Properties

Label 690.2.i.c.47.2
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 47.2
Root \(0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 690.47
Dual form 690.2.i.c.323.2

$q$-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} +(-2.22474 + 0.224745i) q^{10} -5.65685i q^{11} +(1.70711 + 0.292893i) q^{12} +(1.44949 - 1.44949i) q^{13} +3.46410 q^{14} +(-2.92152 + 2.54258i) 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} +2.04989i q^{26} +(2.53553 - 4.53553i) q^{27} +(-2.44949 + 2.44949i) q^{28} -9.12096 q^{29} +(0.267949 - 3.86370i) q^{30} -4.89898 q^{31} +(0.707107 - 0.707107i) q^{32} +(9.65685 + 1.65685i) q^{33} +7.34847i q^{34} +(-0.778539 - 7.70674i) q^{35} +(-1.00000 + 2.82843i) q^{36} +(2.44949 + 2.44949i) q^{37} +(1.73205 + 1.73205i) q^{38} +(2.04989 + 2.89898i) q^{39} +(0.224745 + 2.22474i) q^{40} -8.48528i q^{41} +(-1.01461 + 5.91359i) q^{42} +(-6.89898 + 6.89898i) q^{43} -5.65685 q^{44} +(-3.48477 - 5.73205i) q^{45} +1.00000 q^{46} +(2.04989 - 2.04989i) q^{47} +(0.292893 - 1.70711i) q^{48} +5.00000i q^{49} +(-4.17121 - 2.75699i) q^{50} +(7.34847 + 10.3923i) q^{51} +(-1.44949 - 1.44949i) q^{52} +(9.43879 + 9.43879i) q^{53} +(1.41421 + 5.00000i) q^{54} +(8.00000 - 9.79796i) q^{55} -3.46410i q^{56} +(4.18154 + 0.717439i) q^{57} +(6.44949 - 6.44949i) q^{58} +8.34242 q^{59} +(2.54258 + 2.92152i) q^{60} -8.89898 q^{61} +(3.46410 - 3.46410i) q^{62} +(4.47871 + 9.37769i) q^{63} +1.00000i q^{64} +(4.56048 - 0.460702i) q^{65} +(-8.00000 + 5.65685i) q^{66} +(-1.10102 - 1.10102i) q^{67} +(-5.19615 - 5.19615i) q^{68} +(1.41421 - 1.00000i) q^{69} +(6.00000 + 4.89898i) q^{70} -6.14966i q^{71} +(-1.29289 - 2.70711i) q^{72} +(7.89898 - 7.89898i) q^{73} -3.46410 q^{74} +(-8.65597 + 0.272229i) q^{75} -2.44949 q^{76} +(-13.8564 + 13.8564i) q^{77} +(-3.49938 - 0.600398i) q^{78} -0.449490i 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} +(16.3485 - 1.65153i) q^{85} -9.75663i q^{86} +(2.67147 - 15.5704i) q^{87} +(4.00000 - 4.00000i) q^{88} +2.19275 q^{89} +(6.51727 + 1.58907i) q^{90} -7.10102 q^{91} +(-0.707107 + 0.707107i) q^{92} +(1.43488 - 8.36308i) q^{93} +2.89898i q^{94} +(3.46410 - 4.24264i) q^{95} +(1.00000 + 1.41421i) q^{96} +(4.44949 + 4.44949i) 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 0.0716124 0.997433i \(-0.477186\pi\)
−0.997433 + 0.0716124i \(0.977186\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) −2.82843 1.00000i −0.942809 0.333333i
\(10\) −2.22474 + 0.224745i −0.703526 + 0.0710706i
\(11\) 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
\(13\) 1.44949 1.44949i 0.402016 0.402016i −0.476927 0.878943i \(-0.658249\pi\)
0.878943 + 0.476927i \(0.158249\pi\)
\(14\) 3.46410 0.925820
\(15\) −2.92152 + 2.54258i −0.754333 + 0.656492i
\(16\) −1.00000 −0.250000
\(17\) 5.19615 5.19615i 1.26025 1.26025i 0.309282 0.950971i \(-0.399911\pi\)
0.950971 0.309282i \(-0.100089\pi\)
\(18\) 2.70711 1.29289i 0.638071 0.304738i
