Properties

Label 690.2.i.c.47.1
Level $690$
Weight $2$
Character 690.47
Analytic conductor $5.510$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 690.i (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.50967773947\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \(x^{8} - x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 47.1
Root \(-0.258819 - 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 690.47
Dual form 690.2.i.c.323.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.292893 + 1.70711i) q^{3} -1.00000i q^{4} +(-1.73205 + 1.41421i) q^{5} +(-1.00000 - 1.41421i) q^{6} +(2.44949 + 2.44949i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.82843 - 1.00000i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.292893 + 1.70711i) q^{3} -1.00000i q^{4} +(-1.73205 + 1.41421i) q^{5} +(-1.00000 - 1.41421i) q^{6} +(2.44949 + 2.44949i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.82843 - 1.00000i) q^{9} +(0.224745 - 2.22474i) q^{10} -5.65685i q^{11} +(1.70711 + 0.292893i) q^{12} +(-3.44949 + 3.44949i) q^{13} -3.46410 q^{14} +(-1.90691 - 3.37101i) q^{15} -1.00000 q^{16} +(-5.19615 + 5.19615i) q^{17} +(2.70711 - 1.29289i) q^{18} +2.44949i q^{19} +(1.41421 + 1.73205i) q^{20} +(-4.89898 + 3.46410i) q^{21} +(4.00000 + 4.00000i) q^{22} +(-0.707107 - 0.707107i) q^{23} +(-1.41421 + 1.00000i) q^{24} +(1.00000 - 4.89898i) q^{25} -4.87832i q^{26} +(2.53553 - 4.53553i) q^{27} +(2.44949 - 2.44949i) q^{28} -2.19275 q^{29} +(3.73205 + 1.03528i) q^{30} +4.89898 q^{31} +(0.707107 - 0.707107i) q^{32} +(9.65685 + 1.65685i) q^{33} -7.34847i q^{34} +(-7.70674 - 0.778539i) q^{35} +(-1.00000 + 2.82843i) q^{36} +(-2.44949 - 2.44949i) q^{37} +(-1.73205 - 1.73205i) q^{38} +(-4.87832 - 6.89898i) q^{39} +(-2.22474 - 0.224745i) q^{40} -8.48528i q^{41} +(1.01461 - 5.91359i) q^{42} +(2.89898 - 2.89898i) q^{43} -5.65685 q^{44} +(6.31319 - 2.26795i) q^{45} +1.00000 q^{46} +(-4.87832 + 4.87832i) q^{47} +(0.292893 - 1.70711i) q^{48} +5.00000i q^{49} +(2.75699 + 4.17121i) q^{50} +(-7.34847 - 10.3923i) q^{51} +(3.44949 + 3.44949i) q^{52} +(-0.953512 - 0.953512i) q^{53} +(1.41421 + 5.00000i) q^{54} +(8.00000 + 9.79796i) q^{55} +3.46410i q^{56} +(-4.18154 - 0.717439i) q^{57} +(1.55051 - 1.55051i) q^{58} -5.51399 q^{59} +(-3.37101 + 1.90691i) q^{60} +0.898979 q^{61} +(-3.46410 + 3.46410i) q^{62} +(-4.47871 - 9.37769i) q^{63} +1.00000i q^{64} +(1.09638 - 10.8530i) q^{65} +(-8.00000 + 5.65685i) q^{66} +(-10.8990 - 10.8990i) q^{67} +(5.19615 + 5.19615i) q^{68} +(1.41421 - 1.00000i) q^{69} +(6.00000 - 4.89898i) q^{70} +14.6349i q^{71} +(-1.29289 - 2.70711i) q^{72} +(-1.89898 + 1.89898i) q^{73} +3.46410 q^{74} +(8.07019 + 3.14198i) q^{75} +2.44949 q^{76} +(13.8564 - 13.8564i) q^{77} +(8.32780 + 1.42883i) q^{78} +4.44949i q^{79} +(1.73205 - 1.41421i) q^{80} +(7.00000 + 5.65685i) q^{81} +(6.00000 + 6.00000i) q^{82} +(1.41421 + 1.41421i) q^{83} +(3.46410 + 4.89898i) q^{84} +(1.65153 - 16.3485i) q^{85} +4.09978i q^{86} +(0.642242 - 3.74326i) q^{87} +(4.00000 - 4.00000i) q^{88} +9.12096 q^{89} +(-2.86042 + 6.06778i) q^{90} -16.8990 q^{91} +(-0.707107 + 0.707107i) q^{92} +(-1.43488 + 8.36308i) q^{93} -6.89898i q^{94} +(-3.46410 - 4.24264i) q^{95} +(1.00000 + 1.41421i) q^{96} +(-0.449490 - 0.449490i) q^{97} +(-3.53553 - 3.53553i) q^{98} +(-5.65685 + 16.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 8q^{3} - 8q^{6} + O(q^{10}) \) \( 8q - 8q^{3} - 8q^{6} - 8q^{10} + 8q^{12} - 8q^{13} - 8q^{15} - 8q^{16} + 16q^{18} + 32q^{22} + 8q^{25} - 8q^{27} + 16q^{30} + 32q^{33} - 8q^{36} - 8q^{40} - 16q^{43} + 8q^{46} + 8q^{48} + 8q^{52} + 64q^{55} + 32q^{58} + 8q^{60} - 32q^{61} - 64q^{66} - 48q^{67} + 48q^{70} - 16q^{72} + 24q^{73} - 8q^{75} + 8q^{78} + 56q^{81} + 48q^{82} + 72q^{85} - 32q^{87} + 32q^{88} - 8q^{90} - 96q^{91} + 8q^{96} + 16q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.500000 + 0.500000i
\(3\) −0.292893 + 1.70711i −0.169102 + 0.985599i
\(4\) 1.00000i 0.500000i
\(5\) −1.73205 + 1.41421i −0.774597 + 0.632456i
\(6\) −1.00000 1.41421i −0.408248 0.577350i
\(7\) 2.44949 + 2.44949i 0.925820 + 0.925820i 0.997433 0.0716124i \(-0.0228145\pi\)
−0.0716124 + 0.997433i \(0.522814\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) −2.82843 1.00000i −0.942809 0.333333i
\(10\) 0.224745 2.22474i 0.0710706 0.703526i
\(11\) 5.65685i 1.70561i −0.522233 0.852803i \(-0.674901\pi\)
0.522233 0.852803i \(-0.325099\pi\)
\(12\) 1.70711 + 0.292893i 0.492799 + 0.0845510i
\(13\) −3.44949 + 3.44949i −0.956716 + 0.956716i −0.999101 0.0423850i \(-0.986504\pi\)
0.0423850 + 0.999101i \(0.486504\pi\)
\(14\) −3.46410 −0.925820
\(15\) −1.90691 3.37101i −0.492361 0.870391i
\(16\) −1.00000 −0.250000
\(17\) −5.19615 + 5.19615i −1.26025 + 1.26025i −0.309282 + 0.950971i \(0.600089\pi\)
−0.950971 + 0.309282i \(0.899911\pi\)
\(18\) 2.70711 1.29289i 0.638071 0.304738i
\(19\) 2.44949i 0.561951i 0.959715 + 0.280976i \(0.0906580\pi\)
−0.959715 + 0.280976i \(0.909342\pi\)
\(20\) 1.41421 + 1.73205i 0.316228 + 0.387298i
\(21\) −4.89898 + 3.46410i −1.06904 + 0.755929i
\(22\) 4.00000 + 4.00000i 0.852803 + 0.852803i
\(23\) −0.707107 0.707107i −0.147442 0.147442i
\(24\) −1.41421 + 1.00000i −0.288675 + 0.204124i
\(25\) 1.00000 4.89898i 0.200000 0.979796i
\(26\) 4.87832i 0.956716i
\(27\) 2.53553 4.53553i 0.487964 0.872864i
\(28\) 2.44949 2.44949i 0.462910 0.462910i
\(29\) −2.19275 −0.407184 −0.203592 0.979056i \(-0.565262\pi\)
−0.203592 + 0.979056i \(0.565262\pi\)
\(30\) 3.73205 + 1.03528i 0.681376 + 0.189015i
\(31\) 4.89898 0.879883 0.439941 0.898027i \(-0.354999\pi\)
0.439941 + 0.898027i \(0.354999\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) 9.65685 + 1.65685i 1.68104 + 0.288421i
\(34\) 7.34847i 1.26025i
\(35\) −7.70674 0.778539i −1.30268 0.131597i
