34034i 0.935442 + 0.353480i \(0.115002\pi\)
−0.161599 + 0.986857i \(0.551665\pi\)
\(38\) −0.292893 + 0.507306i −0.0475136 + 0.0822959i
\(39\) −4.62132 + 8.00436i −0.740003 + 1.28172i
\(40\) −0.292893 0.507306i −0.0463105 0.0802121i
\(41\) 5.41421 0.845558 0.422779 0.906233i \(-0.361055\pi\)
0.422779 + 0.906233i \(0.361055\pi\)
\(42\) 0 0
\(43\) −5.65685 −0.862662 −0.431331 0.902194i \(-0.641956\pi\)
−0.431331 + 0.902194i \(0.641956\pi\)
\(44\) −0.500000 0.866025i −0.0753778 0.130558i
\(45\) −0.828427 + 1.43488i −0.123495 + 0.213899i
\(46\) 3.12132 5.40629i 0.460214 0.797113i
\(47\) −5.24264 9.08052i −0.764718 1.32453i −0.940396 0.340082i \(-0.889545\pi\)
0.175678 0.984448i \(-0.443788\pi\)
\(48\) 2.41421 0.348462
\(49\) 0 0
\(50\) −4.65685 −0.658579
\(51\) 4.41421 + 7.64564i 0.618114 + 1.07060i
\(52\) −1.91421 + 3.31552i −0.265454 + 0.459779i
\(53\) −3.94975 + 6.84116i −0.542540 + 0.939706i 0.456218 + 0.889868i \(0.349204\pi\)
−0.998757 + 0.0498379i \(0.984130\pi\)
\(54\) 0.207107 + 0.358719i 0.0281837 + 0.0488155i
\(55\) 0.585786 0.0789874
\(56\) 0 0
\(57\) 1.41421 0.187317
\(58\) −1.32843 2.30090i −0.174431 0.302123i
\(59\) −2.79289 + 4.83743i −0.363604 + 0.629780i −0.988551 0.150887i \(-0.951787\pi\)
0.624947 + 0.780667i \(0.285120\pi\)
\(60\) −0.707107 + 1.22474i −0.0912871 + 0.158114i
\(61\) 5.91421 + 10.2437i 0.757237 + 1.31157i 0.944254 + 0.329217i \(0.106785\pi\)
−0.187017 + 0.982357i \(0.559882\pi\)
\(62\) 4.00000 0.508001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −1.12132 1.94218i −0.139083 0.240898i
\(66\) −1.20711 + 2.09077i −0.148585 + 0.257356i
\(67\) −1.37868 + 2.38794i −0.168433 + 0.291734i −0.937869 0.346990i \(-0.887204\pi\)
0.769436 + 0.638723i \(0.220537\pi\)
\(68\) 1.82843 + 3.16693i 0.221729 + 0.384047i
\(69\) −15.0711 −1.81434
\(70\) 0 0
\(71\) −11.0711 −1.31389 −0.656947 0.753937i \(-0.728152\pi\)
−0.656947 + 0.753937i \(0.728152\pi\)
\(72\) −1.41421 2.44949i −0.166667 0.288675i
\(73\) −4.70711 + 8.15295i −0.550925 + 0.954230i 0.447283 + 0.894393i \(0.352392\pi\)
−0.998208 + 0.0598379i \(0.980942\pi\)
\(74\) 4.70711 8.15295i 0.547190 0.947761i
\(75\) 5.62132 + 9.73641i 0.649094 + 1.12426i
\(76\) 0.585786 0.0671943
\(77\) 0 0
\(78\) 9.24264 1.04652
\(79\) 6.62132 + 11.4685i 0.744957 + 1.29030i 0.950215 + 0.311595i \(0.100863\pi\)
−0.205258 + 0.978708i \(0.565803\pi\)
\(80\) −0.292893 + 0.507306i −0.0327465 + 0.0567185i
\(81\) 4.74264 8.21449i 0.526960 0.912722i
\(82\) −2.70711 4.68885i −0.298950 0.517796i
\(83\) 12.1421 1.33277 0.666386 0.745607i \(-0.267840\pi\)
0.666386 + 0.745607i \(0.267840\pi\)
\(84\) 0 0
\(85\) −2.14214 −0.232347
\(86\) 2.82843 + 4.89898i 0.304997 + 0.528271i
\(87\) −3.20711 + 5.55487i −0.343838 + 0.595545i
\(88\) −0.500000 + 0.866025i −0.0533002 + 0.0923186i
\(89\) 6.24264 + 10.8126i 0.661719 + 1.14613i 0.980164 + 0.198189i \(0.0635060\pi\)
−0.318445 + 0.947941i \(0.603161\pi\)
\(90\) 1.65685 0.174648
\(91\) 0 0
\(92\) −6.24264 −0.650840
\(93\) −4.82843 8.36308i −0.500685 0.867211i
\(94\) −5.24264 + 9.08052i −0.540737 + 0.936584i
\(95\) −0.171573 + 0.297173i −0.0176030 + 0.0304893i
\(96\) −1.20711 2.09077i −0.123200 0.213388i
\(97\) 3.82843 0.388718 0.194359 0.980930i \(-0.437737\pi\)
0.194359 + 0.980930i \(0.437737\pi\)
\(98\) 0 0
\(99\) 2.82843 0.284268
\(100\) 2.32843 + 4.03295i 0.232843 + 0.403295i
\(101\) 3.08579 5.34474i 0.307047 0.531821i −0.670668 0.741758i \(-0.733992\pi\)
0.977715 + 0.209936i \(0.0673257\pi\)
\(102\) 4.41421 7.64564i 0.437072 0.757031i
\(103\) 6.70711 + 11.6170i 0.660871 + 1.14466i 0.980387 + 0.197081i \(0.0631462\pi\)
−0.319516 + 0.947581i \(0.603520\pi\)
\(104\) 3.82843 0.375408
\(105\) 0 0
\(106\) 7.89949 0.767267
\(107\) 1.53553 + 2.65962i 0.148446 + 0.257115i 0.930653 0.365903i \(-0.119240\pi\)
−0.782207 + 0.623018i \(0.785906\pi\)
\(108\) 0.207107 0.358719i 0.0199289 0.0345178i
\(109\) −8.24264 + 14.2767i −0.789502 + 1.36746i 0.136771 + 0.990603i \(0.456328\pi\)
−0.926272 + 0.376854i \(0.877006\pi\)
\(110\) −0.292893 0.507306i −0.0279263 0.0483697i
\(111\) −22.7279 −2.15724
\(112\) 0 0
\(113\) −8.17157 −0.768717 −0.384358 0.923184i \(-0.625577\pi\)
−0.384358 + 0.923184i \(0.625577\pi\)
\(114\) −0.707107 1.22474i −0.0662266 0.114708i
\(115\) 1.82843 3.16693i 0.170502 0.295318i
\(116\) −1.32843 + 2.30090i −0.123341 + 0.213634i
\(117\) −5.41421 9.37769i −0.500544 0.866968i
\(118\) 5.58579 0.514213
\(119\) 0 0
\(120\) 1.41421 0.129099
\(121\) −0.500000 0.866025i −0.0454545 0.0787296i
\(122\) 5.91421 10.2437i 0.535448 0.927423i
\(123\) −6.53553 + 11.3199i −0.589289 + 1.02068i