\(19\) 2.44949i 0.561951i −0.959715 0.280976i \(-0.909342\pi\)
0.959715 0.280976i \(-0.0906580\pi\)
\(20\) 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
\(26\) 2.04989i 0.402016i
\(27\) 2.53553 4.53553i 0.487964 0.872864i
\(28\) −2.44949 + 2.44949i −0.462910 + 0.462910i
\(29\) −9.12096 −1.69372 −0.846859 0.531817i \(-0.821510\pi\)
−0.846859 + 0.531817i \(0.821510\pi\)
\(30\) 0.267949 3.86370i 0.0489206 0.705412i
\(31\) −4.89898 −0.879883 −0.439941 0.898027i \(-0.645001\pi\)
−0.439941 + 0.898027i \(0.645001\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) 9.65685 + 1.65685i 1.68104 + 0.288421i
\(34\) 7.34847i 1.26025i
\(35\) −0.778539 7.70674i −0.131597 1.30268i
\(36\) −1.00000 + 2.82843i −0.166667 + 0.471405i
\(37\) 2.44949 + 2.44949i 0.402694 + 0.402694i 0.879181 0.476488i \(-0.158090\pi\)
−0.476488 + 0.879181i \(0.658090\pi\)
\(38\) 1.73205 + 1.73205i 0.280976 + 0.280976i
\(39\) 2.04989 + 2.89898i 0.328245 + 0.464208i
\(40\) 0.224745 + 2.22474i 0.0355353 + 0.351763i
\(41\) 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
\(43\) −6.89898 + 6.89898i −1.05208 + 1.05208i −0.0535176 + 0.998567i \(0.517043\pi\)
−0.998567 + 0.0535176i \(0.982957\pi\)
\(44\) −5.65685 −0.852803
\(45\) −3.48477 5.73205i −0.519478 0.854484i
\(46\) 1.00000 0.147442
\(47\) 2.04989 2.04989i 0.299007 0.299007i −0.541618 0.840625i \(-0.682188\pi\)
0.840625 + 0.541618i \(0.182188\pi\)
\(48\) 0.292893 1.70711i 0.0422755 0.246400i
\(49\) 5.00000i 0.714286i
\(50\) −4.17121 2.75699i −0.589898 0.389898i
\(51\) 7.34847 + 10.3923i 1.02899 + 1.45521i
\(52\) −1.44949 1.44949i −0.201008 0.201008i
\(53\) 9.43879 + 9.43879i 1.29652 + 1.29652i 0.930678 + 0.365840i \(0.119218\pi\)
0.365840 + 0.930678i \(0.380782\pi\)
\(54\) 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
\(58\) 6.44949 6.44949i 0.846859 0.846859i
\(59\) 8.34242 1.08609 0.543045 0.839704i \(-0.317271\pi\)
0.543045 + 0.839704i \(0.317271\pi\)
\(60\) 2.54258 + 2.92152i 0.328246 + 0.377167i
\(61\) −8.89898 −1.13940 −0.569699 0.821854i \(-0.692940\pi\)
−0.569699 + 0.821854i \(0.692940\pi\)
\(62\) 3.46410 3.46410i 0.439941 0.439941i
\(63\) 4.47871 + 9.37769i 0.564265 + 1.18148i
\(64\) 1.00000i 0.125000i
\(65\) 4.56048 0.460702i 0.565658 0.0571430i
\(66\) −8.00000 + 5.65685i −0.984732 + 0.696311i
\(67\) −1.10102 1.10102i −0.134511 0.134511i 0.636646 0.771157i \(-0.280321\pi\)
−0.771157 + 0.636646i \(0.780321\pi\)
\(68\) −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
\(71\) 6.14966i 0.729831i −0.931041 0.364915i \(-0.881098\pi\)
0.931041 0.364915i \(-0.118902\pi\)
\(72\) −1.29289 2.70711i −0.152369 0.319036i
\(73\) 7.89898 7.89898i 0.924506 0.924506i −0.0728382 0.997344i \(-0.523206\pi\)
0.997344 + 0.0728382i \(0.0232057\pi\)
\(74\) −3.46410 −0.402694
\(75\) −8.65597 + 0.272229i −0.999506 + 0.0314343i
\(76\) −2.44949 −0.280976
\(77\) −13.8564 + 13.8564i −1.57908 + 1.57908i
\(78\) −3.49938 0.600398i −0.396227 0.0679817i