\(36\) −1.00000 + 2.82843i −0.166667 + 0.471405i
\(37\) −2.44949 2.44949i −0.402694 0.402694i 0.476488 0.879181i \(-0.341910\pi\)
−0.879181 + 0.476488i \(0.841910\pi\)
\(38\) −1.73205 1.73205i −0.280976 0.280976i
\(39\) −4.87832 6.89898i −0.781156 1.10472i
\(40\) −2.22474 0.224745i −0.351763 0.0355353i
\(41\) 8.48528i 1.32518i −0.748983 0.662589i \(-0.769458\pi\)
0.748983 0.662589i \(-0.230542\pi\)
\(42\) 1.01461 5.91359i 0.156558 0.912487i
\(43\) 2.89898 2.89898i 0.442090 0.442090i −0.450624 0.892714i \(-0.648798\pi\)
0.892714 + 0.450624i \(0.148798\pi\)
\(44\) −5.65685 −0.852803
\(45\) 6.31319 2.26795i 0.941115 0.338086i
\(46\) 1.00000 0.147442
\(47\) −4.87832 + 4.87832i −0.711575 + 0.711575i −0.966865 0.255289i \(-0.917829\pi\)
0.255289 + 0.966865i \(0.417829\pi\)
\(48\) 0.292893 1.70711i 0.0422755 0.246400i
\(49\) 5.00000i 0.714286i
\(50\) 2.75699 + 4.17121i 0.389898 + 0.589898i
\(51\) −7.34847 10.3923i −1.02899 1.45521i
\(52\) 3.44949 + 3.44949i 0.478358 + 0.478358i
\(53\) −0.953512 0.953512i −0.130975 0.130975i 0.638580 0.769555i \(-0.279522\pi\)
−0.769555 + 0.638580i \(0.779522\pi\)
\(54\) 1.41421 + 5.00000i 0.192450 + 0.680414i
\(55\) 8.00000 + 9.79796i 1.07872 + 1.32116i
\(56\) 3.46410i 0.462910i
\(57\) −4.18154 0.717439i −0.553859 0.0950271i
\(58\) 1.55051 1.55051i 0.203592 0.203592i
\(59\) −5.51399 −0.717860 −0.358930 0.933364i \(-0.616858\pi\)
−0.358930 + 0.933364i \(0.616858\pi\)
\(60\) −3.37101 + 1.90691i −0.435195 + 0.246181i
\(61\) 0.898979 0.115103 0.0575513 0.998343i \(-0.481671\pi\)
0.0575513 + 0.998343i \(0.481671\pi\)
\(62\) −3.46410 + 3.46410i −0.439941 + 0.439941i
\(63\) −4.47871 9.37769i −0.564265 1.18148i
\(64\) 1.00000i 0.125000i
\(65\) 1.09638 10.8530i 0.135989 1.34615i
\(66\) −8.00000 + 5.65685i −0.984732 + 0.696311i
\(67\) −10.8990 10.8990i −1.33152 1.33152i −0.904009 0.427513i \(-0.859390\pi\)
−0.427513 0.904009i \(-0.640610\pi\)
\(68\) 5.19615 + 5.19615i 0.630126 + 0.630126i
\(69\) 1.41421 1.00000i 0.170251 0.120386i
\(70\) 6.00000 4.89898i 0.717137 0.585540i
\(71\) 14.6349i 1.73685i 0.495822 + 0.868424i \(0.334867\pi\)
−0.495822 + 0.868424i \(0.665133\pi\)
\(72\) −1.29289 2.70711i −0.152369 0.319036i
\(73\) −1.89898 + 1.89898i −0.222259 + 0.222259i −0.809449 0.587190i \(-0.800234\pi\)
0.587190 + 0.809449i \(0.300234\pi\)
\(74\) 3.46410 0.402694
\(75\) 8.07019 + 3.14198i 0.931865 + 0.362805i
\(76\) 2.44949 0.280976
\(77\) 13.8564 13.8564i 1.57908 1.57908i
\(78\) 8.32780 + 1.42883i 0.942938 + 0.161783i
\(79\) 4.44949i 0.500607i 0.968167 + 0.250303i \(0.0805304\pi\)
−0.968167 + 0.250303i \(0.919470\pi\)
\(80\) 1.73205 1.41421i 0.193649 0.158114i
\(81\) 7.00000 + 5.65685i 0.777778 + 0.628539i
\(82\) 6.00000 + 6.00000i 0.662589 + 0.662589i
\(83\) 1.41421 + 1.41421i 0.155230 + 0.155230i 0.780449 0.625219i \(-0.214990\pi\)
−0.625219 + 0.780449i \(0.714990\pi\)
\(84\) 3.46410 + 4.89898i 0.377964 + 0.534522i
\(85\) 1.65153 16.3485i 0.179134 1.77324i
\(86\) 4.09978i 0.442090i
\(87\) 0.642242 3.74326i 0.0688556 0.401320i
\(88\) 4.00000 4.00000i 0.426401 0.426401i
\(89\) 9.12096 0.966819 0.483410 0.875394i \(-0.339398\pi\)
0.483410 + 0.875394i \(0.339398\pi\)
\(90\) −2.86042 + 6.06778i −0.301515 + 0.639601i
\(91\) −16.8990 −1.77149
\(92\) −0.707107 + 0.707107i −0.0737210 + 0.0737210i
\(93\) −1.43488 + 8.36308i −0.148790 + 0.867211i
\(94\) 6.89898i 0.711575i
\(95\) −3.46410 4.24264i −0.355409 0.435286i
\(96\) 1.00000 + 1.41421i 0.102062 + 0.144338i
\(97\) −0.449490 0.449490i −0.0456388 0.0456388i 0.683919 0.729558i \(-0.260274\pi\)
−0.729558 + 0.683919i \(0.760274\pi\)
\(98\) −3.53553 3.53553i −0.357143 0.357143i
\(99\) −5.65685 + 16.0000i −0.568535 + 1.60806i
\(100\) −4.89898 1.00000i −0.489898 0.100000i
\(101\) 0.635674i 0.0632520i −0.999500 0.0316260i \(-0.989931\pi\)
0.999500 0.0316260i \(-0.0100685\pi\)
\(102\) 12.5446 + 2.15232i 1.24210 + 0.213111i
\(103\) −10.8990 + 10.8990i −1.07391 + 1.07391i −0.0768670 + 0.997041i \(0.524492\pi\)
−0.997041 + 0.0768670i \(0.975508\pi\)
\(104\) −4.87832 −0.478358
\(105\) 3.58630 12.9282i 0.349987 1.26166i
\(106\) 1.34847 0.130975
\(107\) 7.70674 7.70674i 0.745039 0.745039i −0.228504 0.973543i \(-0.573383\pi\)
0.973543 + 0.228504i \(0.0733834\pi\)
\(108\) −4.53553 2.53553i −0.436432 0.243982i
\(109\) 13.7980i 1.32160i 0.750560 + 0.660802i \(0.229784\pi\)
−0.750560 + 0.660802i \(0.770216\pi\)
\(110\) −12.5851 1.27135i −1.19994 0.121218i
\(111\) 4.89898 3.46410i 0.464991 0.328798i
\(112\) −2.44949 2.44949i −0.231455 0.231455i
\(113\) 8.02458 + 8.02458i 0.754889 + 0.754889i 0.975387 0.220498i \(-0.0707684\pi\)
−0.220498 + 0.975387i \(0.570768\pi\)
\(114\) 3.46410 2.44949i 0.324443 0.229416i
\(115\) 2.22474 + 0.224745i 0.207459 + 0.0209576i
\(116\) 2.19275i 0.203592i
\(117\) 13.2061 6.30714i 1.22091 0.583095i
\(118\) 3.89898 3.89898i 0.358930 0.358930i
\(119\) −25.4558 −2.33353
\(120\) 1.03528 3.73205i 0.0945074 0.340688i
\(121\) −21.0000 −1.90909
\(122\) −0.635674 + 0.635674i −0.0575513 + 0.0575513i
\(123\) 14.4853 + 2.48528i 1.30609 + 0.224090i
\(124\) 4.89898i 0.439941i
\(125\) 5.19615 + 9.89949i 0.464758 + 0.885438i
\(126\) 9.79796 + 3.46410i 0.872872 + 0.308607i
\(127\) −3.55051 3.55051i −0.315057 0.315057i 0.531808 0.846865i \(-0.321513\pi\)
−0.846865 + 0.531808i \(0.821513\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) 4.09978 + 5.79796i 0.360965 + 0.510482i
\(130\) 6.89898 + 8.44949i 0.605081 + 0.741069i
\(131\) 0.142865i 0.0124821i −0.999981 0.00624107i \(-0.998013\pi\)
0.999981 0.00624107i \(-0.00198661\pi\)
\(132\) 1.65685 9.65685i 0.144211 0.840521i
\(133\) −6.00000 + 6.00000i −0.520266 + 0.520266i
\(134\) 15.4135 1.33152
\(135\) 2.02254 + 11.4416i 0.174073 + 0.984733i
\(136\) −7.34847 −0.630126
\(137\) −13.6814 + 13.6814i −1.16888 + 1.16888i −0.186412 + 0.982472i \(0.559686\pi\)
