Properties

Label 690.2.i.c.47.4
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 47.4
Root \(-0.965926 - 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 690.47
Dual form 690.2.i.c.323.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(-1.70711 + 0.292893i) q^{3} -1.00000i q^{4} +(1.73205 - 1.41421i) q^{5} +(-1.00000 + 1.41421i) q^{6} +(2.44949 + 2.44949i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.82843 - 1.00000i) q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(-1.70711 + 0.292893i) 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} +(0.292893 + 1.70711i) q^{12} +(-3.44949 + 3.44949i) q^{13} +3.46410 q^{14} +(-2.54258 + 2.92152i) q^{15} -1.00000 q^{16} +(5.19615 - 5.19615i) q^{17} +(1.29289 - 2.70711i) 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} +(-4.53553 + 2.53553i) q^{27} +(2.44949 - 2.44949i) q^{28} +2.19275 q^{29} +(0.267949 + 3.86370i) q^{30} +4.89898 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-1.65685 - 9.65685i) 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} +(-5.91359 + 1.01461i) q^{42} +(2.89898 - 2.89898i) q^{43} +5.65685 q^{44} +(3.48477 - 5.73205i) q^{45} +1.00000 q^{46} +(4.87832 - 4.87832i) q^{47} +(1.70711 - 0.292893i) 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} +(-0.717439 - 4.18154i) q^{57} +(1.55051 - 1.55051i) q^{58} +5.51399 q^{59} +(2.92152 + 2.54258i) q^{60} +0.898979 q^{61} +(3.46410 - 3.46410i) q^{62} +(9.37769 + 4.47871i) 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} +(-2.70711 - 1.29289i) q^{72} +(-1.89898 + 1.89898i) q^{73} -3.46410 q^{74} +(-0.272229 + 8.65597i) q^{75} +2.44949 q^{76} +(-13.8564 + 13.8564i) q^{77} +(-1.42883 - 8.32780i) 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} +(-3.74326 + 0.642242i) q^{87} +(4.00000 - 4.00000i) q^{88} -9.12096 q^{89} +(-1.58907 - 6.51727i) q^{90} -16.8990 q^{91} +(0.707107 - 0.707107i) q^{92} +(-8.36308 + 1.43488i) 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
\(3\) −1.70711 + 0.292893i −0.985599 + 0.169102i
\(4\) 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 \(0.325099\pi\)
−0.522233 + 0.852803i \(0.674901\pi\)
\(12\) 0.292893 + 1.70711i 0.0845510 + 0.492799i
\(13\) −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
\(15\) −2.54258 + 2.92152i −0.656492 + 0.754333i
\(16\) −1.00000 −0.250000
\(17\) 5.19615 5.19615i 1.26025 1.26025i 0.309282 0.950971i \(-0.399911\pi\)
0.950971 0.309282i \(-0.100089\pi\)
\(18\) 1.29289 2.70711i 0.304738 0.638071i
\(19\) 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
\(27\) −4.53553 + 2.53553i −0.872864 + 0.487964i
\(28\) 2.44949 2.44949i 0.462910 0.462910i
\(29\) 2.19275 0.407184 0.203592 0.979056i \(-0.434738\pi\)
0.203592 + 0.979056i \(0.434738\pi\)
\(30\) 0.267949 + 3.86370i 0.0489206 + 0.705412i
\(31\) 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
\(33\) −1.65685 9.65685i −0.288421 1.68104i
\(34\) 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 \(0.230542\pi\)
−0.748983 + 0.662589i \(0.769458\pi\)
\(42\) −5.91359 + 1.01461i −0.912487 + 0.156558i
\(43\) 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
\(45\) 3.48477 5.73205i 0.519478 0.854484i
\(46\) 1.00000 0.147442
\(47\) 4.87832 4.87832i 0.711575 0.711575i −0.255289 0.966865i \(-0.582171\pi\)
0.966865 + 0.255289i \(0.0821707\pi\)
