Properties

Label 154.2.e.e.23.2
Level $154$
Weight $2$
Character 154.23
Analytic conductor $1.230$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 154 = 2 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 154.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.22969619113\)
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 23.2
Root \(0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 154.23
Dual form 154.2.e.e.67.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(1.20711 + 2.09077i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.292893 - 0.507306i) q^{5} -2.41421 q^{6} +(1.62132 + 2.09077i) q^{7} +1.00000 q^{8} +(-1.41421 + 2.44949i) q^{9} +O(q^{10})\) \(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} +(1.62132 + 2.09077i) q^{7} +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} +(-2.62132 + 0.358719i) q^{14} +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} +(-2.41421 + 5.91359i) q^{21} +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} +(1.00000 - 2.44949i) q^{28} +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} +(1.53553 - 0.210133i) q^{35} +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} +(-3.91421 - 5.04757i) q^{42} -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} +(-1.74264 + 6.77962i) q^{49} -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} +(1.62132 + 2.09077i) q^{56} +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} +(-7.41421 + 1.01461i) q^{63} +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} +(-0.585786 + 1.43488i) q^{70} -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} +(1.00000 - 2.44949i) q^{77} +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} +(6.32843 - 0.866025i) q^{84} -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} +(-6.20711 - 8.00436i) q^{91} -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} +(-5.00000 - 4.89898i) q^{98} +2.82843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} + 2q^{3} - 2q^{4} + 4q^{5} - 4q^{6} - 2q^{7} + 4q^{8} + O(q^{10}) \) \( 4q - 2q^{2} + 2q^{3} - 2q^{4} + 4q^{5} - 4q^{6} - 2q^{7} + 4q^{8} + 4q^{10} - 2q^{11} + 2q^{12} - 4q^{13} - 2q^{14} - 2q^{16} + 4q^{17} + 4q^{19} - 8q^{20} - 4q^{21} + 4q^{22} + 4q^{23} + 2q^{24} - 2q^{25} + 2q^{26} - 4q^{27} + 4q^{28} - 12q^{29} + 8q^{31} - 2q^{32} + 2q^{33} - 8q^{34} - 8q^{35} + 16q^{37} + 4q^{38} - 10q^{39} + 4q^{40} - 16q^{41} - 10q^{42} - 2q^{44} - 8q^{45} + 4q^{46} + 4q^{47} - 4q^{48} + 10q^{49} + 4q^{50} + 12q^{51} + 2q^{52} + 4q^{53} + 2q^{54} - 8q^{55} - 2q^{56} + 6q^{58} + 14q^{59} - 18q^{61} - 16q^{62} - 24q^{63} + 4q^{64} + 4q^{65} + 2q^{66} - 14q^{67} + 4q^{68} + 32q^{69} - 8q^{70} - 16q^{71} + 16q^{73} + 16q^{74} - 14q^{75} - 8q^{76} + 4q^{77} + 20q^{78} + 18q^{79} + 4q^{80} + 2q^{81} + 8q^{82} + 8q^{83} + 14q^{84} + 48q^{85} + 10q^{87} - 2q^{88} - 8q^{89} + 16q^{90} - 22q^{91} - 8q^{92} - 8q^{93} + 4q^{94} - 12q^{95} + 2q^{96} - 4q^{97} - 20q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/154\mathbb{Z}\right)^\times\).