−0.982472 + 0.186412i \(0.940314\pi\)
\(138\) −0.292893 + 1.70711i −0.0249327 + 0.145319i
\(139\) 18.6969i 1.58585i 0.609317 + 0.792927i \(0.291444\pi\)
−0.609317 + 0.792927i \(0.708556\pi\)
\(140\) −0.778539 + 7.70674i −0.0657986 + 0.651339i
\(141\) −6.89898 9.75663i −0.580999 0.821656i
\(142\) −10.3485 10.3485i −0.868424 0.868424i
\(143\) 19.5133 + 19.5133i 1.63178 + 1.63178i
\(144\) 2.82843 + 1.00000i 0.235702 + 0.0833333i
\(145\) 3.79796 3.10102i 0.315403 0.257526i
\(146\) 2.68556i 0.222259i
\(147\) −8.53553 1.46447i −0.703999 0.120787i
\(148\) −2.44949 + 2.44949i −0.201347 + 0.201347i
\(149\) −11.0280 −0.903447 −0.451724 0.892158i \(-0.649191\pi\)
−0.451724 + 0.892158i \(0.649191\pi\)
\(150\) −7.92820 + 3.48477i −0.647335 + 0.284530i
\(151\) −0.898979 −0.0731579 −0.0365790 0.999331i \(-0.511646\pi\)
−0.0365790 + 0.999331i \(0.511646\pi\)
\(152\) −1.73205 + 1.73205i −0.140488 + 0.140488i
\(153\) 19.8931 9.50079i 1.60826 0.768093i
\(154\) 19.5959i 1.57908i
\(155\) −8.48528 + 6.92820i −0.681554 + 0.556487i
\(156\) −6.89898 + 4.87832i −0.552360 + 0.390578i
\(157\) −8.44949 8.44949i −0.674343 0.674343i 0.284371 0.958714i \(-0.408215\pi\)
−0.958714 + 0.284371i \(0.908215\pi\)
\(158\) −3.14626 3.14626i −0.250303 0.250303i
\(159\) 1.90702 1.34847i 0.151237 0.106941i
\(160\) −0.224745 + 2.22474i −0.0177676 + 0.175882i
\(161\) 3.46410i 0.273009i
\(162\) −8.94975 + 0.949747i −0.703159 + 0.0746192i
\(163\) −4.00000 + 4.00000i −0.313304 + 0.313304i −0.846188 0.532884i \(-0.821108\pi\)
0.532884 + 0.846188i \(0.321108\pi\)
\(164\) −8.48528 −0.662589
\(165\) −19.0693 + 10.7871i −1.48454 + 0.839774i
\(166\) −2.00000 −0.155230
\(167\) 5.65685 5.65685i 0.437741 0.437741i −0.453510 0.891251i \(-0.649829\pi\)
0.891251 + 0.453510i \(0.149829\pi\)
\(168\) −5.91359 1.01461i −0.456243 0.0782790i
\(169\) 10.7980i 0.830612i
\(170\) 10.3923 + 12.7279i 0.797053 + 0.976187i
\(171\) 2.44949 6.92820i 0.187317 0.529813i
\(172\) −2.89898 2.89898i −0.221045 0.221045i
\(173\) 3.60697 + 3.60697i 0.274233 + 0.274233i 0.830801 0.556569i \(-0.187882\pi\)
−0.556569 + 0.830801i \(0.687882\pi\)
\(174\) 2.19275 + 3.10102i 0.166232 + 0.235088i
\(175\) 14.4495 9.55051i 1.09228 0.721951i
\(176\) 5.65685i 0.426401i
\(177\) 1.61501 9.41297i 0.121392 0.707522i
\(178\) −6.44949 + 6.44949i −0.483410 + 0.483410i
\(179\) −15.2706 −1.14138 −0.570690 0.821166i \(-0.693324\pi\)
−0.570690 + 0.821166i \(0.693324\pi\)
\(180\) −2.26795 6.31319i −0.169043 0.470558i
\(181\) 8.00000 0.594635 0.297318 0.954779i \(-0.403908\pi\)
0.297318 + 0.954779i \(0.403908\pi\)
\(182\) 11.9494 11.9494i 0.885747 0.885747i
\(183\) −0.263305 + 1.53465i −0.0194641 + 0.113445i
\(184\) 1.00000i 0.0737210i
\(185\) 7.70674 + 0.778539i 0.566611 + 0.0572393i
\(186\) −4.89898 6.92820i −0.359211 0.508001i
\(187\) 29.3939 + 29.3939i 2.14949 + 2.14949i
\(188\) 4.87832 + 4.87832i 0.355788 + 0.355788i
\(189\) 17.3205 4.89898i 1.25988 0.356348i
\(190\) 5.44949 + 0.550510i 0.395348 + 0.0399382i
\(191\) 17.9562i 1.29926i 0.760249 + 0.649632i \(0.225077\pi\)
−0.760249 + 0.649632i \(0.774923\pi\)
\(192\) −1.70711 0.292893i −0.123200 0.0211377i
\(193\) 1.89898 1.89898i 0.136692 0.136692i −0.635450 0.772142i \(-0.719185\pi\)
0.772142 + 0.635450i \(0.219185\pi\)
\(194\) 0.635674 0.0456388
\(195\) 18.2061 + 5.05040i 1.30377 + 0.361667i
\(196\) 5.00000 0.357143
\(197\) −7.70674 + 7.70674i −0.549083 + 0.549083i −0.926175 0.377093i \(-0.876924\pi\)
0.377093 + 0.926175i \(0.376924\pi\)
\(198\) −7.31371 15.3137i −0.519763 1.08830i
\(199\) 7.55051i 0.535241i 0.963524 + 0.267621i \(0.0862374\pi\)
−0.963524 + 0.267621i \(0.913763\pi\)
\(200\) 4.17121 2.75699i 0.294949 0.194949i
\(201\) 21.7980 15.4135i 1.53751 1.08718i
\(202\) 0.449490 + 0.449490i 0.0316260 + 0.0316260i
\(203\) −5.37113 5.37113i −0.376979 0.376979i
\(204\) −10.3923 + 7.34847i −0.727607 + 0.514496i
\(205\) 12.0000 + 14.6969i 0.838116 + 1.02648i
\(206\) 15.4135i 1.07391i
\(207\) 1.29289 + 2.70711i 0.0898623 + 0.188157i
\(208\) 3.44949 3.44949i 0.239179 0.239179i
\(209\) 13.8564 0.958468
\(210\) 6.60572 + 11.6775i 0.455838 + 0.805825i
\(211\) 18.6969 1.28715 0.643575 0.765383i \(-0.277450\pi\)
0.643575 + 0.765383i \(0.277450\pi\)
\(212\) −0.953512 + 0.953512i −0.0654875 + 0.0654875i
\(213\) −24.9834 4.28648i −1.71184 0.293705i
\(214\) 10.8990i 0.745039i
\(215\) −0.921404 + 9.12096i −0.0628392 + 0.622044i
\(216\) 5.00000 1.41421i 0.340207 0.0962250i
\(217\) 12.0000 + 12.0000i 0.814613 + 0.814613i
\(218\) −9.75663 9.75663i −0.660802 0.660802i
\(219\) −2.68556 3.79796i −0.181473 0.256642i
\(220\) 9.79796 8.00000i 0.660578 0.539360i
\(221\) 35.8481i 2.41141i
\(222\) −1.01461 + 5.91359i −0.0680963 + 0.396894i
\(223\) −12.4495 + 12.4495i −0.833679 + 0.833679i −0.988018 0.154339i \(-0.950675\pi\)
0.154339 + 0.988018i \(0.450675\pi\)
\(224\) 3.46410 0.231455
\(225\) −7.72741 + 12.8564i −0.515160 + 0.857094i
\(226\) −11.3485 −0.754889
\(227\) 0.778539 0.778539i 0.0516735 0.0516735i −0.680798 0.732471i \(-0.738367\pi\)
0.732471 + 0.680798i \(0.238367\pi\)
\(228\) −0.717439 + 4.18154i −0.0475136 + 0.276929i
\(229\) 6.69694i 0.442546i −0.975212 0.221273i \(-0.928979\pi\)
0.975212 0.221273i \(-0.0710212\pi\)
\(230\) −1.73205 + 1.41421i −0.114208 + 0.0932505i
\(231\) 19.5959 + 27.7128i 1.28932 + 1.82337i
\(232\) −1.55051 1.55051i −0.101796 0.101796i
\(233\) −3.60697 3.60697i −0.236300 0.236300i 0.579016 0.815316i \(-0.303437\pi\)
−0.815316 + 0.579016i \(0.803437\pi\)
\(234\) −4.87832 + 13.7980i −0.318905 + 0.902001i
\(235\) 1.55051 15.3485i 0.101144 1.00122i
\(236\) 5.51399i 0.358930i
\(237\) −7.59575 1.30323i −0.493397 0.0846536i
\(238\) 18.0000 18.0000i 1.16677 1.16677i
\(239\) 13.3636 0.864419 0.432210 0.901773i \(-0.357734\pi\)
0.432210 + 0.901773i \(0.357734\pi\)