\(48\) 1.70711 0.292893i 0.246400 0.0422755i
\(49\) 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 0.769555 0.638580i \(-0.220478\pi\)
−0.638580 + 0.769555i \(0.720478\pi\)
\(54\) −1.41421 + 5.00000i −0.192450 + 0.680414i
\(55\) 8.00000 + 9.79796i 1.07872 + 1.32116i
\(56\) 3.46410i 0.462910i
\(57\) −0.717439 4.18154i −0.0950271 0.553859i
\(58\) 1.55051 1.55051i 0.203592 0.203592i
\(59\) 5.51399 0.717860 0.358930 0.933364i \(-0.383142\pi\)
0.358930 + 0.933364i \(0.383142\pi\)
\(60\) 2.92152 + 2.54258i 0.377167 + 0.328246i
\(61\) 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
\(63\) 9.37769 + 4.47871i 1.18148 + 0.564265i
\(64\) 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 \(-0.665133\pi\)
0.495822 0.868424i \(-0.334867\pi\)
\(72\) −2.70711 1.29289i −0.319036 0.152369i
\(73\) −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
\(75\) −0.272229 + 8.65597i −0.0314343 + 0.999506i
\(76\) 2.44949 0.280976
\(77\) −13.8564 + 13.8564i −1.57908 + 1.57908i
\(78\) −1.42883 8.32780i −0.161783 0.942938i
\(79\) 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 0.625219 0.780449i \(-0.285010\pi\)
−0.780449 + 0.625219i \(0.785010\pi\)
\(84\) −3.46410 + 4.89898i −0.377964 + 0.534522i
\(85\) 1.65153 16.3485i 0.179134 1.77324i
\(86\) 4.09978i 0.442090i
\(87\) −3.74326 + 0.642242i −0.401320 + 0.0688556i
\(88\) 4.00000 4.00000i 0.426401 0.426401i
\(89\) −9.12096 −0.966819 −0.483410 0.875394i \(-0.660602\pi\)
−0.483410 + 0.875394i \(0.660602\pi\)
\(90\) −1.58907 6.51727i −0.167503 0.686981i
\(91\) −16.8990 −1.77149
\(92\) 0.707107 0.707107i 0.0737210 0.0737210i
\(93\) −8.36308 + 1.43488i −0.867211 + 0.148790i
\(94\) 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 \(0.0100685\pi\)
−0.999500 + 0.0316260i \(0.989931\pi\)
\(102\) 2.15232 + 12.5446i 0.213111 + 1.24210i
\(103\) −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
\(105\) −13.3843 + 0.928203i −1.30617 + 0.0905834i
\(106\) 1.34847 0.130975
\(107\) −7.70674 + 7.70674i −0.745039 + 0.745039i −0.973543 0.228504i \(-0.926617\pi\)
0.228504 + 0.973543i \(0.426617\pi\)
\(108\) 2.53553 + 4.53553i 0.243982 + 0.436432i
\(109\) 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 0.220498 0.975387i \(-0.429232\pi\)
−0.975387 + 0.220498i \(0.929232\pi\)
\(114\) −3.46410 2.44949i −0.324443 0.229416i
\(115\) 2.22474 + 0.224745i 0.207459 + 0.0209576i
\(116\) 2.19275i 0.203592i
\(117\) −6.30714 + 13.2061i −0.583095 + 1.22091i
\(118\) 3.89898 3.89898i 0.358930 0.358930i
\(119\) 25.4558 2.33353
\(120\) 3.86370 0.267949i 0.352706 0.0244603i
\(121\) −21.0000 −1.90909
\(122\) 0.635674 0.635674i 0.0575513 0.0575513i
\(123\) −2.48528 14.4853i −0.224090 1.30609i
\(124\) 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 \(0.00198661\pi\)
−0.999981 + 0.00624107i \(0.998013\pi\)
\(132\) −9.65685 + 1.65685i −0.840521 + 0.144211i
\(133\) −6.00000 + 6.00000i −0.520266 + 0.520266i
\(134\) −15.4135 −1.33152
\(135\) −4.26999 + 10.8059i −0.367502 + 0.930023i
\(136\) −7.34847 −0.630126
\(137\) 13.6814 13.6814i 1.16888 1.16888i 0.186412 0.982472i \(-0.440314\pi\)
0.982472 0.186412i \(-0.0596860\pi\)
\(138\) −1.70711 + 0.292893i −0.145319 + 0.0249327i
\(139\) 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
\(147\) −1.46447 8.53553i −0.120787 0.703999i