\(n\) \(45\) \(57\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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 0.969528 + 0.244981i \(0.0787816\pi\)
−0.272605 + 0.962126i \(0.587885\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0.292893 0.507306i 0.130986 0.226874i −0.793071 0.609129i \(-0.791519\pi\)
0.924057 + 0.382255i \(0.124852\pi\)
\(6\) −2.41421 −0.985599
\(7\) 1.62132 + 2.09077i 0.612801 + 0.790237i
\(8\) 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 \(-0.678149\pi\)
−0.530907 + 0.847430i \(0.678149\pi\)
\(14\) −2.62132 + 0.358719i −0.700577 + 0.0958718i
\(15\) 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 \(-0.312915\pi\)
−0.997943 + 0.0641009i \(0.979582\pi\)
\(18\) −1.41421 2.44949i −0.333333 0.577350i
\(19\) 0.292893 0.507306i 0.0671943 0.116384i −0.830471 0.557062i \(-0.811929\pi\)
0.897665 + 0.440678i \(0.145262\pi\)
\(20\) −0.585786 −0.130986
\(21\) −2.41421 + 5.91359i −0.526825 + 1.29045i
\(22\) 1.00000 0.213201
\(23\) 3.12132 5.40629i 0.650840 1.12729i −0.332079 0.943252i \(-0.607750\pi\)
0.982919 0.184037i \(-0.0589166\pi\)
\(24\) 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
\(28\) 1.00000 2.44949i 0.188982 0.462910i
\(29\) 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 \(-0.0497126\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 1.20711 2.09077i 0.210130 0.363956i
\(34\) 3.65685 0.627145
\(35\) 1.53553 0.210133i 0.259553 0.0355190i
\(36\) 2.82843 0.471405
\(37\) 4.70711 8.15295i 0.773844 1.34034i −0.161599 0.986857i \(-0.551665\pi\)
0.935442 0.353480i \(-0.115002\pi\)
\(38\) 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 \(-0.638945\pi\)
−0.422779 + 0.906233i \(0.638945\pi\)
\(42\) −3.91421 5.04757i −0.603976 0.778856i
\(43\) −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 −0.175678 0.984448i \(-0.556212\pi\)
0.940396 0.340082i \(-0.110455\pi\)
\(48\) −2.41421 −0.348462
\(49\) −1.74264 + 6.77962i −0.248949 + 0.968517i
\(50\) −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 −0.998757 0.0498379i \(-0.984130\pi\)
0.456218 0.889868i \(-0.349204\pi\)
\(54\) −0.207107 + 0.358719i −0.0281837 + 0.0488155i
\(55\) −0.585786 −0.0789874
\(56\) 1.62132 + 2.09077i 0.216658 + 0.279391i
\(57\) 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 \(-0.0482129\pi\)
−0.624947 + 0.780667i \(0.714880\pi\)
\(60\) −0.707107 1.22474i −0.0912871 0.158114i
\(61\) −5.91421 + 10.2437i −0.757237 + 1.31157i 0.187017 + 0.982357i \(0.440118\pi\)
−0.944254 + 0.329217i \(0.893215\pi\)
\(62\) −4.00000 −0.508001
\(63\) −7.41421 + 1.01461i −0.934103 + 0.127829i
\(64\) 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 0.769436 0.638723i \(-0.220537\pi\)
−0.937869 + 0.346990i \(0.887204\pi\)
\(68\) −1.82843 + 3.16693i −0.221729 + 0.384047i
\(69\) 15.0711 1.81434
\(70\) −0.585786 + 1.43488i −0.0700149 + 0.171501i
\(71\) −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 0.998208 + 0.0598379i \(0.0190584\pi\)
−0.447283 + 0.894393i \(0.647608\pi\)
\(74\) 4.70711 + 8.15295i 0.547190 + 0.947761i
\(75\) −5.62132 + 9.73641i −0.649094 + 1.12426i
\(76\) −0.585786 −0.0671943
\(77\) 1.00000 2.44949i 0.113961 0.279145i
\(78\) 9.24264 1.04652
\(79\) 6.62132 11.4685i 0.744957 1.29030i −0.205258 0.978708i \(-0.565803\pi\)
0.950215 0.311595i \(-0.100863\pi\)
\(80\) 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 \(-0.732160\pi\)
−0.666386 + 0.745607i \(0.732160\pi\)
\(84\) 6.32843 0.866025i 0.690488 0.0944911i
\(85\) −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 0.318445 + 0.947941i \(0.396839\pi\)
−0.980164 + 0.198189i \(0.936494\pi\)
\(90\) −1.65685 −0.174648
\(91\) −6.20711 8.00436i −0.650682 0.839085i
\(92\) −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 \(-0.562263\pi\)
−0.194359 + 0.980930i \(0.562263\pi\)