\(240\) 1.90691 + 3.37101i 0.123090 + 0.217598i
\(241\) −9.10102 −0.586248 −0.293124 0.956074i \(-0.594695\pi\)
−0.293124 + 0.956074i \(0.594695\pi\)
\(242\) 14.8492 14.8492i 0.954545 0.954545i
\(243\) −11.7071 + 10.2929i −0.751011 + 0.660289i
\(244\) 0.898979i 0.0575513i
\(245\) −7.07107 8.66025i −0.451754 0.553283i
\(246\) −12.0000 + 8.48528i −0.765092 + 0.541002i
\(247\) −8.44949 8.44949i −0.537628 0.537628i
\(248\) 3.46410 + 3.46410i 0.219971 + 0.219971i
\(249\) −2.82843 + 2.00000i −0.179244 + 0.126745i
\(250\) −10.6742 3.32577i −0.675098 0.210340i
\(251\) 12.8708i 0.812397i 0.913785 + 0.406198i \(0.133146\pi\)
−0.913785 + 0.406198i \(0.866854\pi\)
\(252\) −9.37769 + 4.47871i −0.590739 + 0.282132i
\(253\) −4.00000 + 4.00000i −0.251478 + 0.251478i
\(254\) 5.02118 0.315057
\(255\) 27.4249 + 7.60770i 1.71741 + 0.476412i
\(256\) 1.00000 0.0625000
\(257\) −9.61377 + 9.61377i −0.599690 + 0.599690i −0.940230 0.340540i \(-0.889390\pi\)
0.340540 + 0.940230i \(0.389390\pi\)
\(258\) −6.99876 1.20080i −0.435723 0.0747583i
\(259\) 12.0000i 0.745644i
\(260\) −10.8530 1.09638i −0.673075 0.0679944i
\(261\) 6.20204 + 2.19275i 0.383897 + 0.135728i
\(262\) 0.101021 + 0.101021i 0.00624107 + 0.00624107i
\(263\) −5.65685 5.65685i −0.348817 0.348817i 0.510852 0.859669i \(-0.329330\pi\)
−0.859669 + 0.510852i \(0.829330\pi\)
\(264\) 5.65685 + 8.00000i 0.348155 + 0.492366i
\(265\) 3.00000 + 0.303062i 0.184289 + 0.0186169i
\(266\) 8.48528i 0.520266i
\(267\) −2.67147 + 15.5704i −0.163491 + 0.952896i
\(268\) −10.8990 + 10.8990i −0.665761 + 0.665761i
\(269\) 6.29253 0.383662 0.191831 0.981428i \(-0.438557\pi\)
0.191831 + 0.981428i \(0.438557\pi\)
\(270\) −9.52056 6.66025i −0.579403 0.405330i
\(271\) −24.4949 −1.48796 −0.743980 0.668202i \(-0.767064\pi\)
−0.743980 + 0.668202i \(0.767064\pi\)
\(272\) 5.19615 5.19615i 0.315063 0.315063i
\(273\) 4.94960 28.8484i 0.299563 1.74598i
\(274\) 19.3485i 1.16888i
\(275\) −27.7128 5.65685i −1.67115 0.341121i
\(276\) −1.00000 1.41421i −0.0601929 0.0851257i
\(277\) −9.44949 9.44949i −0.567765 0.567765i 0.363737 0.931502i \(-0.381501\pi\)
−0.931502 + 0.363737i \(0.881501\pi\)
\(278\) −13.2207 13.2207i −0.792927 0.792927i
\(279\) −13.8564 4.89898i −0.829561 0.293294i
\(280\) −4.89898 6.00000i −0.292770 0.358569i
\(281\) 5.65685i 0.337460i 0.985662 + 0.168730i \(0.0539665\pi\)
−0.985662 + 0.168730i \(0.946033\pi\)
\(282\) 11.7773 + 2.02066i 0.701328 + 0.120329i
\(283\) 5.34847 5.34847i 0.317933 0.317933i −0.530039 0.847973i \(-0.677823\pi\)
0.847973 + 0.530039i \(0.177823\pi\)
\(284\) 14.6349 0.868424
\(285\) 8.25725 4.67095i 0.489117 0.276683i
\(286\) −27.5959 −1.63178
\(287\) 20.7846 20.7846i 1.22688 1.22688i
\(288\) −2.70711 + 1.29289i −0.159518 + 0.0761845i
\(289\) 37.0000i 2.17647i
\(290\) −0.492810 + 4.87832i −0.0289388 + 0.286465i
\(291\) 0.898979 0.635674i 0.0526991 0.0372639i
\(292\) 1.89898 + 1.89898i 0.111129 + 0.111129i
\(293\) 13.5386 + 13.5386i 0.790932 + 0.790932i 0.981646 0.190714i \(-0.0610803\pi\)
−0.190714 + 0.981646i \(0.561080\pi\)
\(294\) 7.07107 5.00000i 0.412393 0.291606i
\(295\) 9.55051 7.79796i 0.556052 0.454015i
\(296\) 3.46410i 0.201347i
\(297\) −25.6569 14.3431i −1.48876 0.832274i
\(298\) 7.79796 7.79796i 0.451724 0.451724i
\(299\) 4.87832 0.282120
\(300\) 3.14198 8.07019i 0.181403 0.465933i
\(301\) 14.2020 0.818592
\(302\) 0.635674 0.635674i 0.0365790 0.0365790i
\(303\) 1.08516 + 0.186185i 0.0623411 + 0.0106960i
\(304\) 2.44949i 0.140488i
\(305\) −1.55708 + 1.27135i −0.0891580 + 0.0727972i
\(306\) −7.34847 + 20.7846i −0.420084 + 1.18818i
\(307\) −22.6969 22.6969i −1.29538 1.29538i −0.931409 0.363973i \(-0.881420\pi\)
−0.363973 0.931409i \(-0.618580\pi\)
\(308\) −13.8564 13.8564i −0.789542 0.789542i
\(309\) −15.4135 21.7980i −0.876843 1.24004i
\(310\) 1.10102 10.8990i 0.0625338 0.619020i
\(311\) 14.3492i 0.813669i −0.913502 0.406835i \(-0.866632\pi\)
0.913502 0.406835i \(-0.133368\pi\)
\(312\) 1.42883 8.32780i 0.0808913 0.471469i
\(313\) −15.1464 + 15.1464i −0.856127 + 0.856127i −0.990879 0.134753i \(-0.956976\pi\)
0.134753 + 0.990879i \(0.456976\pi\)
\(314\) 11.9494 0.674343
\(315\) 21.0194 + 9.90878i 1.18431 + 0.558297i
\(316\) 4.44949 0.250303
\(317\) −13.3636 + 13.3636i −0.750574 + 0.750574i −0.974586 0.224012i \(-0.928085\pi\)
0.224012 + 0.974586i \(0.428085\pi\)
\(318\) −0.394957 + 2.30198i −0.0221481 + 0.129089i
\(319\) 12.4041i 0.694495i
\(320\) −1.41421 1.73205i −0.0790569 0.0968246i
\(321\) 10.8990 + 15.4135i 0.608322 + 0.860297i
\(322\) 2.44949 + 2.44949i 0.136505 + 0.136505i
\(323\) −12.7279 12.7279i −0.708201 0.708201i
\(324\) 5.65685 7.00000i 0.314270 0.388889i
\(325\) 13.4495 + 20.3485i 0.746043 + 1.12873i
\(326\) 5.65685i 0.313304i
\(327\) −23.5546 4.04133i −1.30257 0.223486i
\(328\) 6.00000 6.00000i 0.331295 0.331295i
\(329\) −23.8988 −1.31758
\(330\) 5.85641 21.1117i 0.322385 1.16216i
\(331\) −18.6969 −1.02768 −0.513838 0.857887i \(-0.671777\pi\)
−0.513838 + 0.857887i \(0.671777\pi\)
\(332\) 1.41421 1.41421i 0.0776151 0.0776151i
\(333\) 4.47871 + 9.37769i 0.245432 + 0.513894i
\(334\) 8.00000i 0.437741i
\(335\) 34.2911 + 3.46410i 1.87352 + 0.189264i
\(336\) 4.89898 3.46410i 0.267261 0.188982i
\(337\) 14.4495 + 14.4495i 0.787114 + 0.787114i 0.981020 0.193906i \(-0.0621157\pi\)
−0.193906 + 0.981020i \(0.562116\pi\)
\(338\) 7.63531 + 7.63531i 0.415306 + 0.415306i
\(339\) −16.0492 + 11.3485i −0.871671 + 0.616364i
\(340\) −16.3485 1.65153i −0.886620 0.0895668i
\(341\) 27.7128i 1.50073i
\(342\) 3.16693 + 6.63103i 0.171248 + 0.358565i
\(343\) 4.89898 4.89898i 0.264520 0.264520i
\(344\) 4.09978 0.221045
\(345\) −1.03528 + 3.73205i −0.0557374 + 0.200927i
\(346\) −5.10102 −0.274233
\(347\) −0.142865 + 0.142865i −0.00766937 + 0.00766937i −0.710931 0.703262i \(-0.751726\pi\)