\(124\) −2.00000 3.46410i −0.179605 0.311086i
\(125\) −5.65685 −0.505964
\(126\) 0 0
\(127\) 15.7279 1.39563 0.697814 0.716279i \(-0.254156\pi\)
0.697814 + 0.716279i \(0.254156\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 6.82843 11.8272i 0.601209 1.04133i
\(130\) −1.12132 + 1.94218i −0.0983463 + 0.170341i
\(131\) −0.292893 0.507306i −0.0255902 0.0443235i 0.852947 0.521998i \(-0.174813\pi\)
−0.878537 + 0.477674i \(0.841480\pi\)
\(132\) 2.41421 0.210130
\(133\) 0 0
\(134\) 2.75736 0.238200
\(135\) 0.121320 + 0.210133i 0.0104416 + 0.0180854i
\(136\) 1.82843 3.16693i 0.156786 0.271562i
\(137\) 8.32843 14.4253i 0.711546 1.23243i −0.252731 0.967537i \(-0.581329\pi\)
0.964277 0.264897i \(-0.0853378\pi\)
\(138\) 7.53553 + 13.0519i 0.641467 + 1.11105i
\(139\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 0 0
\(141\) 25.3137 2.13180
\(142\) 5.53553 + 9.58783i 0.464532 + 0.804592i
\(143\) −1.91421 + 3.31552i −0.160075 + 0.277257i
\(144\) −1.41421 + 2.44949i −0.117851 + 0.204124i
\(145\) −0.778175 1.34784i −0.0646239 0.111932i
\(146\) 9.41421 0.779126
\(147\) 0 0
\(148\) −9.41421 −0.773844
\(149\) −8.82843 15.2913i −0.723253 1.25271i −0.959689 0.281064i \(-0.909313\pi\)
0.236436 0.971647i \(-0.424021\pi\)
\(150\) 5.62132 9.73641i 0.458979 0.794975i
\(151\) 7.86396 13.6208i 0.639960 1.10844i −0.345481 0.938426i \(-0.612284\pi\)
0.985441 0.170018i \(-0.0543825\pi\)
\(152\) −0.292893 0.507306i −0.0237568 0.0411479i
\(153\) −10.3431 −0.836194
\(154\) 0 0
\(155\) 2.34315 0.188206
\(156\) −4.62132 8.00436i −0.370002 0.640862i
\(157\) 8.82843 15.2913i 0.704585 1.22038i −0.262256 0.964998i \(-0.584466\pi\)
0.966841 0.255379i \(-0.0822002\pi\)
\(158\) 6.62132 11.4685i 0.526764 0.912382i
\(159\) −9.53553 16.5160i −0.756217 1.30981i
\(160\) 0.585786 0.0463105
\(161\) 0 0
\(162\) −9.48528 −0.745234
\(163\) −4.86396 8.42463i −0.380975 0.659868i 0.610227 0.792227i \(-0.291078\pi\)
−0.991202 + 0.132359i \(0.957745\pi\)
\(164\) −2.70711 + 4.68885i −0.211390 + 0.366137i
\(165\) −0.707107 + 1.22474i −0.0550482 + 0.0953463i
\(166\) −6.07107 10.5154i −0.471206 0.816153i
\(167\) −13.7279 −1.06230 −0.531149 0.847278i \(-0.678240\pi\)
−0.531149 + 0.847278i \(0.678240\pi\)
\(168\) 0 0
\(169\) 1.65685 0.127450
\(170\) 1.07107 + 1.85514i 0.0821472 + 0.142283i
\(171\) −0.828427 + 1.43488i −0.0633514 + 0.109728i
\(172\) 2.82843 4.89898i 0.215666 0.373544i
\(173\) −4.91421 8.51167i −0.373621 0.647130i 0.616499 0.787356i \(-0.288551\pi\)
−0.990120 + 0.140226i \(0.955217\pi\)
\(174\) 6.41421 0.486260
\(175\) 0 0
\(176\) 1.00000 0.0753778
\(177\) −6.74264 11.6786i −0.506808 0.877817i
\(178\) 6.24264 10.8126i 0.467906 0.810436i
\(179\) −0.449747 + 0.778985i −0.0336157 + 0.0582241i −0.882344 0.470605i \(-0.844036\pi\)
0.848728 + 0.528829i \(0.177369\pi\)
\(180\) −0.828427 1.43488i −0.0617473 0.106949i
\(181\) 7.65685 0.569129 0.284565 0.958657i \(-0.408151\pi\)
0.284565 + 0.958657i \(0.408151\pi\)
\(182\) 0 0
\(183\) −28.5563 −2.11095
\(184\) 3.12132 + 5.40629i 0.230107 + 0.398557i
\(185\) 2.75736 4.77589i 0.202725 0.351130i
\(186\) −4.82843 + 8.36308i −0.354037 + 0.613211i
\(187\) 1.82843 + 3.16693i 0.133708 + 0.231589i
\(188\) 10.4853 0.764718
\(189\) 0 0
\(190\) 0.343146 0.0248944
\(191\) 3.58579 + 6.21076i 0.259458 + 0.449395i 0.966097 0.258180i \(-0.0831226\pi\)
−0.706639 + 0.707575i \(0.749789\pi\)
\(192\) −1.20711 + 2.09077i −0.0871154 + 0.150888i
\(193\) −10.9497 + 18.9655i −0.788180 + 1.36517i 0.138901 + 0.990306i \(0.455643\pi\)
−0.927081 + 0.374862i \(0.877690\pi\)
\(194\) −1.91421 3.31552i −0.137433 0.238040i
\(195\) 5.41421 0.387720
\(196\) 0 0
\(197\) −0.514719 −0.0366722 −0.0183361 0.999832i \(-0.505837\pi\)
−0.0183361 + 0.999832i \(0.505837\pi\)
\(198\) −1.41421 2.44949i −0.100504 0.174078i
\(199\) 0.0502525 0.0870399i 0.00356231 0.00617010i −0.864239 0.503082i \(-0.832199\pi\)
0.867801 + 0.496912i \(0.165533\pi\)
\(200\) 2.32843 4.03295i 0.164645 0.285173i
\(201\) −3.32843 5.76500i −0.234769 0.406632i
\(202\) −6.17157 −0.434230
\(203\) 0 0
\(204\) −8.82843 −0.618114
\(205\) −1.58579 2.74666i −0.110756 0.191835i
\(206\) 6.70711 11.6170i 0.467306 0.809398i
\(207\) 8.82843 15.2913i 0.613618 1.06282i
\(208\) −1.91421 3.31552i −0.132727 0.229890i
\(209\) 0.585786 0.0405197
\(210\) 0 0
\(211\) 7.41421 0.510416 0.255208 0.966886i \(-0.417856\pi\)
0.255208 + 0.966886i \(0.417856\pi\)
\(212\) −3.94975 6.84116i −0.271270 0.469853i
\(213\) 13.3640 23.1471i 0.915684 1.58601i
\(214\) 1.53553 2.65962i 0.104967 0.181808i
\(215\) 1.65685 + 2.86976i 0.112997 + 0.195716i