\(98\) −5.00000 4.89898i −0.505076 0.494872i
\(99\) 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 \(-0.266008\pi\)
−0.977715 + 0.209936i \(0.932674\pi\)
\(102\) 4.41421 + 7.64564i 0.437072 + 0.757031i
\(103\) −6.70711 + 11.6170i −0.660871 + 1.14466i 0.319516 + 0.947581i \(0.396480\pi\)
−0.980387 + 0.197081i \(0.936854\pi\)
\(104\) −3.82843 −0.375408
\(105\) 2.29289 + 2.95680i 0.223763 + 0.288554i
\(106\) 7.89949 0.767267
\(107\) 1.53553 2.65962i 0.148446 0.257115i −0.782207 0.623018i \(-0.785906\pi\)
0.930653 + 0.365903i \(0.119240\pi\)
\(108\) −0.207107 0.358719i −0.0199289 0.0345178i
\(109\) −8.24264 14.2767i −0.789502 1.36746i −0.926272 0.376854i \(-0.877006\pi\)
0.136771 0.990603i \(-0.456328\pi\)
\(110\) 0.292893 0.507306i 0.0279263 0.0483697i
\(111\) 22.7279 2.15724
\(112\) −2.62132 + 0.358719i −0.247691 + 0.0338958i
\(113\) −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
\(119\) 3.65685 8.95743i 0.335223 0.821126i
\(120\) 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
\(126\) 2.82843 6.92820i 0.251976 0.617213i
\(127\) 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 \(-0.825187\pi\)
0.878537 + 0.477674i \(0.158520\pi\)
\(132\) −2.41421 −0.210130
\(133\) 1.53553 0.210133i 0.133148 0.0182208i
\(134\) 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 0.964277 + 0.264897i \(0.0853378\pi\)
−0.252731 + 0.967537i \(0.581329\pi\)
\(138\) −7.53553 + 13.0519i −0.641467 + 1.11105i
\(139\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) −0.949747 1.22474i −0.0802683 0.103510i
\(141\) 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
\(147\) −16.2782 + 4.54026i −1.34260 + 0.374474i
\(148\) −9.41421 −0.773844
\(149\) −8.82843 + 15.2913i −0.723253 + 1.25271i 0.236436 + 0.971647i \(0.424021\pi\)
−0.959689 + 0.281064i \(0.909313\pi\)
\(150\) −5.62132 9.73641i −0.458979 0.794975i
\(151\) 7.86396 + 13.6208i 0.639960 + 1.10844i 0.985441 + 0.170018i \(0.0543825\pi\)
−0.345481 + 0.938426i \(0.612284\pi\)
\(152\) 0.292893 0.507306i 0.0237568 0.0411479i
\(153\) 10.3431 0.836194
\(154\) 1.62132 + 2.09077i 0.130650 + 0.168479i
\(155\) 2.34315 0.188206
\(156\) −4.62132 + 8.00436i −0.370002 + 0.640862i
\(157\) −8.82843 15.2913i −0.704585 1.22038i −0.966841 0.255379i \(-0.917800\pi\)
0.262256 0.964998i \(-0.415534\pi\)
\(158\) 6.62132 + 11.4685i 0.526764 + 0.912382i
\(159\) 9.53553 16.5160i 0.756217 1.30981i
\(160\) −0.585786 −0.0463105
\(161\) 16.3640 2.23936i 1.28966 0.176486i
\(162\) −9.48528 −0.745234
\(163\) −4.86396 + 8.42463i −0.380975 + 0.659868i −0.991202 0.132359i \(-0.957745\pi\)
0.610227 + 0.792227i \(0.291078\pi\)
\(164\) 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 \(-0.321760\pi\)
0.531149 + 0.847278i \(0.321760\pi\)
\(168\) −2.41421 + 5.91359i −0.186261 + 0.456243i
\(169\) 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 \(-0.711449\pi\)
0.990120 + 0.140226i \(0.0447828\pi\)
\(174\) −6.41421 −0.486260
\(175\) −4.65685 + 11.4069i −0.352025 + 0.862282i
\(176\) 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 0.848728 0.528829i \(-0.177369\pi\)
−0.882344 + 0.470605i \(0.844036\pi\)
\(180\) 0.828427 1.43488i 0.0617473 0.106949i
\(181\) −7.65685 −0.569129 −0.284565 0.958657i \(-0.591849\pi\)
−0.284565 + 0.958657i \(0.591849\pi\)
\(182\) 10.0355 1.37333i 0.743883 0.101798i
\(183\) −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
\(189\) 0.671573 + 0.866025i 0.0488497 + 0.0629941i
\(190\) 0.343146 0.0248944
\(191\) 3.58579 6.21076i 0.259458 0.449395i −0.706639 0.707575i \(-0.749789\pi\)
0.966097 + 0.258180i \(0.0831226\pi\)
\(192\) 1.20711 + 2.09077i 0.0871154 + 0.150888i
\(193\) −10.9497 18.9655i −0.788180 1.36517i −0.927081 0.374862i \(-0.877690\pi\)
0.138901 0.990306i \(-0.455643\pi\)
\(194\) 1.91421 3.31552i 0.137433 0.238040i