0.703262 + 0.710931i \(0.251726\pi\)
\(348\) −3.74326 0.642242i −0.200660 0.0344278i
\(349\) 22.0000i 1.17763i −0.808267 0.588817i \(-0.799594\pi\)
0.808267 0.588817i \(-0.200406\pi\)
\(350\) −3.46410 + 16.9706i −0.185164 + 0.907115i
\(351\) 6.89898 + 24.3916i 0.368240 + 1.30193i
\(352\) −4.00000 4.00000i −0.213201 0.213201i
\(353\) 23.1202 + 23.1202i 1.23057 + 1.23057i 0.963747 + 0.266819i \(0.0859725\pi\)
0.266819 + 0.963747i \(0.414027\pi\)
\(354\) 5.51399 + 7.79796i 0.293065 + 0.414457i
\(355\) −20.6969 25.3485i −1.09848 1.34536i
\(356\) 9.12096i 0.483410i
\(357\) 7.45584 43.4558i 0.394605 2.29993i
\(358\) 10.7980 10.7980i 0.570690 0.570690i
\(359\) 26.7272 1.41061 0.705304 0.708905i \(-0.250811\pi\)
0.705304 + 0.708905i \(0.250811\pi\)
\(360\) 6.06778 + 2.86042i 0.319800 + 0.150757i
\(361\) 13.0000 0.684211
\(362\) −5.65685 + 5.65685i −0.297318 + 0.297318i
\(363\) 6.15076 35.8492i 0.322831 1.88160i
\(364\) 16.8990i 0.885747i
\(365\) 0.603566 5.97469i 0.0315921 0.312730i
\(366\) −0.898979 1.27135i −0.0469904 0.0664545i
\(367\) 19.7980 + 19.7980i 1.03345 + 1.03345i 0.999421 + 0.0340240i \(0.0108323\pi\)
0.0340240 + 0.999421i \(0.489168\pi\)
\(368\) 0.707107 + 0.707107i 0.0368605 + 0.0368605i
\(369\) −8.48528 + 24.0000i −0.441726 + 1.24939i
\(370\) −6.00000 + 4.89898i −0.311925 + 0.254686i
\(371\) 4.67123i 0.242518i
\(372\) 8.36308 + 1.43488i 0.433606 + 0.0743950i
\(373\) 12.4495 12.4495i 0.644610 0.644610i −0.307075 0.951685i \(-0.599350\pi\)
0.951685 + 0.307075i \(0.0993503\pi\)
\(374\) −41.5692 −2.14949
\(375\) −18.4214 + 5.97089i −0.951278 + 0.308336i
\(376\) −6.89898 −0.355788
\(377\) 7.56388 7.56388i 0.389560 0.389560i
\(378\) −8.78335 + 15.7116i −0.451767 + 0.808115i
\(379\) 5.14643i 0.264354i 0.991226 + 0.132177i \(0.0421968\pi\)
−0.991226 + 0.132177i \(0.957803\pi\)
\(380\) −4.24264 + 3.46410i −0.217643 + 0.177705i
\(381\) 7.10102 5.02118i 0.363796 0.257243i
\(382\) −12.6969 12.6969i −0.649632 0.649632i
\(383\) −4.73545 4.73545i −0.241970 0.241970i 0.575695 0.817665i \(-0.304732\pi\)
−0.817665 + 0.575695i \(0.804732\pi\)
\(384\) 1.41421 1.00000i 0.0721688 0.0510310i
\(385\) −4.40408 + 43.5959i −0.224453 + 2.22185i
\(386\) 2.68556i 0.136692i
\(387\) −11.0985 + 5.30057i −0.564170 + 0.269443i
\(388\) −0.449490 + 0.449490i −0.0228194 + 0.0228194i
\(389\) 31.1127 1.57748 0.788738 0.614729i \(-0.210735\pi\)
0.788738 + 0.614729i \(0.210735\pi\)
\(390\) −16.4448 + 9.30250i −0.832717 + 0.471050i
\(391\) 7.34847 0.371628
\(392\) −3.53553 + 3.53553i −0.178571 + 0.178571i
\(393\) 0.243885 + 0.0418441i 0.0123024 + 0.00211075i
\(394\) 10.8990i 0.549083i
\(395\) −6.29253 7.70674i −0.316611 0.387768i
\(396\) 16.0000 + 5.65685i 0.804030 + 0.284268i
\(397\) 8.55051 + 8.55051i 0.429138 + 0.429138i 0.888335 0.459197i \(-0.151863\pi\)
−0.459197 + 0.888335i \(0.651863\pi\)
\(398\) −5.33902 5.33902i −0.267621 0.267621i
\(399\) −8.48528 12.0000i −0.424795 0.600751i
\(400\) −1.00000 + 4.89898i −0.0500000 + 0.244949i
\(401\) 7.84961i 0.391991i −0.980605 0.195995i \(-0.937206\pi\)
0.980605 0.195995i \(-0.0627937\pi\)
\(402\) −4.51451 + 26.3125i −0.225163 + 1.31235i
\(403\) −16.8990 + 16.8990i −0.841798 + 0.841798i
\(404\) −0.635674 −0.0316260
\(405\) −20.1244 + 0.101536i −0.999987 + 0.00504536i
\(406\) 7.59592 0.376979
\(407\) −13.8564 + 13.8564i −0.686837 + 0.686837i
\(408\) 2.15232 12.5446i 0.106556 0.621051i
\(409\) 13.7980i 0.682265i 0.940015 + 0.341133i \(0.110811\pi\)
−0.940015 + 0.341133i \(0.889189\pi\)
\(410\) −18.8776 1.90702i −0.932298 0.0941812i
\(411\) −19.3485 27.3629i −0.954390 1.34971i
\(412\) 10.8990 + 10.8990i 0.536954 + 0.536954i
\(413\) −13.5065 13.5065i −0.664610 0.664610i
\(414\) −2.82843 1.00000i −0.139010 0.0491473i
\(415\) −4.44949 0.449490i −0.218417 0.0220646i
\(416\) 4.87832i 0.239179i
\(417\) −31.9177 5.47621i −1.56302 0.268171i
\(418\) −9.79796 + 9.79796i −0.479234 + 0.479234i
\(419\) −4.38551 −0.214246 −0.107123 0.994246i \(-0.534164\pi\)
−0.107123 + 0.994246i \(0.534164\pi\)
\(420\) −12.9282 3.58630i −0.630832 0.174994i
\(421\) 0.898979 0.0438136 0.0219068 0.999760i \(-0.493026\pi\)
0.0219068 + 0.999760i \(0.493026\pi\)
\(422\) −13.2207 + 13.2207i −0.643575 + 0.643575i
\(423\) 18.6763 8.91964i 0.908072 0.433688i
\(424\) 1.34847i 0.0654875i
\(425\) 20.2597 + 30.6520i 0.982739 + 1.48684i
\(426\) 20.6969 14.6349i 1.00277 0.709065i
\(427\) 2.20204 + 2.20204i 0.106564 + 0.106564i
\(428\) −7.70674 7.70674i −0.372519 0.372519i
\(429\) −39.0265 + 27.5959i −1.88422 + 1.33234i
\(430\) −5.79796 7.10102i −0.279602 0.342442i
\(431\) 22.3417i 1.07616i 0.842893 + 0.538081i \(0.180850\pi\)
−0.842893 + 0.538081i \(0.819150\pi\)
\(432\) −2.53553 + 4.53553i −0.121991 + 0.218216i
\(433\) 29.3485 29.3485i 1.41040 1.41040i 0.653287 0.757110i \(-0.273389\pi\)
0.757110 0.653287i \(-0.226611\pi\)
\(434\) −16.9706 −0.814613
\(435\) 4.18138 + 7.39179i 0.200482 + 0.354409i
\(436\) 13.7980 0.660802
\(437\) 1.73205 1.73205i 0.0828552 0.0828552i
\(438\) 4.58454 + 0.786583i 0.219058 + 0.0375844i
\(439\) 16.0000i 0.763638i −0.924237 0.381819i \(-0.875298\pi\)
0.924237 0.381819i \(-0.124702\pi\)
\(440\) −1.27135 + 12.5851i −0.0606092 + 0.599969i
\(441\) 5.00000 14.1421i 0.238095 0.673435i
\(442\) 25.3485 + 25.3485i 1.20570 + 1.20570i
\(443\) 11.3137 + 11.3137i 0.537531 + 0.537531i 0.922803 0.385272i \(-0.125893\pi\)
−0.385272 + 0.922803i \(0.625893\pi\)
\(444\) −3.46410 4.89898i −0.164399 0.232495i
\(445\) −15.7980 + 12.8990i −0.748895 + 0.611470i
\(446\) 17.6062i 0.833679i
\(447\) 3.23002 18.8259i 0.152775 0.890436i
\(448\) −2.44949 + 2.44949i −0.115728 + 0.115728i
\(449\) 15.1278 0.713923 0.356961 0.934119i \(-0.383813\pi\)
0.356961 + 0.934119i \(0.383813\pi\)
\(450\) −3.62675 14.5550i −0.170967 0.686127i
\(451\) −48.0000 −2.26023