\(216\) −0.414214 −0.0281837
\(217\) 0 0
\(218\) 16.4853 1.11652
\(219\) −11.3640 19.6830i −0.767905 1.33005i
\(220\) −0.292893 + 0.507306i −0.0197469 + 0.0342026i
\(221\) 7.00000 12.1244i 0.470871 0.815572i
\(222\) 11.3640 + 19.6830i 0.762699 + 1.32103i
\(223\) −8.58579 −0.574947 −0.287473 0.957789i \(-0.592815\pi\)
−0.287473 + 0.957789i \(0.592815\pi\)
\(224\) 0 0
\(225\) −13.1716 −0.878105
\(226\) 4.08579 + 7.07679i 0.271782 + 0.470741i
\(227\) −14.4142 + 24.9662i −0.956705 + 1.65706i −0.226288 + 0.974061i \(0.572659\pi\)
−0.730417 + 0.683001i \(0.760674\pi\)
\(228\) −0.707107 + 1.22474i −0.0468293 + 0.0811107i
\(229\) 11.6569 + 20.1903i 0.770307 + 1.33421i 0.937395 + 0.348268i \(0.113230\pi\)
−0.167088 + 0.985942i \(0.553436\pi\)
\(230\) −3.65685 −0.241126
\(231\) 0 0
\(232\) 2.65685 0.174431
\(233\) −0.707107 1.22474i −0.0463241 0.0802357i 0.841934 0.539581i \(-0.181417\pi\)
−0.888258 + 0.459345i \(0.848084\pi\)
\(234\) −5.41421 + 9.37769i −0.353938 + 0.613039i
\(235\) −3.07107 + 5.31925i −0.200334 + 0.346989i
\(236\) −2.79289 4.83743i −0.181802 0.314890i
\(237\) −31.9706 −2.07671
\(238\) 0 0
\(239\) 20.2132 1.30748 0.653742 0.756718i \(-0.273198\pi\)
0.653742 + 0.756718i \(0.273198\pi\)
\(240\) −0.707107 1.22474i −0.0456435 0.0790569i
\(241\) 6.12132 10.6024i 0.394309 0.682963i −0.598704 0.800971i \(-0.704317\pi\)
0.993013 + 0.118007i \(0.0376507\pi\)
\(242\) −0.500000 + 0.866025i −0.0321412 + 0.0556702i
\(243\) 10.8284 + 18.7554i 0.694644 + 1.20316i
\(244\) −11.8284 −0.757237
\(245\) 0 0
\(246\) 13.0711 0.833381
\(247\) −1.12132 1.94218i −0.0713479 0.123578i
\(248\) −2.00000 + 3.46410i −0.127000 + 0.219971i
\(249\) −14.6569 + 25.3864i −0.928840 + 1.60880i
\(250\) 2.82843 + 4.89898i 0.178885 + 0.309839i
\(251\) 26.1421 1.65008 0.825038 0.565077i \(-0.191153\pi\)
0.825038 + 0.565077i \(0.191153\pi\)
\(252\) 0 0
\(253\) −6.24264 −0.392471
\(254\) −7.86396 13.6208i −0.493429 0.854644i
\(255\) 2.58579 4.47871i 0.161928 0.280468i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −12.5711 21.7737i −0.784162 1.35821i −0.929499 0.368826i \(-0.879760\pi\)
0.145337 0.989382i \(-0.453573\pi\)
\(258\) −13.6569 −0.850239
\(259\) 0 0
\(260\) 2.24264 0.139083
\(261\) −3.75736 6.50794i −0.232575 0.402831i
\(262\) −0.292893 + 0.507306i −0.0180950 + 0.0313415i
\(263\) 8.52082 14.7585i 0.525416 0.910047i −0.474146 0.880446i \(-0.657243\pi\)
0.999562 0.0296008i \(-0.00942362\pi\)
\(264\) −1.20711 2.09077i −0.0742923 0.128678i
\(265\) 4.62742 0.284260
\(266\) 0 0
\(267\) −30.1421 −1.84467
\(268\) −1.37868 2.38794i −0.0842163 0.145867i
\(269\) 1.17157 2.02922i 0.0714321 0.123724i −0.828097 0.560585i \(-0.810576\pi\)
0.899529 + 0.436861i \(0.143910\pi\)
\(270\) 0.121320 0.210133i 0.00738332 0.0127883i
\(271\) 2.27817 + 3.94591i 0.138389 + 0.239697i 0.926887 0.375340i \(-0.122474\pi\)
−0.788498 + 0.615038i \(0.789141\pi\)
\(272\) −3.65685 −0.221729
\(273\) 0 0
\(274\) −16.6569 −1.00628
\(275\) 2.32843 + 4.03295i 0.140409 + 0.243196i
\(276\) 7.53553 13.0519i 0.453586 0.785634i
\(277\) −0.914214 + 1.58346i −0.0549298 + 0.0951412i −0.892183 0.451675i \(-0.850827\pi\)
0.837253 + 0.546816i \(0.184160\pi\)
\(278\) 0 0
\(279\) 11.3137 0.677334
\(280\) 0 0
\(281\) 8.72792 0.520664 0.260332 0.965519i \(-0.416168\pi\)
0.260332 + 0.965519i \(0.416168\pi\)
\(282\) −12.6569 21.9223i −0.753705 1.30545i
\(283\) −11.7071 + 20.2773i −0.695915 + 1.20536i 0.273956 + 0.961742i \(0.411668\pi\)
−0.969871 + 0.243618i \(0.921666\pi\)
\(284\) 5.53553 9.58783i 0.328474 0.568933i
\(285\) −0.414214 0.717439i −0.0245359 0.0424974i
\(286\) 3.82843 0.226380
\(287\) 0 0
\(288\) 2.82843 0.166667
\(289\) 1.81371 + 3.14144i 0.106689 + 0.184790i
\(290\) −0.778175 + 1.34784i −0.0456960 + 0.0791478i
\(291\) −4.62132 + 8.00436i −0.270907 + 0.469224i
\(292\) −4.70711 8.15295i −0.275463 0.477115i
\(293\) 10.8284 0.632603 0.316302 0.948659i \(-0.397559\pi\)
0.316302 + 0.948659i \(0.397559\pi\)
\(294\) 0 0
\(295\) 3.27208 0.190508
\(296\) 4.70711 + 8.15295i 0.273595 + 0.473880i
\(297\) 0.207107 0.358719i 0.0120176 0.0208150i
\(298\) −8.82843 + 15.2913i −0.511417 + 0.885800i
\(299\) 11.9497 + 20.6976i 0.691072 + 1.19697i
\(300\) −11.2426 −0.649094
\(301\) 0 0
\(302\) −15.7279 −0.905040
\(303\) 7.44975 + 12.9033i 0.427977 + 0.741278i
\(304\) −0.292893 + 0.507306i −0.0167986 + 0.0290960i
\(305\) 3.46447 6.00063i 0.198375 0.343595i
\(306\) 5.17157 + 8.95743i 0.295639 + 0.512062i
\(307\) −9.89949 −0.564994 −0.282497 0.959268i \(-0.591163\pi\)
−0.282497 + 0.959268i \(0.591163\pi\)
\(308\) 0 0