\(79\) 0.449490i 0.0505715i −0.999680 0.0252858i \(-0.991950\pi\)
0.999680 0.0252858i \(-0.00804957\pi\)
\(80\) −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
\(85\) 16.3485 1.65153i 1.77324 0.179134i
\(86\) 9.75663i 1.05208i
\(87\) 2.67147 15.5704i 0.286411 1.66933i
\(88\) 4.00000 4.00000i 0.426401 0.426401i
\(89\) 2.19275 0.232431 0.116216 0.993224i \(-0.462924\pi\)
0.116216 + 0.993224i \(0.462924\pi\)
\(90\) 6.51727 + 1.58907i 0.686981 + 0.167503i
\(91\) −7.10102 −0.744389
\(92\) −0.707107 + 0.707107i −0.0737210 + 0.0737210i
\(93\) 1.43488 8.36308i 0.148790 0.867211i
\(94\) 2.89898i 0.299007i
\(95\) 3.46410 4.24264i 0.355409 0.435286i
\(96\) 1.00000 + 1.41421i 0.102062 + 0.144338i
\(97\) 4.44949 + 4.44949i 0.451777 + 0.451777i 0.895944 0.444167i \(-0.146500\pi\)
−0.444167 + 0.895944i \(0.646500\pi\)
\(98\) −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
\(101\) 6.29253i 0.626130i 0.949732 + 0.313065i \(0.101356\pi\)
−0.949732 + 0.313065i \(0.898644\pi\)
\(102\) −12.5446 2.15232i −1.24210 0.213111i
\(103\) −1.10102 + 1.10102i −0.108487 + 0.108487i −0.759267 0.650780i \(-0.774442\pi\)
0.650780 + 0.759267i \(0.274442\pi\)
\(104\) 2.04989 0.201008
\(105\) 13.3843 + 0.928203i 1.30617 + 0.0905834i
\(106\) −13.3485 −1.29652
\(107\) 0.778539 0.778539i 0.0752642 0.0752642i −0.668473 0.743737i \(-0.733052\pi\)
0.743737 + 0.668473i \(0.233052\pi\)
\(108\) −4.53553 2.53553i −0.436432 0.243982i
\(109\) 5.79796i 0.555344i −0.960676 0.277672i \(-0.910437\pi\)
0.960676 0.277672i \(-0.0895628\pi\)
\(110\) 1.27135 + 12.5851i 0.121218 + 1.19994i
\(111\) −4.89898 + 3.46410i −0.464991 + 0.328798i
\(112\) 2.44949 + 2.44949i 0.231455 + 0.231455i
\(113\) −2.36773 2.36773i −0.222737 0.222737i 0.586913 0.809650i \(-0.300343\pi\)
−0.809650 + 0.586913i \(0.800343\pi\)
\(114\) −3.46410 + 2.44949i −0.324443 + 0.229416i
\(115\) −0.224745 2.22474i −0.0209576 0.207459i
\(116\) 9.12096i 0.846859i
\(117\) −5.54927 + 2.65029i −0.513030 + 0.245019i
\(118\) −5.89898 + 5.89898i −0.543045 + 0.543045i
\(119\) −25.4558 −2.33353
\(120\) −3.86370 0.267949i −0.352706 0.0244603i
\(121\) −21.0000 −1.90909
\(122\) 6.29253 6.29253i 0.569699 0.569699i
\(123\) 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
\(127\) −8.44949 8.44949i −0.749771 0.749771i 0.224665 0.974436i \(-0.427871\pi\)
−0.974436 + 0.224665i \(0.927871\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) −9.75663 13.7980i −0.859023 1.21484i
\(130\) −2.89898 + 3.55051i −0.254257 + 0.311400i
\(131\) 13.9993i 1.22312i −0.791197 0.611561i \(-0.790542\pi\)
0.791197 0.611561i \(-0.209458\pi\)
\(132\) 1.65685 9.65685i 0.144211 0.840521i
\(133\) −6.00000 + 6.00000i −0.520266 + 0.520266i
\(134\) 1.55708 0.134511
\(135\) 10.8059 4.26999i 0.930023 0.367502i
\(136\) 7.34847 0.630126
\(137\) −3.28913 + 3.28913i −0.281009 + 0.281009i −0.833511 0.552502i \(-0.813673\pi\)
0.552502 + 0.833511i \(0.313673\pi\)