\(452\) 8.02458 8.02458i 0.377444 0.377444i
\(453\) 0.263305 1.53465i 0.0123711 0.0721043i
\(454\) 1.10102i 0.0516735i
\(455\) 29.2699 23.8988i 1.37219 1.12039i
\(456\) −2.44949 3.46410i −0.114708 0.162221i
\(457\) 1.55051 + 1.55051i 0.0725298 + 0.0725298i 0.742441 0.669911i \(-0.233668\pi\)
−0.669911 + 0.742441i \(0.733668\pi\)
\(458\) 4.73545 + 4.73545i 0.221273 + 0.221273i
\(459\) 10.3923 + 36.7423i 0.485071 + 1.71499i
\(460\) 0.224745 2.22474i 0.0104788 0.103729i
\(461\) 31.4626i 1.46536i −0.680573 0.732681i \(-0.738269\pi\)
0.680573 0.732681i \(-0.261731\pi\)
\(462\) −33.4523 5.73951i −1.55634 0.267026i
\(463\) 26.0454 26.0454i 1.21043 1.21043i 0.239548 0.970884i \(-0.423001\pi\)
0.970884 0.239548i \(-0.0769993\pi\)
\(464\) 2.19275 0.101796
\(465\) −9.34190 16.5145i −0.433220 0.765842i
\(466\) 5.10102 0.236300
\(467\) −3.60697 + 3.60697i −0.166910 + 0.166910i −0.785620 0.618709i \(-0.787656\pi\)
0.618709 + 0.785620i \(0.287656\pi\)
\(468\) −6.30714 13.2061i −0.291548 0.610453i
\(469\) 53.3939i 2.46550i
\(470\) 9.75663 + 11.9494i 0.450040 + 0.551184i
\(471\) 16.8990 11.9494i 0.778664 0.550599i
\(472\) −3.89898 3.89898i −0.179465 0.179465i
\(473\) −16.3991 16.3991i −0.754032 0.754032i
\(474\) 6.29253 4.44949i 0.289025 0.204372i
\(475\) 12.0000 + 2.44949i 0.550598 + 0.112390i
\(476\) 25.4558i 1.16677i
\(477\) 1.74343 + 3.65045i 0.0798260 + 0.167143i
\(478\) −9.44949 + 9.44949i −0.432210 + 0.432210i
\(479\) 26.4415 1.20814 0.604071 0.796931i \(-0.293544\pi\)
0.604071 + 0.796931i \(0.293544\pi\)
\(480\) −3.73205 1.03528i −0.170344 0.0472537i
\(481\) 16.8990 0.770527
\(482\) 6.43539 6.43539i 0.293124 0.293124i
\(483\) 5.91359 + 1.01461i 0.269078 + 0.0461664i
\(484\) 21.0000i 0.954545i
\(485\) 1.41421 + 0.142865i 0.0642161 + 0.00648715i
\(486\) 1.00000 15.5563i 0.0453609 0.705650i
\(487\) 19.3485 + 19.3485i 0.876763 + 0.876763i 0.993198 0.116435i \(-0.0371468\pi\)
−0.116435 + 0.993198i \(0.537147\pi\)
\(488\) 0.635674 + 0.635674i 0.0287756 + 0.0287756i
\(489\) −5.65685 8.00000i −0.255812 0.361773i
\(490\) 11.1237 + 1.12372i 0.502519 + 0.0507647i
\(491\) 25.3130i 1.14236i 0.820825 + 0.571179i \(0.193514\pi\)
−0.820825 + 0.571179i \(0.806486\pi\)
\(492\) 2.48528 14.4853i 0.112045 0.653047i
\(493\) 11.3939 11.3939i 0.513154 0.513154i
\(494\) 11.9494 0.537628
\(495\) −12.8295 35.7128i −0.576641 1.60517i
\(496\) −4.89898 −0.219971
\(497\) −35.8481 + 35.8481i −1.60801 + 1.60801i
\(498\) 0.585786 3.41421i 0.0262497 0.152995i
\(499\) 33.7980i 1.51300i −0.653991 0.756502i \(-0.726907\pi\)
0.653991 0.756502i \(-0.273093\pi\)
\(500\) 9.89949 5.19615i 0.442719 0.232379i
\(501\) 8.00000 + 11.3137i 0.357414 + 0.505459i
\(502\) −9.10102 9.10102i −0.406198 0.406198i
\(503\) −1.90702 1.90702i −0.0850300 0.0850300i 0.663313 0.748342i \(-0.269150\pi\)
−0.748342 + 0.663313i \(0.769150\pi\)
\(504\) 3.46410 9.79796i 0.154303 0.436436i
\(505\) 0.898979 + 1.10102i 0.0400041 + 0.0489948i
\(506\) 5.65685i 0.251478i
\(507\) 18.4333 + 3.16265i 0.818650 + 0.140458i
\(508\) −3.55051 + 3.55051i −0.157528 + 0.157528i
\(509\) −19.8632 −0.880421 −0.440211 0.897895i \(-0.645096\pi\)
−0.440211 + 0.897895i \(0.645096\pi\)
\(510\) −24.7718 + 14.0129i −1.09691 + 0.620500i
\(511\) −9.30306 −0.411543
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 11.1097 + 6.21076i 0.490507 + 0.274212i
\(514\) 13.5959i 0.599690i
\(515\) 3.46410 34.2911i 0.152647 1.51105i
\(516\) 5.79796 4.09978i 0.255241 0.180483i
\(517\) 27.5959 + 27.5959i 1.21367 + 1.21367i
\(518\) 8.48528 + 8.48528i 0.372822 + 0.372822i
\(519\) −7.21393 + 5.10102i −0.316656 + 0.223910i
\(520\) 8.44949 6.89898i 0.370535 0.302540i
\(521\) 19.8632i 0.870223i 0.900377 + 0.435111i \(0.143291\pi\)
−0.900377 + 0.435111i \(0.856709\pi\)
\(522\) −5.93602 + 2.83500i −0.259812 + 0.124084i
\(523\) −22.2474 + 22.2474i −0.972813 + 0.972813i −0.999640 0.0268271i \(-0.991460\pi\)
0.0268271 + 0.999640i \(0.491460\pi\)
\(524\) −0.142865 −0.00624107
\(525\) 12.0716 + 27.4641i 0.526847 + 1.19863i
\(526\) 8.00000 0.348817
\(527\) −25.4558 + 25.4558i −1.10887 + 1.10887i
\(528\) −9.65685 1.65685i −0.420261 0.0721053i
\(529\) 1.00000i 0.0434783i
\(530\) −2.33562 + 1.90702i −0.101453 + 0.0828358i
\(531\) 15.5959 + 5.51399i 0.676805 + 0.239287i
\(532\) 6.00000 + 6.00000i 0.260133 + 0.260133i
\(533\) 29.2699 + 29.2699i 1.26782 + 1.26782i
\(534\) −9.12096 12.8990i −0.394702 0.558193i
\(535\) −2.44949 + 24.2474i −0.105901 + 1.04831i
\(536\) 15.4135i 0.665761i
\(537\) 4.47266 26.0686i 0.193010 1.12494i
\(538\) −4.44949 + 4.44949i −0.191831 + 0.191831i
\(539\) 28.2843 1.21829
\(540\) 11.4416 2.02254i 0.492366 0.0870363i
\(541\) 18.6969 0.803844 0.401922 0.915674i \(-0.368342\pi\)
0.401922 + 0.915674i \(0.368342\pi\)
\(542\) 17.3205 17.3205i 0.743980 0.743980i
\(543\) −2.34315 + 13.6569i −0.100554 + 0.586072i
\(544\) 7.34847i 0.315063i
\(545\) −19.5133 23.8988i −0.835856 1.02371i
\(546\) 16.8990 + 23.8988i 0.723210 + 1.02277i
\(547\) −11.5959 11.5959i −0.495806 0.495806i 0.414324 0.910130i \(-0.364018\pi\)
−0.910130 + 0.414324i \(0.864018\pi\)
\(548\) 13.6814 + 13.6814i 0.584442 + 0.584442i
\(549\) −2.54270 0.898979i −0.108520 0.0383675i
\(550\) 23.5959 15.5959i 1.00613 0.665012i
\(551\) 5.37113i 0.228818i
\(552\) 1.70711 + 0.292893i 0.0726593 + 0.0124664i
\(553\) −10.8990 + 10.8990i −0.463472 + 0.463472i
\(554\) 13.3636 0.567765
\(555\) −3.58630 + 12.9282i −0.152230 + 0.548772i
\(556\) 18.6969 0.792927
\(557\) 21.1024 21.1024i 0.894139 0.894139i −0.100770 0.994910i \(-0.532131\pi\)
0.994910 + 0.100770i \(0.0321307\pi\)
\(558\) 13.2621 6.33386i 0.561428 0.268134i
\(559\) 20.0000i 0.845910i
\(560\) 7.70674 + 0.778539i 0.325669 + 0.0328993i
\(561\) −58.7878 + 41.5692i −2.48202 + 1.75505i
\(562\) −4.00000 4.00000i −0.168730 0.168730i