\(309\) −32.3848 −1.84231
\(310\) −1.17157 2.02922i −0.0665409 0.115252i
\(311\) 8.36396 14.4868i 0.474277 0.821471i −0.525289 0.850924i \(-0.676043\pi\)
0.999566 + 0.0294522i \(0.00937629\pi\)
\(312\) −4.62132 + 8.00436i −0.261631 + 0.453158i
\(313\) −10.3284 17.8894i −0.583797 1.01117i −0.995024 0.0996335i \(-0.968233\pi\)
0.411227 0.911533i \(-0.365100\pi\)
\(314\) −17.6569 −0.996434
\(315\) 0 0
\(316\) −13.2426 −0.744957
\(317\) −4.34315 7.52255i −0.243935 0.422508i 0.717896 0.696150i \(-0.245105\pi\)
−0.961832 + 0.273642i \(0.911772\pi\)
\(318\) −9.53553 + 16.5160i −0.534726 + 0.926173i
\(319\) −1.32843 + 2.30090i −0.0743776 + 0.128826i
\(320\) −0.292893 0.507306i −0.0163732 0.0283593i
\(321\) −7.41421 −0.413821
\(322\) 0 0
\(323\) −2.14214 −0.119192
\(324\) 4.74264 + 8.21449i 0.263480 + 0.456361i
\(325\) 8.91421 15.4399i 0.494472 0.856450i
\(326\) −4.86396 + 8.42463i −0.269390 + 0.466597i
\(327\) −19.8995 34.4669i −1.10044 1.90603i
\(328\) 5.41421 0.298950
\(329\) 0 0
\(330\) 1.41421 0.0778499
\(331\) 12.0355 + 20.8462i 0.661533 + 1.14581i 0.980213 + 0.197946i \(0.0634271\pi\)
−0.318680 + 0.947862i \(0.603240\pi\)
\(332\) −6.07107 + 10.5154i −0.333193 + 0.577107i
\(333\) 13.3137 23.0600i 0.729587 1.26368i
\(334\) 6.86396 + 11.8887i 0.375579 + 0.650522i
\(335\) 1.61522 0.0882491
\(336\) 0 0
\(337\) −28.2426 −1.53847 −0.769237 0.638963i \(-0.779364\pi\)
−0.769237 + 0.638963i \(0.779364\pi\)
\(338\) −0.828427 1.43488i −0.0450605 0.0780471i
\(339\) 9.86396 17.0849i 0.535737 0.927923i
\(340\) 1.07107 1.85514i 0.0580868 0.100609i
\(341\) −2.00000 3.46410i −0.108306 0.187592i
\(342\) 1.65685 0.0895924
\(343\) 0 0
\(344\) −5.65685 −0.304997
\(345\) 4.41421 + 7.64564i 0.237653 + 0.411628i
\(346\) −4.91421 + 8.51167i −0.264190 + 0.457590i
\(347\) −8.70711 + 15.0812i −0.467422 + 0.809599i −0.999307 0.0372179i \(-0.988150\pi\)
0.531885 + 0.846816i \(0.321484\pi\)
\(348\) −3.20711 5.55487i −0.171919 0.297772i
\(349\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(350\) 0 0
\(351\) −1.58579 −0.0846430
\(352\) −0.500000 0.866025i −0.0266501 0.0461593i
\(353\) −1.34315 + 2.32640i −0.0714884 + 0.123822i −0.899554 0.436810i \(-0.856108\pi\)
0.828065 + 0.560632i \(0.189442\pi\)
\(354\) −6.74264 + 11.6786i −0.358367 + 0.620710i
\(355\) 3.24264 + 5.61642i 0.172101 + 0.298089i
\(356\) −12.4853 −0.661719
\(357\) 0 0
\(358\) 0.899495 0.0475398
\(359\) −9.62132 16.6646i −0.507794 0.879525i −0.999959 0.00902308i \(-0.997128\pi\)
0.492165 0.870502i \(-0.336206\pi\)
\(360\) −0.828427 + 1.43488i −0.0436619 + 0.0756247i
\(361\) 9.32843 16.1573i 0.490970 0.850385i
\(362\) −3.82843 6.63103i −0.201218 0.348519i
\(363\) 2.41421 0.126713
\(364\) 0 0
\(365\) 5.51472 0.288654
\(366\) 14.2782 + 24.7305i 0.746332 + 1.29269i
\(367\) −5.36396 + 9.29065i −0.279996 + 0.484968i −0.971384 0.237516i \(-0.923667\pi\)
0.691387 + 0.722485i \(0.257000\pi\)
\(368\) 3.12132 5.40629i 0.162710 0.281822i
\(369\) −7.65685 13.2621i −0.398600 0.690395i
\(370\) −5.51472 −0.286697
\(371\) 0 0
\(372\) 9.65685 0.500685
\(373\) 9.98528 + 17.2950i 0.517018 + 0.895502i 0.999805 + 0.0197638i \(0.00629142\pi\)
−0.482786 + 0.875738i \(0.660375\pi\)
\(374\) 1.82843 3.16693i 0.0945457 0.163758i
\(375\) 6.82843 11.8272i 0.352618 0.610753i
\(376\) −5.24264 9.08052i −0.270369 0.468292i
\(377\) 10.1716 0.523863
\(378\) 0 0
\(379\) 27.8701 1.43159 0.715794 0.698311i \(-0.246065\pi\)
0.715794 + 0.698311i \(0.246065\pi\)
\(380\) −0.171573 0.297173i −0.00880150 0.0152447i
\(381\) −18.9853 + 32.8835i −0.972645 + 1.68467i
\(382\) 3.58579 6.21076i 0.183465 0.317770i
\(383\) −3.19239 5.52938i −0.163123 0.282538i 0.772864 0.634572i \(-0.218824\pi\)
−0.935987 + 0.352034i \(0.885490\pi\)
\(384\) 2.41421 0.123200
\(385\) 0 0
\(386\) 21.8995 1.11465
\(387\) 8.00000 + 13.8564i 0.406663 + 0.704361i
\(388\) −1.91421 + 3.31552i −0.0971795 + 0.168320i
\(389\) 11.3640 19.6830i 0.576176 0.997966i −0.419737 0.907646i \(-0.637878\pi\)
0.995913 0.0903199i \(-0.0287889\pi\)
\(390\) −2.70711 4.68885i −0.137080 0.237429i
\(391\) 22.8284 1.15448
\(392\) 0 0
\(393\) 1.41421 0.0713376
\(394\) 0.257359 + 0.445759i 0.0129656 + 0.0224570i
\(395\) 3.87868 6.71807i 0.195158 0.338023i
\(396\) −1.41421 + 2.44949i −0.0710669 + 0.123091i
\(397\) 11.0000 + 19.0526i 0.552074 + 0.956221i 0.998125 + 0.0612128i \(0.0194968\pi\)
−0.446051 + 0.895008i \(0.647170\pi\)
\(398\) −0.100505 −0.00503786
\(399\) 0 0
\(400\) −4.65685 −0.232843
\(401\) −9.15685 15.8601i −0.457271 0.792017i 0.541544 0.840672i \(-0.317840\pi\)
−0.998816 + 0.0486549i \(0.984507\pi\)