\(148\) −2.44949 + 2.44949i −0.201347 + 0.201347i
\(149\) 11.0280 0.903447 0.451724 0.892158i \(-0.350809\pi\)
0.451724 + 0.892158i \(0.350809\pi\)
\(150\) 5.92820 + 6.31319i 0.484036 + 0.515470i
\(151\) −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
\(153\) 9.50079 19.8931i 0.768093 1.60826i
\(154\) 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
\(162\) 0.949747 8.94975i 0.0746192 0.703159i
\(163\) −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
\(165\) −16.5266 14.3830i −1.28659 1.11972i
\(166\) −2.00000 −0.155230
\(167\) −5.65685 + 5.65685i −0.437741 + 0.437741i −0.891251 0.453510i \(-0.850171\pi\)
0.453510 + 0.891251i \(0.350171\pi\)
\(168\) 1.01461 + 5.91359i 0.0782790 + 0.456243i
\(169\) 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 0.556569 0.830801i \(-0.312118\pi\)
−0.830801 + 0.556569i \(0.812118\pi\)
\(174\) −2.19275 + 3.10102i −0.166232 + 0.235088i
\(175\) 14.4495 9.55051i 1.09228 0.721951i
\(176\) 5.65685i 0.426401i
\(177\) −9.41297 + 1.61501i −0.707522 + 0.121392i
\(178\) −6.44949 + 6.44949i −0.483410 + 0.483410i
\(179\) 15.2706 1.14138 0.570690 0.821166i \(-0.306676\pi\)
0.570690 + 0.821166i \(0.306676\pi\)
\(180\) −5.73205 3.48477i −0.427242 0.259739i
\(181\) 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
\(183\) −1.53465 + 0.263305i −0.113445 + 0.0194641i
\(184\) 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 \(-0.774923\pi\)
0.760249 0.649632i \(-0.225077\pi\)
\(192\) −0.292893 1.70711i −0.0211377 0.123200i
\(193\) 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
\(195\) −1.30714 18.8484i −0.0936063 1.34976i
\(196\) 5.00000 0.357143
\(197\) 7.70674 7.70674i 0.549083 0.549083i −0.377093 0.926175i \(-0.623076\pi\)
0.926175 + 0.377093i \(0.123076\pi\)
\(198\) 15.3137 + 7.31371i 1.08830 + 0.519763i
\(199\) 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
\(207\) 2.70711 + 1.29289i 0.188157 + 0.0898623i
\(208\) 3.44949 3.44949i 0.239179 0.239179i
\(209\) −13.8564 −0.958468
\(210\) −8.80776 + 10.1204i −0.607793 + 0.698377i
\(211\) 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
\(213\) 4.28648 + 24.9834i 0.293705 + 1.71184i
\(214\) 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
\(222\) 5.91359 1.01461i 0.396894 0.0680963i
\(223\) −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
\(225\) −2.07055 14.8564i −0.138037 0.990427i
\(226\) −11.3485 −0.754889
\(227\) −0.778539 + 0.778539i −0.0516735 + 0.0516735i −0.732471 0.680798i \(-0.761633\pi\)
0.680798 + 0.732471i \(0.261633\pi\)
\(228\) −4.18154 + 0.717439i −0.276929 + 0.0475136i
\(229\) 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 0.815316 0.579016i \(-0.196563\pi\)
−0.579016 + 0.815316i \(0.696563\pi\)
\(234\) 4.87832 + 13.7980i 0.318905 + 0.902001i
\(235\) 1.55051 15.3485i 0.101144 1.00122i
\(236\) 5.51399i 0.358930i
\(237\) −1.30323 7.59575i −0.0846536 0.493397i
\(238\) 18.0000 18.0000i 1.16677 1.16677i
\(239\) −13.3636 −0.864419 −0.432210 0.901773i \(-0.642266\pi\)
−0.432210 + 0.901773i \(0.642266\pi\)
\(240\) 2.54258 2.92152i 0.164123 0.188583i
\(241\) −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
\(243\) −10.2929 + 11.7071i −0.660289 + 0.751011i
\(244\) 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 \(-0.866854\pi\)
0.913785 0.406198i \(-0.133146\pi\)