\(195\) −5.41421 −0.387720
\(196\) 6.74264 1.88064i 0.481617 0.134331i
\(197\) −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 \(-0.167801\pi\)
−0.867801 + 0.496912i \(0.834467\pi\)
\(200\) 2.32843 + 4.03295i 0.164645 + 0.285173i
\(201\) 3.32843 5.76500i 0.234769 0.406632i
\(202\) 6.17157 0.434230
\(203\) 4.30761 + 5.55487i 0.302335 + 0.389876i
\(204\) −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
\(210\) −3.70711 + 0.507306i −0.255815 + 0.0350074i
\(211\) 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
\(217\) −4.00000 + 9.79796i −0.271538 + 0.665129i
\(218\) 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 \(-0.407185\pi\)
0.287473 + 0.957789i \(0.407185\pi\)
\(224\) 1.00000 2.44949i 0.0668153 0.163663i
\(225\) −13.1716 −0.878105
\(226\) 4.08579 7.07679i 0.271782 0.470741i
\(227\) 14.4142 + 24.9662i 0.956705 + 1.65706i 0.730417 + 0.683001i \(0.239326\pi\)
0.226288 + 0.974061i \(0.427341\pi\)
\(228\) −0.707107 1.22474i −0.0468293 0.0811107i
\(229\) −11.6569 + 20.1903i −0.770307 + 1.33421i 0.167088 + 0.985942i \(0.446564\pi\)
−0.937395 + 0.348268i \(0.886770\pi\)
\(230\) 3.65685 0.241126
\(231\) 6.32843 0.866025i 0.416380 0.0569803i
\(232\) 2.65685 0.174431
\(233\) −0.707107 + 1.22474i −0.0463241 + 0.0802357i −0.888258 0.459345i \(-0.848084\pi\)
0.841934 + 0.539581i \(0.181417\pi\)
\(234\) 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
\(238\) 5.92893 + 7.64564i 0.384316 + 0.495593i
\(239\) 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 \(-0.295683\pi\)
−0.993013 + 0.118007i \(0.962349\pi\)
\(242\) −0.500000 0.866025i −0.0321412 0.0556702i
\(243\) −10.8284 + 18.7554i −0.694644 + 1.20316i
\(244\) 11.8284 0.757237
\(245\) 2.92893 + 2.86976i 0.187123 + 0.183342i
\(246\) 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 \(-0.808847\pi\)
−0.825038 + 0.565077i \(0.808847\pi\)
\(252\) 4.58579 + 5.91359i 0.288877 + 0.372521i
\(253\) −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 −0.145337 0.989382i \(-0.546427\pi\)
0.929499 0.368826i \(-0.120240\pi\)
\(258\) 13.6569 0.850239
\(259\) 24.6777 3.37706i 1.53340 0.209840i
\(260\) 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 0.999562 + 0.0296008i \(0.00942362\pi\)
−0.474146 + 0.880446i \(0.657243\pi\)
\(264\) 1.20711 2.09077i 0.0742923 0.128678i
\(265\) −4.62742 −0.284260
\(266\) −0.585786 + 1.43488i −0.0359169 + 0.0879780i
\(267\) −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 \(-0.189424\pi\)
−0.899529 + 0.436861i \(0.856090\pi\)
\(270\) 0.121320 + 0.210133i 0.00738332 + 0.0127883i
\(271\) −2.27817 + 3.94591i −0.138389 + 0.239697i −0.926887 0.375340i \(-0.877526\pi\)
0.788498 + 0.615038i \(0.210859\pi\)
\(272\) 3.65685 0.221729
\(273\) 9.24264 22.6398i 0.559390 1.37022i
\(274\) −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 0.837253 0.546816i \(-0.184160\pi\)
−0.892183 + 0.451675i \(0.850827\pi\)
\(278\) 0 0
\(279\) −11.3137 −0.677334
\(280\) 1.53553 0.210133i 0.0917657 0.0125578i
\(281\) 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 0.969871 + 0.243618i \(0.0783344\pi\)
−0.273956 + 0.961742i \(0.588332\pi\)
\(284\) 5.53553 + 9.58783i 0.328474 + 0.568933i
\(285\) 0.414214 0.717439i 0.0245359 0.0424974i
\(286\) −3.82843 −0.226380
\(287\) −8.77817 11.3199i −0.518159 0.668191i
\(288\) 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 \(-0.602441\pi\)
−0.316302 + 0.948659i \(0.602441\pi\)
\(294\) 4.20711 16.3674i 0.245363 0.954569i
\(295\) 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
\(301\) −9.17157 11.8272i −0.528641 0.681707i
\(302\) −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 \(-0.408837\pi\)
0.282497 + 0.959268i \(0.408837\pi\)
\(308\) −2.62132 + 0.358719i −0.149364 + 0.0204399i
\(309\) −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 \(-0.323957\pi\)