\(138\) −0.292893 + 1.70711i −0.0249327 + 0.145319i
\(139\) 10.6969i 0.907302i −0.891179 0.453651i \(-0.850121\pi\)
0.891179 0.453651i \(-0.149879\pi\)
\(140\) −7.70674 + 0.778539i −0.651339 + 0.0657986i
\(141\) 2.89898 + 4.09978i 0.244138 + 0.345263i
\(142\) 4.34847 + 4.34847i 0.364915 + 0.364915i
\(143\) −8.19955 8.19955i −0.685681 0.685681i
\(144\) 2.82843 + 1.00000i 0.235702 + 0.0833333i
\(145\) −15.7980 12.8990i −1.31195 1.07120i
\(146\) 11.1708i 0.924506i
\(147\) −8.53553 1.46447i −0.703999 0.120787i
\(148\) 2.44949 2.44949i 0.201347 0.201347i
\(149\) 16.6848 1.36687 0.683437 0.730009i \(-0.260484\pi\)
0.683437 + 0.730009i \(0.260484\pi\)
\(150\) 5.92820 6.31319i 0.484036 0.515470i
\(151\) 8.89898 0.724189 0.362094 0.932141i \(-0.382062\pi\)
0.362094 + 0.932141i \(0.382062\pi\)
\(152\) 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
\(156\) 2.89898 2.04989i 0.232104 0.164122i
\(157\) −3.55051 3.55051i −0.283362 0.283362i 0.551087 0.834448i \(-0.314213\pi\)
−0.834448 + 0.551087i \(0.814213\pi\)
\(158\) 0.317837 + 0.317837i 0.0252858 + 0.0252858i
\(159\) −18.8776 + 13.3485i −1.49709 + 1.05860i
\(160\) 2.22474 0.224745i 0.175882 0.0177676i
\(161\) 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
\(165\) 14.3830 + 16.5266i 1.11972 + 1.28659i
\(166\) −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
\(169\) 8.79796i 0.676766i
\(170\) −10.3923 + 12.7279i −0.797053 + 0.976187i
\(171\) −2.44949 + 6.92820i −0.187317 + 0.529813i
\(172\) 6.89898 + 6.89898i 0.526042 + 0.526042i
\(173\) 10.5352 + 10.5352i 0.800974 + 0.800974i 0.983248 0.182274i \(-0.0583457\pi\)
−0.182274 + 0.983248i \(0.558346\pi\)
\(174\) 9.12096 + 12.8990i 0.691458 + 0.977869i
\(175\) 9.55051 14.4495i 0.721951 1.09228i
\(176\) 5.65685i 0.426401i
\(177\) −2.44344 + 14.2414i −0.183660 + 1.07045i
\(178\) −1.55051 + 1.55051i −0.116216 + 0.116216i
\(179\) 12.4422 0.929973 0.464987 0.885318i \(-0.346059\pi\)
0.464987 + 0.885318i \(0.346059\pi\)
\(180\) −5.73205 + 3.48477i −0.427242 + 0.259739i
\(181\) 8.00000 0.594635 0.297318 0.954779i \(-0.403908\pi\)
0.297318 + 0.954779i \(0.403908\pi\)
\(182\) 5.02118 5.02118i 0.372195 0.372195i
\(183\) 2.60645 15.1915i 0.192674 1.12299i
\(184\) 1.00000i 0.0737210i
\(185\) 0.778539 + 7.70674i 0.0572393 + 0.566611i
\(186\) 4.89898 + 6.92820i 0.359211 + 0.508001i
\(187\) −29.3939 29.3939i −2.14949 2.14949i
\(188\) −2.04989 2.04989i −0.149503 0.149503i
\(189\) −17.3205 + 4.89898i −1.25988 + 0.356348i
\(190\) 0.550510 + 5.44949i 0.0399382 + 0.395348i
\(191\) 23.6130i 1.70858i −0.519797 0.854290i \(-0.673992\pi\)
0.519797 0.854290i \(-0.326008\pi\)
\(192\) −1.70711 0.292893i −0.123200 0.0211377i
\(193\) −7.89898 + 7.89898i −0.568581 + 0.568581i −0.931731 0.363150i \(-0.881701\pi\)
0.363150 + 0.931731i \(0.381701\pi\)
\(194\) −6.29253 −0.451777
\(195\) −0.549266 + 7.92016i −0.0393337 + 0.567174i
\(196\) 5.00000 0.357143