\(402\) −3.32843 + 5.76500i −0.166007 + 0.287532i
\(403\) −7.65685 + 13.2621i −0.381415 + 0.660630i
\(404\) 3.08579 + 5.34474i 0.153524 + 0.265911i
\(405\) −5.55635 −0.276097
\(406\) 0 0
\(407\) −9.41421 −0.466645
\(408\) 4.41421 + 7.64564i 0.218536 + 0.378516i
\(409\) 1.36396 2.36245i 0.0674435 0.116816i −0.830332 0.557269i \(-0.811849\pi\)
0.897775 + 0.440454i \(0.145182\pi\)
\(410\) −1.58579 + 2.74666i −0.0783164 + 0.135648i
\(411\) 20.1066 + 34.8257i 0.991786 + 1.71782i
\(412\) −13.4142 −0.660871
\(413\) 0 0
\(414\) −17.6569 −0.867787
\(415\) −3.55635 6.15978i −0.174574 0.302372i
\(416\) −1.91421 + 3.31552i −0.0938520 + 0.162557i
\(417\) 0 0
\(418\) −0.292893 0.507306i −0.0143259 0.0248131i
\(419\) 26.1421 1.27713 0.638563 0.769569i \(-0.279529\pi\)
0.638563 + 0.769569i \(0.279529\pi\)
\(420\) 0 0
\(421\) 0.686292 0.0334478 0.0167239 0.999860i \(-0.494676\pi\)
0.0167239 + 0.999860i \(0.494676\pi\)
\(422\) −3.70711 6.42090i −0.180459 0.312564i
\(423\) −14.8284 + 25.6836i −0.720983 + 1.24878i
\(424\) −3.94975 + 6.84116i −0.191817 + 0.332236i
\(425\) −8.51472 14.7479i −0.413025 0.715379i
\(426\) −26.7279 −1.29497
\(427\) 0 0
\(428\) −3.07107 −0.148446
\(429\) −4.62132 8.00436i −0.223119 0.386454i
\(430\) 1.65685 2.86976i 0.0799006 0.138392i
\(431\) 8.79289 15.2297i 0.423539 0.733591i −0.572744 0.819734i \(-0.694121\pi\)
0.996283 + 0.0861437i \(0.0274544\pi\)
\(432\) 0.207107 + 0.358719i 0.00996443 + 0.0172589i
\(433\) −26.1421 −1.25631 −0.628155 0.778088i \(-0.716190\pi\)
−0.628155 + 0.778088i \(0.716190\pi\)
\(434\) 0 0
\(435\) 3.75736 0.180152
\(436\) −8.24264 14.2767i −0.394751 0.683729i
\(437\) 1.82843 3.16693i 0.0874655 0.151495i
\(438\) −11.3640 + 19.6830i −0.542991 + 0.940488i
\(439\) −13.6924 23.7159i −0.653502 1.13190i −0.982267 0.187487i \(-0.939966\pi\)
0.328765 0.944412i \(-0.393368\pi\)
\(440\) 0.585786 0.0279263
\(441\) 0 0
\(442\) −14.0000 −0.665912
\(443\) −6.31371 10.9357i −0.299973 0.519569i 0.676156 0.736758i \(-0.263644\pi\)
−0.976130 + 0.217189i \(0.930311\pi\)
\(444\) 11.3640 19.6830i 0.539310 0.934112i
\(445\) 3.65685 6.33386i 0.173352 0.300254i
\(446\) 4.29289 + 7.43551i 0.203274 + 0.352082i
\(447\) 42.6274 2.01621
\(448\) 0 0
\(449\) 22.3431 1.05444 0.527219 0.849729i \(-0.323235\pi\)
0.527219 + 0.849729i \(0.323235\pi\)
\(450\) 6.58579 + 11.4069i 0.310457 + 0.537727i
\(451\) −2.70711 + 4.68885i −0.127473 + 0.220789i
\(452\) 4.08579 7.07679i 0.192179 0.332864i
\(453\) 18.9853 + 32.8835i 0.892006 + 1.54500i
\(454\) 28.8284 1.35299
\(455\) 0 0
\(456\) 1.41421 0.0662266
\(457\) 5.82843 + 10.0951i 0.272642 + 0.472230i 0.969538 0.244943i \(-0.0787691\pi\)
−0.696895 + 0.717173i \(0.745436\pi\)
\(458\) 11.6569 20.1903i 0.544689 0.943429i
\(459\) −0.757359 + 1.31178i −0.0353505 + 0.0612289i
\(460\) 1.82843 + 3.16693i 0.0852509 + 0.147659i
\(461\) 8.31371 0.387208 0.193604 0.981080i \(-0.437982\pi\)
0.193604 + 0.981080i \(0.437982\pi\)
\(462\) 0 0
\(463\) 12.8284 0.596188 0.298094 0.954537i \(-0.403649\pi\)
0.298094 + 0.954537i \(0.403649\pi\)
\(464\) −1.32843 2.30090i −0.0616707 0.106817i
\(465\) −2.82843 + 4.89898i −0.131165 + 0.227185i
\(466\) −0.707107 + 1.22474i −0.0327561 + 0.0567352i
\(467\) −17.0000 29.4449i −0.786666 1.36255i −0.927999 0.372584i \(-0.878472\pi\)
0.141332 0.989962i \(-0.454861\pi\)
\(468\) 10.8284 0.500544
\(469\) 0 0
\(470\) 6.14214 0.283316
\(471\) 21.3137 + 36.9164i 0.982084 + 1.70102i
\(472\) −2.79289 + 4.83743i −0.128553 + 0.222661i
\(473\) 2.82843 4.89898i 0.130051 0.225255i
\(474\) 15.9853 + 27.6873i 0.734228 + 1.27172i
\(475\) −2.72792 −0.125166
\(476\) 0 0
\(477\) 22.3431 1.02302
\(478\) −10.1066 17.5051i −0.462265 0.800667i
\(479\) −5.96447 + 10.3308i −0.272523 + 0.472024i −0.969507 0.245062i \(-0.921192\pi\)
0.696984 + 0.717087i \(0.254525\pi\)
\(480\) −0.707107 + 1.22474i −0.0322749 + 0.0559017i
\(481\) 18.0208 + 31.2130i 0.821678 + 1.42319i
\(482\) −12.2426 −0.557637
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) −1.12132 1.94218i −0.0509165 0.0881900i
\(486\) 10.8284 18.7554i 0.491187 0.850762i
\(487\) 4.82843 8.36308i 0.218797 0.378967i −0.735644 0.677369i \(-0.763120\pi\)
0.954440 + 0.298402i \(0.0964534\pi\)
\(488\) 5.91421 + 10.2437i 0.267724 + 0.463711i
\(489\) 23.4853 1.06204
\(490\) 0 0
\(491\) 19.1716 0.865201 0.432600 0.901586i \(-0.357596\pi\)
0.432600 + 0.901586i \(0.357596\pi\)
\(492\) −6.53553 11.3199i −0.294645 0.510339i
\(493\) 4.85786 8.41407i 0.218787 0.378951i
\(494\) −1.12132 + 1.94218i −0.0504506 + 0.0873830i
\(495\) −0.828427 1.43488i −0.0372350 0.0644930i
\(496\) 4.00000 0.179605