\(252\) 4.47871 9.37769i 0.282132 0.590739i
\(253\) −4.00000 + 4.00000i −0.251478 + 0.251478i
\(254\) −5.02118 −0.315057
\(255\) 1.96902 + 28.3923i 0.123305 + 1.77800i
\(256\) 1.00000 0.0625000
\(257\) 9.61377 9.61377i 0.599690 0.599690i −0.340540 0.940230i \(-0.610610\pi\)
0.940230 + 0.340540i \(0.110610\pi\)
\(258\) 1.20080 + 6.99876i 0.0747583 + 0.435723i
\(259\) 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 0.859669 0.510852i \(-0.170670\pi\)
−0.510852 + 0.859669i \(0.670670\pi\)
\(264\) −5.65685 + 8.00000i −0.348155 + 0.492366i
\(265\) 3.00000 + 0.303062i 0.184289 + 0.0186169i
\(266\) 8.48528i 0.520266i
\(267\) 15.5704 2.67147i 0.952896 0.163491i
\(268\) −10.8990 + 10.8990i −0.665761 + 0.665761i
\(269\) −6.29253 −0.383662 −0.191831 0.981428i \(-0.561443\pi\)
−0.191831 + 0.981428i \(0.561443\pi\)
\(270\) 4.62158 + 10.6603i 0.281260 + 0.648762i
\(271\) −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
\(273\) 28.8484 4.94960i 1.74598 0.299563i
\(274\) 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 \(-0.946033\pi\)
0.985662 0.168730i \(-0.0539665\pi\)
\(282\) 2.02066 + 11.7773i 0.120329 + 0.701328i
\(283\) 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
\(285\) −7.15623 6.22803i −0.423899 0.368917i
\(286\) −27.5959 −1.63178
\(287\) −20.7846 + 20.7846i −1.22688 + 1.22688i
\(288\) −1.29289 + 2.70711i −0.0761845 + 0.159518i
\(289\) 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 0.190714 0.981646i \(-0.438920\pi\)
−0.981646 + 0.190714i \(0.938920\pi\)
\(294\) −7.07107 5.00000i −0.412393 0.291606i
\(295\) 9.55051 7.79796i 0.556052 0.454015i
\(296\) 3.46410i 0.201347i
\(297\) −14.3431 25.6569i −0.832274 1.48876i
\(298\) 7.79796 7.79796i 0.451724 0.451724i
\(299\) −4.87832 −0.282120
\(300\) 8.65597 + 0.272229i 0.499753 + 0.0157171i
\(301\) 14.2020 0.818592
\(302\) −0.635674 + 0.635674i −0.0365790 + 0.0365790i
\(303\) −0.186185 1.08516i −0.0106960 0.0623411i
\(304\) 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 \(0.133368\pi\)
−0.913502 + 0.406835i \(0.866632\pi\)
\(312\) −8.32780 + 1.42883i −0.471469 + 0.0808913i
\(313\) −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
\(315\) 22.5765 5.50470i 1.27204 0.310155i
\(316\) 4.44949 0.250303
\(317\) 13.3636 13.3636i 0.750574 0.750574i −0.224012 0.974586i \(-0.571915\pi\)
0.974586 + 0.224012i \(0.0719155\pi\)
\(318\) −2.30198 + 0.394957i −0.129089 + 0.0221481i
\(319\) 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
\(327\) −4.04133 23.5546i −0.223486 1.30257i
\(328\) 6.00000 6.00000i 0.331295 0.331295i
\(329\) 23.8988 1.31758
\(330\) −21.8564 + 1.51575i −1.20316 + 0.0834393i
\(331\) −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
\(333\) −9.37769 4.47871i −0.513894 0.245432i
\(334\) 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
\(342\) 6.63103 + 3.16693i 0.358565 + 0.171248i
\(343\) 4.89898 4.89898i 0.264520 0.264520i
\(344\) −4.09978 −0.221045
\(345\) −3.86370 + 0.267949i −0.208015 + 0.0144259i
\(346\) −5.10102 −0.274233
\(347\) 0.142865 0.142865i 0.00766937 0.00766937i −0.703262 0.710931i \(-0.748274\pi\)
0.710931 + 0.703262i \(0.248274\pi\)
\(348\) 0.642242 + 3.74326i 0.0344278 + 0.200660i
\(349\) 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 \(-0.914027\pi\)
−0.266819 0.963747i \(-0.585973\pi\)