−0.999566 + 0.0294522i \(0.990624\pi\)
\(312\) −4.62132 8.00436i −0.261631 0.453158i
\(313\) 10.3284 17.8894i 0.583797 1.01117i −0.411227 0.911533i \(-0.634900\pi\)
0.995024 0.0996335i \(-0.0317670\pi\)
\(314\) 17.6569 0.996434
\(315\) −1.65685 + 4.05845i −0.0933532 + 0.228668i
\(316\) −13.2426 −0.744957
\(317\) −4.34315 + 7.52255i −0.243935 + 0.422508i −0.961832 0.273642i \(-0.911772\pi\)
0.717896 + 0.696150i \(0.245105\pi\)
\(318\) 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
\(322\) −6.24264 + 15.2913i −0.347889 + 0.852150i
\(323\) −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
\(329\) 27.4853 3.76127i 1.51531 0.207366i
\(330\) 1.41421 0.0778499
\(331\) 12.0355 20.8462i 0.661533 1.14581i −0.318680 0.947862i \(-0.603240\pi\)
0.980213 0.197946i \(-0.0634271\pi\)
\(332\) 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
\(336\) −3.91421 5.04757i −0.213538 0.275367i
\(337\) −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
\(343\) −17.0000 + 7.34847i −0.917914 + 0.396780i
\(344\) −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 0.531885 0.846816i \(-0.321484\pi\)
−0.999307 + 0.0372179i \(0.988150\pi\)
\(348\) 3.20711 5.55487i 0.171919 0.297772i
\(349\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(350\) −7.55025 9.73641i −0.403578 0.520433i
\(351\) −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 \(-0.143892\pi\)
−0.828065 + 0.560632i \(0.810558\pi\)
\(354\) −6.74264 11.6786i −0.358367 0.620710i
\(355\) −3.24264 + 5.61642i −0.172101 + 0.298089i
\(356\) 12.4853 0.661719
\(357\) 23.1421 3.16693i 1.22481 0.167612i
\(358\) 0.899495 0.0475398
\(359\) −9.62132 + 16.6646i −0.507794 + 0.879525i 0.492165 + 0.870502i \(0.336206\pi\)
−0.999959 + 0.00902308i \(0.997128\pi\)
\(360\) 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
\(364\) −3.82843 + 9.37769i −0.200664 + 0.491525i
\(365\) 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 \(-0.0763334\pi\)
−0.691387 + 0.722485i \(0.743000\pi\)
\(368\) 3.12132 + 5.40629i 0.162710 + 0.281822i
\(369\) 7.65685 13.2621i 0.398600 0.690395i
\(370\) 5.51472 0.286697
\(371\) 7.89949 19.3497i 0.410121 1.00459i
\(372\) 9.65685 0.500685
\(373\) 9.98528 17.2950i 0.517018 0.895502i −0.482786 0.875738i \(-0.660375\pi\)
0.999805 0.0197638i \(-0.00629142\pi\)
\(374\) −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
\(378\) −1.08579 + 0.148586i −0.0558468 + 0.00764246i
\(379\) 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 \(-0.781176\pi\)
0.935987 + 0.352034i \(0.114510\pi\)
\(384\) −2.41421 −0.123200
\(385\) −0.949747 1.22474i −0.0484036 0.0624188i
\(386\) 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 0.995913 + 0.0903199i \(0.0287889\pi\)
−0.419737 + 0.907646i \(0.637878\pi\)
\(390\) 2.70711 4.68885i 0.137080 0.237429i
\(391\) −22.8284 −1.15448
\(392\) −1.74264 + 6.77962i −0.0880166 + 0.342422i
\(393\) 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 0.446051 + 0.895008i \(0.352830\pi\)
−0.998125 + 0.0612128i \(0.980503\pi\)
\(398\) 0.100505 0.00503786
\(399\) 2.29289 + 2.95680i 0.114788 + 0.148025i
\(400\) −4.65685 −0.232843
\(401\) −9.15685 + 15.8601i −0.457271 + 0.792017i −0.998816 0.0486549i \(-0.984507\pi\)
0.541544 + 0.840672i \(0.317840\pi\)
\(402\) 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
\(406\) −6.96447 + 0.953065i −0.345641 + 0.0472998i
\(407\) −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 \(-0.188151\pi\)
−0.897775 + 0.440454i \(0.854818\pi\)
\(410\) −1.58579 2.74666i −0.0783164 0.135648i
\(411\) −20.1066 + 34.8257i −0.991786 + 1.71782i
\(412\) 13.4142 0.660871
\(413\) −5.58579 + 13.6823i −0.274859 + 0.673263i
\(414\) −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 \(-0.720471\pi\)
−0.638563 + 0.769569i \(0.720471\pi\)