\(497\) 0 0
\(498\) 29.3137 1.31358
\(499\) −11.0711 19.1757i −0.495609 0.858420i 0.504378 0.863483i \(-0.331722\pi\)
−0.999987 + 0.00506282i \(0.998388\pi\)
\(500\) 2.82843 4.89898i 0.126491 0.219089i
\(501\) 16.5711 28.7019i 0.740341 1.28231i
\(502\) −13.0711 22.6398i −0.583390 1.01046i
\(503\) −4.21320 −0.187857 −0.0939287 0.995579i \(-0.529943\pi\)
−0.0939287 + 0.995579i \(0.529943\pi\)
\(504\) 0 0
\(505\) −3.61522 −0.160875
\(506\) 3.12132 + 5.40629i 0.138760 + 0.240339i
\(507\) −2.00000 + 3.46410i −0.0888231 + 0.153846i
\(508\) −7.86396 + 13.6208i −0.348907 + 0.604324i
\(509\) 4.65685 + 8.06591i 0.206411 + 0.357515i 0.950582 0.310475i \(-0.100488\pi\)
−0.744170 + 0.667990i \(0.767155\pi\)
\(510\) −5.17157 −0.229001
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 0.121320 + 0.210133i 0.00535642 + 0.00927760i
\(514\) −12.5711 + 21.7737i −0.554486 + 0.960398i
\(515\) 3.92893 6.80511i 0.173129 0.299869i
\(516\) 6.82843 + 11.8272i 0.300605 + 0.520663i
\(517\) 10.4853 0.461142
\(518\) 0 0
\(519\) 23.7279 1.04154
\(520\) −1.12132 1.94218i −0.0491731 0.0851704i
\(521\) −14.1421 + 24.4949i −0.619578 + 1.07314i 0.369984 + 0.929038i \(0.379363\pi\)
−0.989563 + 0.144103i \(0.953970\pi\)
\(522\) −3.75736 + 6.50794i −0.164455 + 0.284845i
\(523\) −6.36396 11.0227i −0.278277 0.481989i 0.692680 0.721245i \(-0.256430\pi\)
−0.970957 + 0.239256i \(0.923097\pi\)
\(524\) 0.585786 0.0255902
\(525\) 0 0
\(526\) −17.0416 −0.743050
\(527\) 7.31371 + 12.6677i 0.318590 + 0.551814i
\(528\) −1.20711 + 2.09077i −0.0525326 + 0.0909891i
\(529\) −7.98528 + 13.8309i −0.347186 + 0.601344i
\(530\) −2.31371 4.00746i −0.100501 0.174073i
\(531\) 15.7990 0.685618
\(532\) 0 0
\(533\) 20.7279 0.897826
\(534\) 15.0711 + 26.1039i 0.652189 + 1.12962i
\(535\) 0.899495 1.55797i 0.0388886 0.0673570i
\(536\) −1.37868 + 2.38794i −0.0595499 + 0.103143i
\(537\) −1.08579 1.88064i −0.0468551 0.0811555i
\(538\) −2.34315 −0.101020
\(539\) 0 0
\(540\) −0.242641 −0.0104416
\(541\) 6.42893 + 11.1352i 0.276401 + 0.478741i 0.970488 0.241151i \(-0.0775248\pi\)
−0.694086 + 0.719892i \(0.744191\pi\)
\(542\) 2.27817 3.94591i 0.0978560 0.169492i
\(543\) −9.24264 + 16.0087i −0.396640 + 0.687000i
\(544\) 1.82843 + 3.16693i 0.0783932 + 0.135781i
\(545\) 9.65685 0.413654
\(546\) 0 0
\(547\) 34.8701 1.49094 0.745468 0.666541i \(-0.232226\pi\)
0.745468 + 0.666541i \(0.232226\pi\)
\(548\) 8.32843 + 14.4253i 0.355773 + 0.616217i
\(549\) 16.7279 28.9736i 0.713930 1.23656i
\(550\) 2.32843 4.03295i 0.0992845 0.171966i
\(551\) −0.778175 1.34784i −0.0331514 0.0574198i
\(552\) −15.0711 −0.641467
\(553\) 0 0
\(554\) 1.82843 0.0776824
\(555\) 6.65685 + 11.5300i 0.282568 + 0.489422i
\(556\) 0 0
\(557\) −3.75736 + 6.50794i −0.159204 + 0.275750i −0.934582 0.355748i \(-0.884226\pi\)
0.775378 + 0.631498i \(0.217560\pi\)
\(558\) −5.65685 9.79796i −0.239474 0.414781i
\(559\) −21.6569 −0.915987
\(560\) 0 0
\(561\) −8.82843 −0.372736
\(562\) −4.36396 7.55860i −0.184083 0.318840i
\(563\) 4.53553 7.85578i 0.191150 0.331081i −0.754482 0.656321i \(-0.772112\pi\)
0.945632 + 0.325240i \(0.105445\pi\)
\(564\) −12.6569 + 21.9223i −0.532950 + 0.923096i
\(565\) 2.39340 + 4.14549i 0.100691 + 0.174402i
\(566\) 23.4142 0.984173
\(567\) 0 0
\(568\) −11.0711 −0.464532
\(569\) 2.00000 + 3.46410i 0.0838444 + 0.145223i 0.904898 0.425628i \(-0.139947\pi\)
−0.821054 + 0.570851i \(0.806613\pi\)
\(570\) −0.414214 + 0.717439i −0.0173495 + 0.0300502i
\(571\) −13.1924 + 22.8499i −0.552084 + 0.956238i 0.446040 + 0.895013i \(0.352834\pi\)
−0.998124 + 0.0612248i \(0.980499\pi\)
\(572\) −1.91421 3.31552i −0.0800373 0.138629i
\(573\) −17.3137 −0.723291
\(574\) 0 0
\(575\) 29.0711 1.21235
\(576\) −1.41421 2.44949i −0.0589256 0.102062i
\(577\) −4.84315 + 8.38857i −0.201623 + 0.349221i −0.949051 0.315121i \(-0.897955\pi\)
0.747429 + 0.664342i \(0.231288\pi\)
\(578\) 1.81371 3.14144i 0.0754403 0.130666i
\(579\) −26.4350 45.7868i −1.09860 1.90284i
\(580\) 1.55635 0.0646239
\(581\) 0 0
\(582\) 9.24264 0.383120
\(583\) −3.94975 6.84116i −0.163582 0.283332i
\(584\) −4.70711 + 8.15295i −0.194781 + 0.337371i
\(585\) −3.17157 + 5.49333i −0.131128 + 0.227121i
\(586\) −5.41421 9.37769i −0.223659 0.387389i
\(587\) 25.1005 1.03601 0.518004 0.855378i \(-0.326675\pi\)
0.518004 + 0.855378i \(0.326675\pi\)
\(588\) 0 0
\(589\) 2.34315 0.0965476
\(590\) −1.63604 2.83370i −0.0673547 0.116662i
\(591\) 0.621320 1.07616i 0.0255577 0.0442672i
\(592\) 4.70711 8.15295i 0.193461 0.335084i
\(593\) 11.8492 + 20.5235i 0.486590 + 0.842799i 0.999881 0.0154159i \(-0.00490721\pi\)