\(354\) −5.51399 + 7.79796i −0.293065 + 0.414457i
\(355\) −20.6969 25.3485i −1.09848 1.34536i
\(356\) 9.12096i 0.483410i
\(357\) −43.4558 + 7.45584i −2.29993 + 0.394605i
\(358\) 10.7980 10.7980i 0.570690 0.570690i
\(359\) −26.7272 −1.41061 −0.705304 0.708905i \(-0.749189\pi\)
−0.705304 + 0.708905i \(0.749189\pi\)
\(360\) −6.51727 + 1.58907i −0.343490 + 0.0837514i
\(361\) 13.0000 0.684211
\(362\) 5.65685 5.65685i 0.297318 0.297318i
\(363\) 35.8492 6.15076i 1.88160 0.322831i
\(364\) 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
\(372\) 1.43488 + 8.36308i 0.0743950 + 0.433606i
\(373\) 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
\(375\) 11.7699 + 15.3776i 0.607794 + 0.794095i
\(376\) −6.89898 −0.355788
\(377\) −7.56388 + 7.56388i −0.389560 + 0.389560i
\(378\) −15.7116 + 8.78335i −0.808115 + 0.451767i
\(379\) 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 0.817665 0.575695i \(-0.195268\pi\)
−0.575695 + 0.817665i \(0.695268\pi\)
\(384\) −1.41421 1.00000i −0.0721688 0.0510310i
\(385\) −4.40408 + 43.5959i −0.224453 + 2.22185i
\(386\) 2.68556i 0.136692i
\(387\) 5.30057 11.0985i 0.269443 0.564170i
\(388\) −0.449490 + 0.449490i −0.0228194 + 0.0228194i
\(389\) −31.1127 −1.57748 −0.788738 0.614729i \(-0.789265\pi\)
−0.788738 + 0.614729i \(0.789265\pi\)
\(390\) −14.2521 12.4035i −0.721683 0.628076i
\(391\) 7.34847 0.371628
\(392\) 3.53553 3.53553i 0.178571 0.178571i
\(393\) −0.0418441 0.243885i −0.00211075 0.0123024i
\(394\) 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 \(0.0627937\pi\)
−0.980605 + 0.195995i \(0.937206\pi\)
\(402\) 26.3125 4.51451i 1.31235 0.225163i
\(403\) −16.8990 + 16.8990i −0.841798 + 0.841798i
\(404\) 0.635674 0.0316260
\(405\) 4.12436 19.6975i 0.204941 0.978774i
\(406\) 7.59592 0.376979
\(407\) 13.8564 13.8564i 0.686837 0.686837i
\(408\) 12.5446 2.15232i 0.621051 0.106556i
\(409\) 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
\(417\) −5.47621 31.9177i −0.268171 1.56302i
\(418\) −9.79796 + 9.79796i −0.479234 + 0.479234i
\(419\) 4.38551 0.214246 0.107123 0.994246i \(-0.465836\pi\)
0.107123 + 0.994246i \(0.465836\pi\)
\(420\) 0.928203 + 13.3843i 0.0452917 + 0.653085i
\(421\) 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
\(423\) 8.91964 18.6763i 0.433688 0.908072i
\(424\) 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 \(-0.819150\pi\)
0.842893 0.538081i \(-0.180850\pi\)
\(432\) 4.53553 2.53553i 0.218216 0.121991i
\(433\) 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
\(435\) −5.57525 + 6.40617i −0.267313 + 0.307152i
\(436\) 13.7980 0.660802
\(437\) −1.73205 + 1.73205i −0.0828552 + 0.0828552i
\(438\) −0.786583 4.58454i −0.0375844 0.219058i
\(439\) 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 0.385272 0.922803i \(-0.374107\pi\)
−0.922803 + 0.385272i \(0.874107\pi\)
\(444\) 3.46410 4.89898i 0.164399 0.232495i
\(445\) −15.7980 + 12.8990i −0.748895 + 0.611470i
\(446\) 17.6062i 0.833679i
\(447\) −18.8259 + 3.23002i −0.890436 + 0.152775i
\(448\) −2.44949 + 2.44949i −0.115728 + 0.115728i
\(449\) −15.1278 −0.713923 −0.356961 0.934119i \(-0.616187\pi\)
−0.356961 + 0.934119i \(0.616187\pi\)
\(450\) −11.9692 9.04096i −0.564232 0.426195i
\(451\) −48.0000 −2.26023
\(452\) −8.02458 + 8.02458i −0.377444 + 0.377444i
\(453\) 1.53465 0.263305i 0.0721043 0.0123711i