\(197\) −0.778539 + 0.778539i −0.0554686 + 0.0554686i −0.734297 0.678828i \(-0.762488\pi\)
0.678828 + 0.734297i \(0.262488\pi\)
\(198\) −7.31371 15.3137i −0.519763 1.08830i
\(199\) 12.4495i 0.882521i 0.897379 + 0.441260i \(0.145469\pi\)
−0.897379 + 0.441260i \(0.854531\pi\)
\(200\) −2.75699 + 4.17121i −0.194949 + 0.294949i
\(201\) 2.20204 1.55708i 0.155320 0.109828i
\(202\) −4.44949 4.44949i −0.313065 0.313065i
\(203\) 22.3417 + 22.3417i 1.56808 + 1.56808i
\(204\) 10.3923 7.34847i 0.727607 0.514496i
\(205\) 12.0000 14.6969i 0.838116 1.02648i
\(206\) 1.55708i 0.108487i
\(207\) 1.29289 + 2.70711i 0.0898623 + 0.188157i
\(208\) −1.44949 + 1.44949i −0.100504 + 0.100504i
\(209\) −13.8564 −0.958468
\(210\) −10.1204 + 8.80776i −0.698377 + 0.607793i
\(211\) −10.6969 −0.736408 −0.368204 0.929745i \(-0.620027\pi\)
−0.368204 + 0.929745i \(0.620027\pi\)
\(212\) 9.43879 9.43879i 0.648259 0.648259i
\(213\) 10.4981 + 1.80119i 0.719320 + 0.123416i
\(214\) 1.10102i 0.0752642i
\(215\) −21.7060 + 2.19275i −1.48034 + 0.149544i
\(216\) 5.00000 1.41421i 0.340207 0.0962250i
\(217\) 12.0000 + 12.0000i 0.814613 + 0.814613i
\(218\) 4.09978 + 4.09978i 0.277672 + 0.277672i
\(219\) 11.1708 + 15.7980i 0.754856 + 1.06753i
\(220\) −9.79796 8.00000i −0.660578 0.539360i
\(221\) 15.0635i 1.01328i
\(222\) 1.01461 5.91359i 0.0680963 0.396894i
\(223\) −7.55051 + 7.55051i −0.505620 + 0.505620i −0.913179 0.407559i \(-0.866380\pi\)
0.407559 + 0.913179i \(0.366380\pi\)
\(224\) −3.46410 −0.231455
\(225\) 2.07055 14.8564i 0.138037 0.990427i
\(226\) 3.34847 0.222737
\(227\) 7.70674 7.70674i 0.511514 0.511514i −0.403476 0.914990i \(-0.632198\pi\)
0.914990 + 0.403476i \(0.132198\pi\)
\(228\) 0.717439 4.18154i 0.0475136 0.276929i
\(229\) 22.6969i 1.49986i 0.661520 + 0.749928i \(0.269912\pi\)
−0.661520 + 0.749928i \(0.730088\pi\)
\(230\) 1.73205 + 1.41421i 0.114208 + 0.0932505i
\(231\) −19.5959 27.7128i −1.28932 1.82337i
\(232\) −6.44949 6.44949i −0.423430 0.423430i
\(233\) −10.5352 10.5352i −0.690182 0.690182i 0.272090 0.962272i \(-0.412285\pi\)
−0.962272 + 0.272090i \(0.912285\pi\)
\(234\) 2.04989 5.79796i 0.134005 0.379024i
\(235\) 6.44949 0.651531i 0.420718 0.0425012i
\(236\) 8.34242i 0.543045i
\(237\) 0.767327 + 0.131652i 0.0498432 + 0.00855175i
\(238\) 18.0000 18.0000i 1.16677 1.16677i
\(239\) 6.43539 0.416271 0.208135 0.978100i \(-0.433261\pi\)
0.208135 + 0.978100i \(0.433261\pi\)
\(240\) 2.92152 2.54258i 0.188583 0.164123i
\(241\) −18.8990 −1.21739 −0.608695 0.793404i \(-0.708307\pi\)
−0.608695 + 0.793404i \(0.708307\pi\)
\(242\) 14.8492 14.8492i 0.954545 0.954545i
\(243\) −11.7071 + 10.2929i −0.751011 + 0.660289i
\(244\) 8.89898i 0.569699i
\(245\) −7.07107 + 8.66025i −0.451754 + 0.553283i
\(246\) −12.0000 + 8.48528i −0.765092 + 0.541002i
\(247\) −3.55051 3.55051i −0.225914 0.225914i
\(248\) −3.46410 3.46410i −0.219971 0.219971i
\(249\) −2.82843 + 2.00000i −0.179244 + 0.126745i
\(250\) −3.32577 10.6742i −0.210340 0.675098i