−0.513291 + 0.858215i \(0.671574\pi\)
\(594\) −0.414214 −0.0169954
\(595\) 0 0
\(596\) 17.6569 0.723253
\(597\) 0.121320 + 0.210133i 0.00496531 + 0.00860017i
\(598\) 11.9497 20.6976i 0.488662 0.846387i
\(599\) −21.3137 + 36.9164i −0.870855 + 1.50836i −0.00974040 + 0.999953i \(0.503101\pi\)
−0.861114 + 0.508412i \(0.830233\pi\)
\(600\) 5.62132 + 9.73641i 0.229489 + 0.397487i
\(601\) −31.9411 −1.30291 −0.651453 0.758689i \(-0.725840\pi\)
−0.651453 + 0.758689i \(0.725840\pi\)
\(602\) 0 0
\(603\) 7.79899 0.317599
\(604\) 7.86396 + 13.6208i 0.319980 + 0.554222i
\(605\) −0.292893 + 0.507306i −0.0119078 + 0.0206249i
\(606\) 7.44975 12.9033i 0.302625 0.524162i
\(607\) −21.4853 37.2136i −0.872061 1.51045i −0.859861 0.510528i \(-0.829450\pi\)
−0.0121994 0.999926i \(-0.503883\pi\)
\(608\) 0.585786 0.0237568
\(609\) 0 0
\(610\) −6.92893 −0.280544
\(611\) −20.0711 34.7641i −0.811988 1.40641i
\(612\) 5.17157 8.95743i 0.209048 0.362083i
\(613\) −14.3137 + 24.7921i −0.578125 + 1.00134i 0.417569 + 0.908645i \(0.362882\pi\)
−0.995694 + 0.0926971i \(0.970451\pi\)
\(614\) 4.94975 + 8.57321i 0.199756 + 0.345987i
\(615\) 7.65685 0.308754
\(616\) 0 0
\(617\) −41.9706 −1.68967 −0.844836 0.535026i \(-0.820302\pi\)
−0.844836 + 0.535026i \(0.820302\pi\)
\(618\) 16.1924 + 28.0460i 0.651353 + 1.12818i
\(619\) −10.9706 + 19.0016i −0.440944 + 0.763738i −0.997760 0.0668984i \(-0.978690\pi\)
0.556816 + 0.830636i \(0.312023\pi\)
\(620\) −1.17157 + 2.02922i −0.0470515 + 0.0814956i
\(621\) −1.29289 2.23936i −0.0518820 0.0898623i
\(622\) −16.7279 −0.670729
\(623\) 0 0
\(624\) 9.24264 0.370002
\(625\) −9.98528 17.2950i −0.399411 0.691801i
\(626\) −10.3284 + 17.8894i −0.412807 + 0.715003i
\(627\) −0.707107 + 1.22474i −0.0282391 + 0.0489116i
\(628\) 8.82843 + 15.2913i 0.352293 + 0.610189i
\(629\) 34.4264 1.37267
\(630\) 0 0
\(631\) 23.2721 0.926447 0.463223 0.886242i \(-0.346693\pi\)
0.463223 + 0.886242i \(0.346693\pi\)
\(632\) 6.62132 + 11.4685i 0.263382 + 0.456191i
\(633\) −8.94975 + 15.5014i −0.355721 + 0.616126i
\(634\) −4.34315 + 7.52255i −0.172488 + 0.298759i
\(635\) −4.60660 7.97887i −0.182807 0.316632i
\(636\) 19.0711 0.756217
\(637\) 0 0
\(638\) 2.65685 0.105186
\(639\) 15.6569 + 27.1185i 0.619376 + 1.07279i
\(640\) −0.292893 + 0.507306i −0.0115776 + 0.0200530i
\(641\) −7.64214 + 13.2366i −0.301846 + 0.522813i −0.976554 0.215272i \(-0.930936\pi\)
0.674708 + 0.738085i \(0.264270\pi\)
\(642\) 3.70711 + 6.42090i 0.146308 + 0.253413i
\(643\) −1.58579 −0.0625373 −0.0312687 0.999511i \(-0.509955\pi\)
−0.0312687 + 0.999511i \(0.509955\pi\)
\(644\) 0 0
\(645\) −8.00000 −0.315000
\(646\) 1.07107 + 1.85514i 0.0421406 + 0.0729897i
\(647\) 15.0919 26.1399i 0.593323 1.02767i −0.400458 0.916315i \(-0.631149\pi\)
0.993781 0.111351i \(-0.0355177\pi\)
\(648\) 4.74264 8.21449i 0.186309 0.322696i
\(649\) −2.79289 4.83743i −0.109631 0.189886i
\(650\) −17.8284 −0.699288
\(651\) 0 0
\(652\) 9.72792 0.380975
\(653\) 9.19239 + 15.9217i 0.359726 + 0.623064i 0.987915 0.154997i \(-0.0495369\pi\)
−0.628189 + 0.778061i \(0.716204\pi\)
\(654\) −19.8995 + 34.4669i −0.778132 + 1.34776i
\(655\) −0.171573 + 0.297173i −0.00670391 + 0.0116115i
\(656\) −2.70711 4.68885i −0.105695 0.183069i
\(657\) 26.6274 1.03883
\(658\) 0 0
\(659\) −12.0000 −0.467454 −0.233727 0.972302i \(-0.575092\pi\)
−0.233727 + 0.972302i \(0.575092\pi\)
\(660\) −0.707107 1.22474i −0.0275241 0.0476731i
\(661\) 9.48528 16.4290i 0.368935 0.639014i −0.620465 0.784234i \(-0.713056\pi\)
0.989399 + 0.145221i \(0.0463893\pi\)
\(662\) 12.0355 20.8462i 0.467774 0.810209i
\(663\) 16.8995 + 29.2708i 0.656322 + 1.13678i
\(664\) 12.1421 0.471206
\(665\) 0 0
\(666\) −26.6274 −1.03179
\(667\) 8.29289 + 14.3637i 0.321102 + 0.556165i
\(668\) 6.86396 11.8887i 0.265575 0.459989i
\(669\) 10.3640 17.9509i 0.400694 0.694022i
\(670\) −0.807612 1.39882i −0.0312008 0.0540413i
\(671\) −11.8284 −0.456631
\(672\) 0 0
\(673\) 5.55635 0.214182 0.107091 0.994249i \(-0.465846\pi\)
0.107091 + 0.994249i \(0.465846\pi\)
\(674\) 14.1213 + 24.4588i 0.543933 + 0.942119i
\(675\) −0.964466 + 1.67050i −0.0371223 + 0.0642977i
\(676\) −0.828427 + 1.43488i −0.0318626 + 0.0551876i
\(677\) −17.6569 30.5826i −0.678608 1.17538i −0.975400 0.220441i \(-0.929250\pi\)
0.296792 0.954942i \(-0.404083\pi\)
\(678\) −19.7279 −0.757646
\(679\) 0 0
\(680\) −2.14214 −0.0821472
\(681\) −34.7990 60.2736i −1.33350 2.30969i
\(682\) −2.00000 + 3.46410i −0.0765840 + 0.132647i
\(683\) −6.79289 + 11.7656i −0.259923 + 0.450200i −0.966221 0.257715i \(-0.917030\pi\)
0.706298 + 0.707914i \(0.250364\pi\)