\(454\) 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 \(0.261731\pi\)
−0.680573 + 0.732681i \(0.738269\pi\)
\(462\) −5.73951 33.4523i −0.267026 1.55634i
\(463\) 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
\(465\) −12.4561 + 14.3125i −0.577636 + 0.663725i
\(466\) 5.10102 0.236300
\(467\) 3.60697 3.60697i 0.166910 0.166910i −0.618709 0.785620i \(-0.712344\pi\)
0.785620 + 0.618709i \(0.212344\pi\)
\(468\) 13.2061 + 6.30714i 0.610453 + 0.291548i
\(469\) 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
\(477\) 3.65045 + 1.74343i 0.167143 + 0.0798260i
\(478\) −9.44949 + 9.44949i −0.432210 + 0.432210i
\(479\) −26.4415 −1.20814 −0.604071 0.796931i \(-0.706456\pi\)
−0.604071 + 0.796931i \(0.706456\pi\)
\(480\) −0.267949 3.86370i −0.0122302 0.176353i
\(481\) 16.8990 0.770527
\(482\) −6.43539 + 6.43539i −0.293124 + 0.293124i
\(483\) −1.01461 5.91359i −0.0461664 0.269078i
\(484\) 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 \(-0.806486\pi\)
0.820825 0.571179i \(-0.193514\pi\)
\(492\) −14.4853 + 2.48528i −0.653047 + 0.112045i
\(493\) 11.3939 11.3939i 0.513154 0.513154i
\(494\) −11.9494 −0.537628
\(495\) 32.4254 + 19.7128i 1.45741 + 0.886025i
\(496\) −4.89898 −0.219971
\(497\) 35.8481 35.8481i 1.60801 1.60801i
\(498\) 3.41421 0.585786i 0.152995 0.0262497i
\(499\) 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 0.748342 0.663313i \(-0.230850\pi\)
−0.663313 + 0.748342i \(0.730850\pi\)
\(504\) −3.46410 9.79796i −0.154303 0.436436i
\(505\) 0.898979 + 1.10102i 0.0400041 + 0.0489948i
\(506\) 5.65685i 0.251478i
\(507\) 3.16265 + 18.4333i 0.140458 + 0.818650i
\(508\) −3.55051 + 3.55051i −0.157528 + 0.157528i
\(509\) 19.8632 0.880421 0.440211 0.897895i \(-0.354904\pi\)
0.440211 + 0.897895i \(0.354904\pi\)
\(510\) 21.4687 + 18.6841i 0.950650 + 0.827345i
\(511\) −9.30306 −0.411543
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) −6.21076 11.1097i −0.274212 0.490507i
\(514\) 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 \(-0.856709\pi\)
0.900377 0.435111i \(-0.143291\pi\)
\(522\) 2.83500 5.93602i 0.124084 0.259812i
\(523\) −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
\(525\) −21.8695 + 20.5359i −0.954465 + 0.896260i
\(526\) 8.00000 0.348817
\(527\) 25.4558 25.4558i 1.10887 1.10887i
\(528\) 1.65685 + 9.65685i 0.0721053 + 0.420261i
\(529\) 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
\(537\) −26.0686 + 4.47266i −1.12494 + 0.193010i
\(538\) −4.44949 + 4.44949i −0.191831 + 0.191831i
\(539\) −28.2843 −1.21829
\(540\) 10.8059 + 4.26999i 0.465011 + 0.183751i
\(541\) 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
\(543\) −13.6569 + 2.34315i −0.586072 + 0.100554i
\(544\) 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
\(552\) 0.292893 + 1.70711i 0.0124664 + 0.0726593i
\(553\) −10.8990 + 10.8990i −0.463472 + 0.463472i
\(554\) −13.3636 −0.567765
\(555\) 13.3843 0.928203i 0.568130 0.0394000i
\(556\) 18.6969 0.792927
\(557\) −21.1024 + 21.1024i −0.894139 + 0.894139i −0.994910 0.100770i \(-0.967869\pi\)
0.100770 + 0.994910i \(0.467869\pi\)
\(558\) 6.33386 13.2621i 0.268134 0.561428i
\(559\) 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 \(0.0410850\pi\)
0.128714 + 0.991682i \(0.458915\pi\)
\(564\) 9.75663 + 6.89898i 0.410828 + 0.290499i