\(563\) −26.5843 26.5843i −1.12040 1.12040i −0.991682 0.128714i \(-0.958915\pi\)
−0.128714 0.991682i \(-0.541085\pi\)
\(564\) −9.75663 + 6.89898i −0.410828 + 0.290499i
\(565\) −25.2474 2.55051i −1.06217 0.107301i
\(566\) 7.56388i 0.317933i
\(567\) 3.29002 + 31.0028i 0.138168 + 1.30200i
\(568\) −10.3485 + 10.3485i −0.434212 + 0.434212i
\(569\) −23.8988 −1.00189 −0.500944 0.865480i \(-0.667014\pi\)
−0.500944 + 0.865480i \(0.667014\pi\)
\(570\) −2.53590 + 9.14162i −0.106217 + 0.382900i
\(571\) 21.5505 0.901861 0.450930 0.892559i \(-0.351092\pi\)
0.450930 + 0.892559i \(0.351092\pi\)
\(572\) 19.5133 19.5133i 0.815890 0.815890i
\(573\) −30.6531 5.25924i −1.28055 0.219708i
\(574\) 29.3939i 1.22688i
\(575\) −4.17121 + 2.75699i −0.173951 + 0.114975i
\(576\) 1.00000 2.82843i 0.0416667 0.117851i
\(577\) −0.797959 0.797959i −0.0332195 0.0332195i 0.690302 0.723521i \(-0.257478\pi\)
−0.723521 + 0.690302i \(0.757478\pi\)
\(578\) 26.1630 + 26.1630i 1.08824 + 1.08824i
\(579\) 2.68556 + 3.79796i 0.111608 + 0.157838i
\(580\) −3.10102 3.79796i −0.128763 0.157702i
\(581\) 6.92820i 0.287430i
\(582\) −0.186185 + 1.08516i −0.00771761 + 0.0449815i
\(583\) −5.39388 + 5.39388i −0.223392 + 0.223392i
\(584\) −2.68556 −0.111129
\(585\) −13.9540 + 29.6006i −0.576928 + 1.22383i
\(586\) −19.1464 −0.790932
\(587\) 13.9993 13.9993i 0.577812 0.577812i −0.356488 0.934300i \(-0.616026\pi\)
0.934300 + 0.356488i \(0.116026\pi\)
\(588\) −1.46447 + 8.53553i −0.0603936 + 0.351999i
\(589\) 12.0000i 0.494451i
\(590\) −1.23924 + 12.2672i −0.0510187 + 0.505033i
\(591\) −10.8990 15.4135i −0.448324 0.634026i
\(592\) 2.44949 + 2.44949i 0.100673 + 0.100673i
\(593\) −11.1708 11.1708i −0.458732 0.458732i 0.439507 0.898239i \(-0.355153\pi\)
−0.898239 + 0.439507i \(0.855153\pi\)
\(594\) 28.2843 8.00000i 1.16052 0.328244i
\(595\) 44.0908 36.0000i 1.80755 1.47586i
\(596\) 11.0280i 0.451724i
\(597\) −12.8895 2.21149i −0.527533 0.0905104i
\(598\) −3.44949 + 3.44949i −0.141060 + 0.141060i
\(599\) 3.32124 0.135702 0.0678510 0.997695i \(-0.478386\pi\)
0.0678510 + 0.997695i \(0.478386\pi\)
\(600\) 3.48477 + 7.92820i 0.142265 + 0.323668i
\(601\) −16.2020 −0.660895 −0.330448 0.943824i \(-0.607200\pi\)
−0.330448 + 0.943824i \(0.607200\pi\)
\(602\) −10.0424 + 10.0424i −0.409296 + 0.409296i
\(603\) 19.9280 + 41.7259i 0.811530 + 1.69921i
\(604\) 0.898979i 0.0365790i
\(605\) 36.3731 29.6985i 1.47878 1.20742i
\(606\) −0.898979 + 0.635674i −0.0365185 + 0.0258225i
\(607\) −7.34847 7.34847i −0.298265 0.298265i 0.542069 0.840334i \(-0.317641\pi\)
−0.840334 + 0.542069i \(0.817641\pi\)
\(608\) 1.73205 + 1.73205i 0.0702439 + 0.0702439i
\(609\) 10.7423 7.59592i 0.435298 0.307802i
\(610\) 0.202041 2.00000i 0.00818040 0.0809776i
\(611\) 33.6554i 1.36155i
\(612\) −9.50079 19.8931i −0.384047 0.804131i
\(613\) 3.34847 3.34847i 0.135243 0.135243i −0.636244 0.771488i \(-0.719513\pi\)
0.771488 + 0.636244i \(0.219513\pi\)
\(614\) 32.0983 1.29538
\(615\) −28.6040 + 16.1806i −1.15342 + 0.652467i
\(616\) 19.5959 0.789542
\(617\) 18.4169 18.4169i 0.741436 0.741436i −0.231418 0.972854i \(-0.574337\pi\)
0.972854 + 0.231418i \(0.0743366\pi\)
\(618\) 26.3125 + 4.51451i 1.05844 + 0.181600i
\(619\) 30.0454i 1.20763i 0.797126 + 0.603813i \(0.206353\pi\)
−0.797126 + 0.603813i \(0.793647\pi\)
\(620\) 6.92820 + 8.48528i 0.278243 + 0.340777i
\(621\) −5.00000 + 1.41421i −0.200643 + 0.0567504i
\(622\) 10.1464 + 10.1464i 0.406835 + 0.406835i
\(623\) 22.3417 + 22.3417i 0.895101 + 0.895101i
\(624\) 4.87832 + 6.89898i 0.195289 + 0.276180i
\(625\) −23.0000 9.79796i −0.920000 0.391918i
\(626\) 21.4203i 0.856127i
\(627\) −4.05845 + 23.6544i −0.162079 + 0.944664i
\(628\) −8.44949 + 8.44949i −0.337171 + 0.337171i
\(629\) 25.4558 1.01499
\(630\) −21.8695 + 7.85641i −0.871303 + 0.313007i
\(631\) 24.4495 0.973319 0.486659 0.873592i \(-0.338215\pi\)
0.486659 + 0.873592i \(0.338215\pi\)
\(632\) −3.14626 + 3.14626i −0.125152 + 0.125152i
\(633\) −5.47621 + 31.9177i −0.217660 + 1.26861i
\(634\) 18.8990i 0.750574i
\(635\) 11.1708 + 1.12848i 0.443301 + 0.0447825i
\(636\) −1.34847 1.90702i −0.0534703 0.0756184i
\(637\) −17.2474 17.2474i −0.683369 0.683369i
\(638\) −8.77101 8.77101i −0.347248 0.347248i
\(639\) 14.6349 41.3939i 0.578949 1.63752i
\(640\) 2.22474 + 0.224745i 0.0879408 + 0.00888382i
\(641\) 20.4347i 0.807121i 0.914953 + 0.403560i \(0.132227\pi\)
−0.914953 + 0.403560i \(0.867773\pi\)
\(642\) −18.6057 3.19224i −0.734309 0.125988i
\(643\) −22.8990 + 22.8990i −0.903048 + 0.903048i −0.995699 0.0926510i \(-0.970466\pi\)
0.0926510 + 0.995699i \(0.470466\pi\)
\(644\) −3.46410 −0.136505
\(645\) −15.3006 4.24440i −0.602459 0.167123i
\(646\) 18.0000 0.708201
\(647\) −34.4339 + 34.4339i −1.35374 + 1.35374i −0.472300 + 0.881438i \(0.656576\pi\)
−0.881438 + 0.472300i \(0.843424\pi\)
\(648\) 0.949747 + 8.94975i 0.0373096 + 0.351579i
\(649\) 31.1918i 1.22439i
\(650\) −23.8988 4.87832i −0.937387 0.191343i
\(651\) −24.0000 + 16.9706i −0.940634 + 0.665129i
\(652\) 4.00000 + 4.00000i 0.156652 + 0.156652i
\(653\) −16.1920 16.1920i −0.633643 0.633643i 0.315337 0.948980i \(-0.397882\pi\)
−0.948980 + 0.315337i \(0.897882\pi\)
\(654\) 19.5133 13.7980i 0.763029 0.539543i
\(655\) 0.202041 + 0.247449i 0.00789440 + 0.00966862i
\(656\) 8.48528i 0.331295i
\(657\) 7.27010 3.47215i 0.283634 0.135461i
\(658\) 16.8990 16.8990i 0.658791 0.658791i
\(659\) −9.75663 −0.380064 −0.190032 0.981778i \(-0.560859\pi\)
−0.190032 + 0.981778i \(0.560859\pi\)
\(660\) 10.7871 + 19.0693i 0.419887 + 0.742272i
\(661\) 16.8990 0.657294 0.328647 0.944453i \(-0.393407\pi\)
0.328647 + 0.944453i \(0.393407\pi\)
\(662\) 13.2207 13.2207i 0.513838 0.513838i
\(663\) 61.1966 + 10.4997i 2.37668 + 0.407774i
\(664\) 2.00000i 0.0776151i
\(665\) 1.90702 18.8776i 0.0739512 0.732041i
\(666\) −9.79796 3.46410i −0.379663 0.134231i