\(684\) −0.828427 1.43488i −0.0316757 0.0548639i
\(685\) −9.75736 −0.372810
\(686\) 0 0
\(687\) −56.2843 −2.14738
\(688\) 2.82843 + 4.89898i 0.107833 + 0.186772i
\(689\) −15.1213 + 26.1909i −0.576076 + 0.997794i
\(690\) 4.41421 7.64564i 0.168046 0.291065i
\(691\) 14.0355 + 24.3103i 0.533937 + 0.924806i 0.999214 + 0.0396407i \(0.0126213\pi\)
−0.465277 + 0.885165i \(0.654045\pi\)
\(692\) 9.82843 0.373621
\(693\) 0 0
\(694\) 17.4142 0.661035
\(695\) 0 0
\(696\) −3.20711 + 5.55487i −0.121565 + 0.210557i
\(697\) 9.89949 17.1464i 0.374970 0.649467i
\(698\) 0 0
\(699\) 3.41421 0.129137
\(700\) 0 0
\(701\) −26.1127 −0.986263 −0.493132 0.869955i \(-0.664148\pi\)
−0.493132 + 0.869955i \(0.664148\pi\)
\(702\) 0.792893 + 1.37333i 0.0299258 + 0.0518331i
\(703\) 2.75736 4.77589i 0.103996 0.180126i
\(704\) −0.500000 + 0.866025i −0.0188445 + 0.0326396i
\(705\) −7.41421 12.8418i −0.279235 0.483650i
\(706\) 2.68629 0.101100
\(707\) 0 0
\(708\) 13.4853 0.506808
\(709\) 6.02082 + 10.4284i 0.226116 + 0.391645i 0.956654 0.291228i \(-0.0940637\pi\)
−0.730537 + 0.682873i \(0.760730\pi\)
\(710\) 3.24264 5.61642i 0.121694 0.210780i
\(711\) 18.7279 32.4377i 0.702352 1.21651i
\(712\) 6.24264 + 10.8126i 0.233953 + 0.405218i
\(713\) −24.9706 −0.935155
\(714\) 0 0
\(715\) 2.24264 0.0838700
\(716\) −0.449747 0.778985i −0.0168079 0.0291121i
\(717\) −24.3995 + 42.2612i −0.911216 + 1.57827i
\(718\) −9.62132 + 16.6646i −0.359064 + 0.621918i
\(719\) −0.757359 1.31178i −0.0282447 0.0489213i 0.851558 0.524261i \(-0.175658\pi\)
−0.879802 + 0.475340i \(0.842325\pi\)
\(720\) 1.65685 0.0617473
\(721\) 0 0
\(722\) −18.6569 −0.694336
\(723\) 14.7782 + 25.5965i 0.549606 + 0.951946i
\(724\) −3.82843 + 6.63103i −0.142282 + 0.246440i
\(725\) 6.18629 10.7150i 0.229753 0.397944i
\(726\) −1.20711 2.09077i −0.0447999 0.0775958i
\(727\) −36.4264 −1.35098 −0.675490 0.737369i \(-0.736068\pi\)
−0.675490 + 0.737369i \(0.736068\pi\)
\(728\) 0 0
\(729\) −23.8284 −0.882534
\(730\) −2.75736 4.77589i −0.102054 0.176763i
\(731\) −10.3431 + 17.9149i −0.382555 + 0.662605i
\(732\) 14.2782 24.7305i 0.527737 0.914066i
\(733\) −6.50000 11.2583i −0.240083 0.415836i 0.720655 0.693294i \(-0.243841\pi\)
−0.960738 + 0.277458i \(0.910508\pi\)
\(734\) 10.7279 0.395975
\(735\) 0 0
\(736\) −6.24264 −0.230107
\(737\) −1.37868 2.38794i −0.0507843 0.0879610i
\(738\) −7.65685 + 13.2621i −0.281853 + 0.488183i
\(739\) 26.2132 45.4026i 0.964268 1.67016i 0.252700 0.967545i \(-0.418681\pi\)
0.711568 0.702617i \(-0.247985\pi\)
\(740\) 2.75736 + 4.77589i 0.101363 + 0.175565i
\(741\) 5.41421 0.198896
\(742\) 0 0
\(743\) −13.3137 −0.488433 −0.244216 0.969721i \(-0.578531\pi\)
−0.244216 + 0.969721i \(0.578531\pi\)
\(744\) −4.82843 8.36308i −0.177019 0.306605i
\(745\) −5.17157 + 8.95743i −0.189472 + 0.328175i
\(746\) 9.98528 17.2950i 0.365587 0.633215i
\(747\) −17.1716 29.7420i −0.628275 1.08820i
\(748\) −3.65685 −0.133708
\(749\) 0 0
\(750\) −13.6569 −0.498678
\(751\) −22.8284 39.5400i −0.833021 1.44283i −0.895631 0.444797i \(-0.853276\pi\)
0.0626103 0.998038i \(-0.480057\pi\)
\(752\) −5.24264 + 9.08052i −0.191179 + 0.331132i
\(753\) −31.5563 + 54.6572i −1.14998 + 1.99182i
\(754\) −5.08579 8.80884i −0.185213 0.320799i
\(755\) −9.21320 −0.335303
\(756\) 0 0
\(757\) 8.34315 0.303237 0.151618 0.988439i \(-0.451552\pi\)
0.151618 + 0.988439i \(0.451552\pi\)
\(758\) −13.9350 24.1362i −0.506143 0.876665i
\(759\) 7.53553 13.0519i 0.273523 0.473755i
\(760\) −0.171573 + 0.297173i −0.00622360 + 0.0107796i
\(761\) 15.4853 + 26.8213i 0.561341 + 0.972271i 0.997380 + 0.0723433i \(0.0230477\pi\)
−0.436039 + 0.899928i \(0.643619\pi\)
\(762\) 37.9706 1.37553
\(763\) 0 0
\(764\) −7.17157 −0.259458
\(765\) 3.02944 + 5.24714i 0.109530 + 0.189711i
\(766\) −3.19239 + 5.52938i −0.115346 + 0.199785i
\(767\) −10.6924 + 18.5198i −0.386080 + 0.668710i
\(768\) −1.20711 2.09077i −0.0435577 0.0754442i
\(769\) −22.9706 −0.828340 −0.414170 0.910200i \(-0.635928\pi\)
−0.414170 + 0.910200i \(0.635928\pi\)
\(770\) 0 0
\(771\) 60.6985 2.18600
\(772\) −10.9497 18.9655i −0.394090 0.682584i
\(773\) −10.9706 + 19.0016i −0.394584 + 0.683439i −0.993048 0.117710i \(-0.962445\pi\)
0.598464 + 0.801150i \(0.295778\pi\)
\(774\) 8.00000 13.8564i 0.287554 0.498058i
\(775\) 9.31371 + 16.1318i 0.334558 + 0.579472i
\(776\) 3.82843 0.137433
\(777\) 0 0
\(778\) −22.7279 −0.814835
\(779\) −1.58579 2.74666i −0.0568167 0.0984094i
\(780\) −2.70711 + 4.68885i −0.0969300 + 0.167888i
\(781\) 5.53553 9.58783i 0.198077 0.343079i
\(782\) −11.4142 19.7700i −0.408171 0.706974i
\(783\) −1.10051 −0.0393288
\(784\)