\(565\) −25.2474 2.55051i −1.06217 0.107301i
\(566\) 7.56388i 0.317933i
\(567\) 31.0028 + 3.29002i 1.30200 + 0.138168i
\(568\) −10.3485 + 10.3485i −0.434212 + 0.434212i
\(569\) 23.8988 1.00189 0.500944 0.865480i \(-0.332986\pi\)
0.500944 + 0.865480i \(0.332986\pi\)
\(570\) −9.46410 + 0.656339i −0.396408 + 0.0274910i
\(571\) 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
\(573\) 5.25924 + 30.6531i 0.219708 + 1.28055i
\(574\) 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
\(582\) 1.08516 0.186185i 0.0449815 0.00771761i
\(583\) −5.39388 + 5.39388i −0.223392 + 0.223392i
\(584\) 2.68556 0.111129
\(585\) 7.75199 + 31.7933i 0.320505 + 1.31449i
\(586\) −19.1464 −0.790932
\(587\) −13.9993 + 13.9993i −0.577812 + 0.577812i −0.934300 0.356488i \(-0.883974\pi\)
0.356488 + 0.934300i \(0.383974\pi\)
\(588\) −8.53553 + 1.46447i −0.351999 + 0.0603936i
\(589\) 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 0.898239 0.439507i \(-0.144847\pi\)
−0.439507 + 0.898239i \(0.644847\pi\)
\(594\) −28.2843 8.00000i −1.16052 0.328244i
\(595\) 44.0908 36.0000i 1.80755 1.47586i
\(596\) 11.0280i 0.451724i
\(597\) −2.21149 12.8895i −0.0905104 0.527533i
\(598\) −3.44949 + 3.44949i −0.141060 + 0.141060i
\(599\) −3.32124 −0.135702 −0.0678510 0.997695i \(-0.521614\pi\)
−0.0678510 + 0.997695i \(0.521614\pi\)
\(600\) 6.31319 5.92820i 0.257735 0.242018i
\(601\) −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
\(603\) −41.7259 19.9280i −1.69921 0.811530i
\(604\) 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
\(612\) −19.8931 9.50079i −0.804131 0.384047i
\(613\) 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
\(615\) −24.7899 21.5745i −0.999626 0.869969i
\(616\) 19.5959 0.789542
\(617\) −18.4169 + 18.4169i −0.741436 + 0.741436i −0.972854 0.231418i \(-0.925663\pi\)
0.231418 + 0.972854i \(0.425663\pi\)
\(618\) −4.51451 26.3125i −0.181600 1.05844i
\(619\) 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
\(627\) 23.6544 4.05845i 0.944664 0.162079i
\(628\) −8.44949 + 8.44949i −0.337171 + 0.337171i
\(629\) −25.4558 −1.01499
\(630\) 12.0716 19.8564i 0.480943 0.791098i
\(631\) 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
\(633\) −31.9177 + 5.47621i −1.26861 + 0.217660i
\(634\) 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 \(-0.867773\pi\)
0.914953 0.403560i \(-0.132227\pi\)
\(642\) −3.19224 18.6057i −0.125988 0.734309i
\(643\) −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
\(645\) 1.09853 + 15.8403i 0.0432546 + 0.623712i
\(646\) 18.0000 0.708201
\(647\) 34.4339 34.4339i 1.35374 1.35374i 0.472300 0.881438i \(-0.343424\pi\)
0.881438 0.472300i \(-0.156576\pi\)
\(648\) −8.94975 0.949747i −0.351579 0.0373096i
\(649\) 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 0.948980 0.315337i \(-0.102118\pi\)
−0.315337 + 0.948980i \(0.602118\pi\)
\(654\) −19.5133 13.7980i −0.763029 0.539543i
\(655\) 0.202041 + 0.247449i 0.00789440 + 0.00966862i
\(656\) 8.48528i 0.331295i
\(657\) −3.47215 + 7.27010i −0.135461 + 0.283634i
\(658\) 16.8990 16.8990i 0.658791 0.658791i
\(659\) 9.75663 0.380064 0.190032 0.981778i \(-0.439141\pi\)
0.190032 + 0.981778i \(0.439141\pi\)
\(660\) −14.3830 + 16.5266i −0.559858 + 0.643297i
\(661\) 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
\(663\) −10.4997 61.1966i −0.407774 2.37668i