\(420\) 1.41421 3.46410i 0.0690066 0.169031i
\(421\) 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
\(427\) −31.0061 + 4.24309i −1.50049 + 0.205337i
\(428\) −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 0.996283 0.0861437i \(-0.0274544\pi\)
−0.572744 + 0.819734i \(0.694121\pi\)
\(432\) −0.207107 + 0.358719i −0.00996443 + 0.0172589i
\(433\) 26.1421 1.25631 0.628155 0.778088i \(-0.283810\pi\)
0.628155 + 0.778088i \(0.283810\pi\)
\(434\) −6.48528 8.36308i −0.311303 0.401441i
\(435\) 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 −0.328765 0.944412i \(-0.606632\pi\)
0.982267 0.187487i \(-0.0600342\pi\)
\(440\) −0.585786 −0.0279263
\(441\) −14.1421 13.8564i −0.673435 0.659829i
\(442\) −14.0000 −0.665912
\(443\) −6.31371 + 10.9357i −0.299973 + 0.519569i −0.976130 0.217189i \(-0.930311\pi\)
0.676156 + 0.736758i \(0.263644\pi\)
\(444\) −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
\(448\) 1.62132 + 2.09077i 0.0766002 + 0.0987796i
\(449\) 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
\(455\) −5.87868 + 0.804479i −0.275597 + 0.0377146i
\(456\) 1.41421 0.0662266
\(457\) 5.82843 10.0951i 0.272642 0.472230i −0.696895 0.717173i \(-0.745436\pi\)
0.969538 + 0.244943i \(0.0787691\pi\)
\(458\) −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 \(-0.562018\pi\)
−0.193604 + 0.981080i \(0.562018\pi\)
\(462\) −2.41421 + 5.91359i −0.112319 + 0.275125i
\(463\) 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 −0.141332 0.989962i \(-0.545139\pi\)
0.927999 0.372584i \(-0.121528\pi\)
\(468\) −10.8284 −0.500544
\(469\) 2.75736 6.75412i 0.127323 0.311876i
\(470\) 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
\(476\) −9.58579 + 1.31178i −0.439364 + 0.0601256i
\(477\) 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 \(-0.0788084\pi\)
−0.696984 + 0.717087i \(0.745475\pi\)
\(480\) −0.707107 1.22474i −0.0322749 0.0559017i
\(481\) −18.0208 + 31.2130i −0.821678 + 1.42319i
\(482\) 12.2426 0.557637
\(483\) 24.4350 + 31.5101i 1.11183 + 1.43376i
\(484\) 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 0.954440 0.298402i \(-0.0964534\pi\)
−0.735644 + 0.677369i \(0.763120\pi\)
\(488\) −5.91421 + 10.2437i −0.267724 + 0.463711i
\(489\) −23.4853 −1.06204
\(490\) −3.94975 + 1.10165i −0.178431 + 0.0497676i
\(491\) 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
\(497\) −17.9497 23.1471i −0.805156 1.03829i
\(498\) 29.3137 1.31358
\(499\) −11.0711 + 19.1757i −0.495609 + 0.858420i −0.999987 0.00506282i \(-0.998388\pi\)
0.504378 + 0.863483i \(0.331722\pi\)
\(500\) −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 \(-0.470057\pi\)
0.0939287 + 0.995579i \(0.470057\pi\)
\(504\) −7.41421 + 1.01461i −0.330255 + 0.0451944i
\(505\) −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 \(-0.899512\pi\)
0.744170 + 0.667990i \(0.232845\pi\)
\(510\) 5.17157 0.229001
\(511\) −9.41421 + 23.0600i −0.416460 + 1.02012i
\(512\) 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
\(518\) −9.41421 + 23.0600i −0.413637 + 1.01320i
\(519\) 23.7279 1.04154
\(520\) −1.12132 + 1.94218i −0.0491731 + 0.0851704i
\(521\) 14.1421 + 24.4949i 0.619578 + 1.07314i 0.989563 + 0.144103i \(0.0460297\pi\)
−0.369984 + 0.929038i \(0.620637\pi\)
\(522\) −3.75736 6.50794i −0.164455 0.284845i
\(523\) 6.36396 11.0227i 0.278277 0.481989i −0.692680 0.721245i \(-0.743570\pi\)
0.970957 + 0.239256i \(0.0769035\pi\)
\(524\) −0.585786 −0.0255902
\(525\) −29.4706 + 4.03295i −1.28620 + 0.176013i
\(526\) −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
\(532\) −0.949747 1.22474i −0.0411768 0.0530994i
\(533\) 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
\(539\) 6.74264 1.88064i 0.290426 0.0810048i
\(540\) −0.242641 −0.0104416
\(541\) 6.42893 11.1352i 0.276401 0.478741i −0.694086 0.719892i \(-0.744191\pi\)