\(667\) 1.55051 + 1.55051i 0.0600360 + 0.0600360i
\(668\) −5.65685 5.65685i −0.218870 0.218870i
\(669\) −17.6062 24.8990i −0.680696 0.962650i
\(670\) −26.6969 + 21.7980i −1.03139 + 0.842129i
\(671\) 5.08540i 0.196320i
\(672\) −1.01461 + 5.91359i −0.0391395 + 0.228122i
\(673\) 3.00000 3.00000i 0.115642 0.115642i −0.646918 0.762560i \(-0.723942\pi\)
0.762560 + 0.646918i \(0.223942\pi\)
\(674\) −20.4347 −0.787114
\(675\) −19.6840 16.9571i −0.757636 0.652678i
\(676\) −10.7980 −0.415306
\(677\) −8.51739 + 8.51739i −0.327350 + 0.327350i −0.851578 0.524228i \(-0.824354\pi\)
0.524228 + 0.851578i \(0.324354\pi\)
\(678\) 3.32389 19.3730i 0.127653 0.744017i
\(679\) 2.20204i 0.0845066i
\(680\) 12.7279 10.3923i 0.488094 0.398527i
\(681\) 1.10102 + 1.55708i 0.0421912 + 0.0596674i
\(682\) 19.5959 + 19.5959i 0.750366 + 0.750366i
\(683\) 4.24264 + 4.24264i 0.162340 + 0.162340i 0.783603 0.621262i \(-0.213380\pi\)
−0.621262 + 0.783603i \(0.713380\pi\)
\(684\) −6.92820 2.44949i −0.264906 0.0936586i
\(685\) 4.34847 43.0454i 0.166146 1.64468i
\(686\) 6.92820i 0.264520i
\(687\) 11.4324 + 1.96149i 0.436173 + 0.0748354i
\(688\) −2.89898 + 2.89898i −0.110523 + 0.110523i
\(689\) 6.57826 0.250612
\(690\) −1.90691 3.37101i −0.0725947 0.128332i
\(691\) −28.0000 −1.06517 −0.532585 0.846376i \(-0.678779\pi\)
−0.532585 + 0.846376i \(0.678779\pi\)
\(692\) 3.60697 3.60697i 0.137116 0.137116i
\(693\) −53.0482 + 25.3354i −2.01514 + 0.962413i
\(694\) 0.202041i 0.00766937i
\(695\) −26.4415 32.3840i −1.00298 1.22840i
\(696\) 3.10102 2.19275i 0.117544 0.0831161i
\(697\) 44.0908 + 44.0908i 1.67006 + 1.67006i
\(698\) 15.5563 + 15.5563i 0.588817 + 0.588817i
\(699\) 7.21393 5.10102i 0.272856 0.192938i
\(700\) −9.55051 14.4495i −0.360975 0.546139i
\(701\) 36.1339i 1.36476i 0.730999 + 0.682379i \(0.239055\pi\)
−0.730999 + 0.682379i \(0.760945\pi\)
\(702\) −22.1258 12.3691i −0.835083 0.466843i
\(703\) 6.00000 6.00000i 0.226294 0.226294i
\(704\) 5.65685 0.213201
\(705\) 25.7473 + 7.14235i 0.969701 + 0.268996i
\(706\) −32.6969 −1.23057
\(707\) 1.55708 1.55708i 0.0585600 0.0585600i
\(708\) −9.41297 1.61501i −0.353761 0.0606958i
\(709\) 16.8990i 0.634654i −0.948316 0.317327i \(-0.897215\pi\)
0.948316 0.317327i \(-0.102785\pi\)
\(710\) 32.5590 + 3.28913i 1.22192 + 0.123439i
\(711\) 4.44949 12.5851i 0.166869 0.471977i
\(712\) 6.44949 + 6.44949i 0.241705 + 0.241705i
\(713\) −3.46410 3.46410i −0.129732 0.129732i
\(714\) 25.4558 + 36.0000i 0.952661 + 1.34727i
\(715\) −61.3939 6.20204i −2.29600 0.231943i
\(716\) 15.2706i 0.570690i
\(717\) −3.91411 + 22.8131i −0.146175 + 0.851970i
\(718\) −18.8990 + 18.8990i −0.705304 + 0.705304i
\(719\) 1.76416 0.0657920 0.0328960 0.999459i \(-0.489527\pi\)
0.0328960 + 0.999459i \(0.489527\pi\)
\(720\) −6.31319 + 2.26795i −0.235279 + 0.0845215i
\(721\) −53.3939 −1.98849
\(722\) −9.19239 + 9.19239i −0.342105 + 0.342105i
\(723\) 2.66563 15.5364i 0.0991357 0.577805i
\(724\) 8.00000i 0.297318i
\(725\) −2.19275 + 10.7423i −0.0814368 + 0.398957i
\(726\) 21.0000 + 29.6985i 0.779383 + 1.10221i
\(727\) 24.2474 + 24.2474i 0.899288 + 0.899288i 0.995373 0.0960850i \(-0.0306321\pi\)
−0.0960850 + 0.995373i \(0.530632\pi\)
\(728\) −11.9494 11.9494i −0.442874 0.442874i
\(729\) −14.1421 23.0000i −0.523783 0.851852i
\(730\) 3.79796 + 4.65153i 0.140569 + 0.172161i
\(731\) 30.1271i 1.11429i
\(732\) 1.53465 + 0.263305i 0.0567224 + 0.00973203i
\(733\) −25.1464 + 25.1464i −0.928805 + 0.928805i −0.997629 0.0688243i \(-0.978075\pi\)
0.0688243 + 0.997629i \(0.478075\pi\)
\(734\) −27.9985 −1.03345
\(735\) 16.8550 9.53454i 0.621708 0.351687i
\(736\) −1.00000 −0.0368605
\(737\) −61.6539 + 61.6539i −2.27105 + 2.27105i
\(738\) −10.9706 22.9706i −0.403832 0.845558i
\(739\) 30.6969i 1.12921i 0.825363 + 0.564603i \(0.190971\pi\)
−0.825363 + 0.564603i \(0.809029\pi\)
\(740\) 0.778539 7.70674i 0.0286197 0.283305i
\(741\) 16.8990 11.9494i 0.620800 0.438972i
\(742\) 3.30306 + 3.30306i 0.121259 + 0.121259i
\(743\) 10.6780 + 10.6780i 0.391739 + 0.391739i 0.875307 0.483568i \(-0.160659\pi\)
−0.483568 + 0.875307i \(0.660659\pi\)
\(744\) −6.92820 + 4.89898i −0.254000 + 0.179605i
\(745\) 19.1010 15.5959i 0.699807 0.571390i
\(746\) 17.6062i 0.644610i
\(747\) −2.58579 5.41421i −0.0946090 0.198096i
\(748\) 29.3939 29.3939i 1.07475 1.07475i
\(749\) 37.7552 1.37954
\(750\) 8.80385 17.2480i 0.321471 0.629807i
\(751\) −42.2474 −1.54163 −0.770816 0.637058i \(-0.780151\pi\)
−0.770816 + 0.637058i \(0.780151\pi\)
\(752\) 4.87832 4.87832i 0.177894 0.177894i
\(753\) −21.9718 3.76977i −0.800697 0.137378i
\(754\) 10.6969i 0.389560i
\(755\) 1.55708 1.27135i 0.0566679 0.0462691i
\(756\) −4.89898 17.3205i −0.178174 0.629941i
\(757\) −25.3485 25.3485i −0.921306 0.921306i 0.0758160 0.997122i \(-0.475844\pi\)
−0.997122 + 0.0758160i \(0.975844\pi\)
\(758\) −3.63907 3.63907i −0.132177 0.132177i
\(759\) −5.65685 8.00000i −0.205331 0.290382i
\(760\) 0.550510 5.44949i 0.0199691 0.197674i
\(761\) 42.1407i 1.52760i −0.645454 0.763799i \(-0.723332\pi\)
0.645454 0.763799i \(-0.276668\pi\)
\(762\) −1.47067 + 8.57169i −0.0532767 + 0.310520i
\(763\) −33.7980 + 33.7980i −1.22357 + 1.22357i
\(764\) 17.9562 0.649632
\(765\) −21.0197 + 44.5889i −0.759969 + 1.61212i
\(766\) 6.69694 0.241970
\(767\) 19.0205 19.0205i 0.686789 0.686789i
\(768\) −0.292893 + 1.70711i −0.0105689 + 0.0615999i
\(769\) 28.6969i 1.03484i 0.855732 + 0.517419i \(0.173107\pi\)
−0.855732 + 0.517419i \(0.826893\pi\)
\(770\) −27.7128 33.9411i −0.998700 1.22315i
\(771\) −13.5959 19.2275i −0.489645 0.692463i
\(772\) −1.89898 1.89898i −0.0683458 0.0683458i
\(773\) 26.7593 + 26.7593i 0.962465 + 0.962465i 0.999321 0.0368554i \(-0.0117341\pi\)
−0.0368554 + 0.999321i \(0.511734\pi\)
\(774\) 4.09978 11.5959i 0.147363 0.416807i
\(775\) 4.89898 24.0000i 0.175977 0.862105i