\(664\) 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
\(672\) 5.91359 1.01461i 0.228122 0.0391395i
\(673\) 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
\(675\) 7.88599 + 24.7550i 0.303532 + 0.952821i
\(676\) −10.7980 −0.415306
\(677\) 8.51739 8.51739i 0.327350 0.327350i −0.524228 0.851578i \(-0.675646\pi\)
0.851578 + 0.524228i \(0.175646\pi\)
\(678\) 19.3730 3.32389i 0.744017 0.127653i
\(679\) 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 0.621262 0.783603i \(-0.286620\pi\)
−0.783603 + 0.621262i \(0.786620\pi\)
\(684\) 6.92820 2.44949i 0.264906 0.0936586i
\(685\) 4.34847 43.0454i 0.166146 1.64468i
\(686\) 6.92820i 0.264520i
\(687\) 1.96149 + 11.4324i 0.0748354 + 0.436173i
\(688\) −2.89898 + 2.89898i −0.110523 + 0.110523i
\(689\) −6.57826 −0.250612
\(690\) −2.54258 + 2.92152i −0.0967944 + 0.111220i
\(691\) −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
\(693\) −25.3354 + 53.0482i −0.962413 + 2.01514i
\(694\) 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 \(-0.760945\pi\)
0.730999 0.682379i \(-0.239055\pi\)
\(702\) −12.3691 22.1258i −0.466843 0.835083i
\(703\) 6.00000 6.00000i 0.226294 0.226294i
\(704\) −5.65685 −0.213201
\(705\) 1.84858 + 26.6556i 0.0696214 + 1.00391i
\(706\) −32.6969 −1.23057
\(707\) −1.55708 + 1.55708i −0.0585600 + 0.0585600i
\(708\) 1.61501 + 9.41297i 0.0606958 + 0.353761i
\(709\) 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
\(717\) 22.8131 3.91411i 0.851970 0.146175i
\(718\) −18.8990 + 18.8990i −0.705304 + 0.705304i
\(719\) −1.76416 −0.0657920 −0.0328960 0.999459i \(-0.510473\pi\)
−0.0328960 + 0.999459i \(0.510473\pi\)
\(720\) −3.48477 + 5.73205i −0.129870 + 0.213621i
\(721\) −53.3939 −1.98849
\(722\) 9.19239 9.19239i 0.342105 0.342105i
\(723\) 15.5364 2.66563i 0.577805 0.0991357i
\(724\) 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
\(732\) 0.263305 + 1.53465i 0.00973203 + 0.0567224i
\(733\) −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
\(735\) −14.6076 12.7129i −0.538809 0.468923i
\(736\) −1.00000 −0.0368605
\(737\) 61.6539 61.6539i 2.27105 2.27105i
\(738\) 22.9706 + 10.9706i 0.845558 + 0.403832i
\(739\) 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 0.483568 0.875307i \(-0.339341\pi\)
−0.875307 + 0.483568i \(0.839341\pi\)
\(744\) 6.92820 + 4.89898i 0.254000 + 0.179605i
\(745\) 19.1010 15.5959i 0.699807 0.571390i
\(746\) 17.6062i 0.644610i
\(747\) −5.41421 2.58579i −0.198096 0.0946090i
\(748\) 29.3939 29.3939i 1.07475 1.07475i
\(749\) −37.7552 −1.37954
\(750\) 19.1962 + 2.55103i 0.700944 + 0.0931503i
\(751\) −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
\(753\) 3.76977 + 21.9718i 0.137378 + 0.800697i
\(754\) 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 \(0.276668\pi\)
−0.645454 + 0.763799i \(0.723332\pi\)
\(762\) 8.57169 1.47067i 0.310520 0.0532767i
\(763\) −33.7980 + 33.7980i −1.22357 + 1.22357i
\(764\) −17.9562 −0.649632
\(765\) −11.6772 47.8920i −0.422191 1.73154i
\(766\) 6.69694 0.241970
\(767\) −19.0205 + 19.0205i −0.686789 + 0.686789i
\(768\) −1.70711 + 0.292893i −0.0615999 + 0.0105689i
\(769\) 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 0.0368554 0.999321i \(-0.488266\pi\)
−0.999321 + 0.0368554i \(0.988266\pi\)
\(774\) −4.09978 11.5959i −0.147363 0.416807i
\(775\) 4.89898