0.970488 + 0.241151i \(0.0775248\pi\)
\(542\) −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
\(546\) 14.9853 + 19.3242i 0.641311 + 0.827001i
\(547\) 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
\(553\) 34.7132 4.75039i 1.47616 0.202007i
\(554\) 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 0.775378 0.631498i \(-0.217560\pi\)
−0.934582 + 0.355748i \(0.884226\pi\)
\(558\) 5.65685 9.79796i 0.239474 0.414781i
\(559\) 21.6569 0.915987
\(560\) −0.585786 + 1.43488i −0.0247540 + 0.0606347i
\(561\) −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 \(-0.227888\pi\)
−0.945632 + 0.325240i \(0.894555\pi\)
\(564\) −12.6569 21.9223i −0.532950 0.923096i
\(565\) −2.39340 + 4.14549i −0.100691 + 0.174402i
\(566\) −23.4142 −0.984173
\(567\) −9.48528 + 23.2341i −0.398344 + 0.975740i
\(568\) −11.0711 −0.464532
\(569\) 2.00000 3.46410i 0.0838444 0.145223i −0.821054 0.570851i \(-0.806613\pi\)
0.904898 + 0.425628i \(0.139947\pi\)
\(570\) 0.414214 + 0.717439i 0.0173495 + 0.0300502i
\(571\) −13.1924 22.8499i −0.552084 0.956238i −0.998124 0.0612248i \(-0.980499\pi\)
0.446040 0.895013i \(-0.352834\pi\)
\(572\) 1.91421 3.31552i 0.0800373 0.138629i
\(573\) 17.3137 0.723291
\(574\) 14.1924 1.94218i 0.592379 0.0810652i
\(575\) 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 \(-0.102045\pi\)
−0.747429 + 0.664342i \(0.768712\pi\)
\(578\) 1.81371 + 3.14144i 0.0754403 + 0.130666i
\(579\) 26.4350 45.7868i 1.09860 1.90284i
\(580\) −1.55635 −0.0646239
\(581\) −19.6863 25.3864i −0.816725 1.05321i
\(582\) 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 \(-0.673325\pi\)
−0.518004 + 0.855378i \(0.673325\pi\)
\(588\) 12.0711 + 11.8272i 0.497802 + 0.487745i
\(589\) 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 \(-0.995093\pi\)
0.513291 + 0.858215i \(0.328426\pi\)
\(594\) 0.414214 0.0169954
\(595\) −3.47309 4.47871i −0.142383 0.183609i
\(596\) 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 −0.861114 0.508412i \(-0.830233\pi\)
−0.00974040 0.999953i \(-0.503101\pi\)
\(600\) −5.62132 + 9.73641i −0.229489 + 0.397487i
\(601\) 31.9411 1.30291 0.651453 0.758689i \(-0.274160\pi\)
0.651453 + 0.758689i \(0.274160\pi\)
\(602\) 14.8284 2.02922i 0.604362 0.0827050i
\(603\) 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 0.0121994 0.999926i \(-0.496117\pi\)
0.859861 0.510528i \(-0.170550\pi\)
\(608\) −0.585786 −0.0237568
\(609\) −6.41421 + 15.7116i −0.259917 + 0.636664i
\(610\) −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 −0.995694 0.0926971i \(-0.970451\pi\)
0.417569 0.908645i \(-0.362882\pi\)
\(614\) −4.94975 + 8.57321i −0.199756 + 0.345987i
\(615\) −7.65685 −0.308754
\(616\) 1.00000 2.44949i 0.0402911 0.0986928i
\(617\) −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 \(-0.0213104\pi\)
−0.556816 + 0.830636i \(0.687977\pi\)
\(620\) −1.17157 2.02922i −0.0470515 0.0814956i
\(621\) 1.29289 2.23936i 0.0518820 0.0898623i
\(622\) 16.7279 0.670729
\(623\) −32.7279 + 4.47871i −1.31122 + 0.179436i
\(624\) 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
\(630\) −2.68629 3.46410i −0.107024 0.138013i
\(631\) 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
\(637\) 6.67157 25.9553i 0.264337 1.02839i
\(638\) 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 0.674708 0.738085i \(-0.264270\pi\)
−0.976554 + 0.215272i \(0.930936\pi\)
\(642\) −3.70711 + 6.42090i −0.146308 + 0.253413i
\(643\) 1.58579 0.0625373 0.0312687 0.999511i \(-0.490045\pi\)
0.0312687 + 0.999511i \(0.490045\pi\)
\(644\) −10.1213 13.0519i −0.398836 0.514318i
\(645\) −8.00000 −0.315000
\(646\) 1.07107 1.85514i 0.0421406 0.0729897i
\(647\) −15.0919 26.1399i −0.593323 1.02767i −0.993781 0.111351i \(-0.964482\pi\)
0.400458 0.916315i \(-0.368851\pi\)
\(648\) 4.74264 + 8.21449i 0.186309 + 0.322696i
\(649\) 2.79289 4.83743i 0.109631 0.189886i
\(650\) 17.8284 0.699288
\(651\) −25.3137 + 3.46410i −0.992122 + 0.135769i
\(652\) 9.72792 0.380975
\(653\) 9.19239 15.9217i 0.359726 0.623064i −0.628189 0.778061i \(-0.716204\pi\)
0.987915 + 0.154997i \(0.0495369\pi\)
\(654\) 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
\(658\) −10.4853 + 25.6836i −0.408759 + 1.00125i
\(659\) −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 \(-0.286944\pi\)
−0.989399 + 0.145221i \(0.953611\pi\)
\(662\) 12.0355 + 20.8462i 0.467774 + 0.810209i
\(663\) −16.8995 + 29.2708i −0.656322 + 1.13678i
\(664\) −12.1421 −0.471206
\(665\) 0.343146 0.840532i 0.0133066 0.0325944i
\(666\) −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
\(672\) 6.32843 0.866025i 0.244124 0.0334077i
\(673\) 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 −0.296792 0.954942i \(-0.595917\pi\)
0.975400 0.220441i \(-0.0707498\pi\)
\(678\) 19.7279 0.757646
\(679\) −6.20711 8.00436i −0.238207 0.307179i
\(680\) −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 0.706298 0.707914i \(-0.250364\pi\)
−0.966221 + 0.257715i \(0.917030\pi\)
\(684\) 0.828427 1.43488i 0.0316757 0.0548639i
\(685\) 9.75736 0.372810
\(686\) 2.13604 18.3967i 0.0815543 0.702388i
\(687\) −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 0.465277 + 0.885165i \(0.345955\pi\)
−0.999214 + 0.0396407i \(0.987379\pi\)
\(692\) −9.82843 −0.373621
\(693\) 4.58579 + 5.91359i 0.174200 + 0.224639i
\(694\) 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
\(700\) 12.2071 1.67050i 0.461385 0.0631391i
\(701\) −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
\(707\) 6.17157 15.1172i 0.232106 0.568541i
\(708\) 13.4853 0.506808
\(709\) 6.02082 10.4284i 0.226116 0.391645i −0.730537 0.682873i \(-0.760730\pi\)
0.956654 + 0.291228i \(0.0940637\pi\)
\(710\) −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
\(714\) −8.82843 + 21.6251i −0.330396 + 0.809301i
\(715\) 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 \(-0.824342\pi\)
0.879802 + 0.475340i \(0.157675\pi\)
\(720\) −1.65685 −0.0617473
\(721\) −35.1630 + 4.81194i −1.30954 + 0.179206i
\(722\) −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 \(-0.263932\pi\)
0.675490 + 0.737369i \(0.263932\pi\)
\(728\) −6.20711 8.00436i −0.230051 0.296661i
\(729\) −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 \(-0.756159\pi\)
0.960738 + 0.277458i \(0.0894920\pi\)
\(734\) −10.7279 −0.395975
\(735\) −2.46447 + 9.58783i −0.0909032 + 0.353652i
\(736\) −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 0.711568 + 0.702617i \(0.247985\pi\)
0.252700 + 0.967545i \(0.418681\pi\)
\(740\) −2.75736 + 4.77589i −0.101363 + 0.175565i
\(741\) −5.41421 −0.198896
\(742\) 12.8076 + 16.5160i 0.470182 + 0.606323i
\(743\) −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
\(749\) 8.05025 1.10165i 0.294150 0.0402535i
\(750\) −13.6569 −0.498678
\(751\) −22.8284 + 39.5400i −0.833021 + 1.44283i 0.0626103 + 0.998038i \(0.480057\pi\)
−0.895631 + 0.444797i \(0.853276\pi\)
\(752\) 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
\(756\) 0.414214 1.01461i 0.0150648 0.0369011i
\(757\) 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 0.436039 + 0.899928i \(0.356381\pi\)
−0.997380 + 0.0723433i \(0.976952\pi\)
\(762\) −37.9706 −1.37553
\(763\) 16.4853 40.3805i 0.596807 1.46187i
\(764\) −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 \(-0.364072\pi\)
0.414170 + 0.910200i \(0.364072\pi\)
\(770\) 1.53553 0.210133i 0.0553368 0.00757267i
\(771\) 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 \(-0.0375555\pi\)
−0.598464 + 0.801150i \(0.704222\pi\)
\(774\) 8.00000 + 13.8564i 0.287554 + 0.498058i
\(775\) −9.31371 + 16.1318i −0.334558 + 0.579472i
\(776\) −3.82843 −0.137433
\(777\) 36.8492 + 47.5189i 1.32196 + 1.70473i
\(778\) −22.7279