\(251\) 26.7272i 1.68701i 0.537125 + 0.843503i \(0.319510\pi\)
−0.537125 + 0.843503i \(0.680490\pi\)
\(252\) 9.37769 4.47871i 0.590739 0.282132i
\(253\) −4.00000 + 4.00000i −0.251478 + 0.251478i
\(254\) 11.9494 0.749771
\(255\) −1.96902 + 28.3923i −0.123305 + 1.77800i
\(256\) 1.00000 0.0625000
\(257\) 18.0990 18.0990i 1.12899 1.12899i 0.138645 0.990342i \(-0.455725\pi\)
0.990342 0.138645i \(-0.0442748\pi\)
\(258\) 16.6556 + 2.85765i 1.03693 + 0.177910i
\(259\) 12.0000i 0.745644i
\(260\) −0.460702 4.56048i −0.0285715 0.282829i
\(261\) 25.7980 + 9.12096i 1.59685 + 0.564573i
\(262\) 9.89898 + 9.89898i 0.611561 + 0.611561i
\(263\) −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 + 29.6969i 0.184289 + 1.82427i
\(266\) 8.48528i 0.520266i
\(267\) −0.642242 + 3.74326i −0.0393046 + 0.229084i
\(268\) −1.10102 + 1.10102i −0.0672555 + 0.0672555i
\(269\) −0.635674 −0.0387578 −0.0193789 0.999812i \(-0.506169\pi\)
−0.0193789 + 0.999812i \(0.506169\pi\)
\(270\) −4.62158 + 10.6603i −0.281260 + 0.648762i
\(271\) 24.4949 1.48796 0.743980 0.668202i \(-0.232936\pi\)
0.743980 + 0.668202i \(0.232936\pi\)
\(272\) −5.19615 + 5.19615i −0.315063 + 0.315063i
\(273\) 2.07984 12.1222i 0.125878 0.733669i
\(274\) 4.65153i 0.281009i
\(275\) 27.7128 5.65685i 1.67115 0.341121i
\(276\) −1.00000 1.41421i −0.0601929 0.0851257i
\(277\) −4.55051 4.55051i −0.273414 0.273414i 0.557059 0.830473i \(-0.311930\pi\)
−0.830473 + 0.557059i \(0.811930\pi\)
\(278\) 7.56388 + 7.56388i 0.453651 + 0.453651i
\(279\) 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 \(0.946033\pi\)
\(282\) −4.94887 0.849091i −0.294701 0.0505627i
\(283\) −9.34847 + 9.34847i −0.555709 + 0.555709i −0.928083 0.372374i \(-0.878544\pi\)
0.372374 + 0.928083i \(0.378544\pi\)
\(284\) −6.14966 −0.364915
\(285\) 6.22803 + 7.15623i 0.368917 + 0.423899i
\(286\) 11.5959 0.685681
\(287\) −20.7846 + 20.7846i −1.22688 + 1.22688i
\(288\) −2.70711 + 1.29289i −0.159518 + 0.0761845i
\(289\) 37.0000i 2.17647i
\(290\) 20.2918 2.04989i 1.19158 0.120374i
\(291\) −8.89898 + 6.29253i −0.521667 + 0.368875i
\(292\) −7.89898 7.89898i −0.462253 0.462253i
\(293\) −10.7101 10.7101i −0.625693 0.625693i 0.321288 0.946981i \(-0.395884\pi\)
−0.946981 + 0.321288i \(0.895884\pi\)
\(294\) 7.07107 5.00000i 0.412393 0.291606i
\(295\) 14.4495 + 11.7980i 0.841282 + 0.686904i
\(296\) 3.46410i 0.201347i
\(297\) −25.6569 14.3431i −1.48876 0.832274i
\(298\) −11.7980 + 11.7980i −0.683437 + 0.683437i
\(299\) −2.04989 −0.118548
\(300\) 0.272229 + 8.65597i 0.0157171 + 0.499753i
\(301\) 33.7980 1.94808
\(302\) −6.29253 + 6.29253i −0.362094 + 0.362094i
\(303\) −10.7420 1.84304i −0.617113 0.105880i
\(304\) 2.44949i 0.140488i
\(305\) −15.4135 12.5851i −0.882574 0.720618i
\(306\) 7.34847 20.7846i 0.420084 1.18818i
\(307\) 6.69694 + 6.69694i 0.382214 + 0.382214i 0.871899 0.489685i \(-0.162888\pi\)
−0.489685 + 0.871899i \(0.662888\pi\)
\(308\) 13.8564 + 13.8564i 0.789542 + 0.789542i
\(309\) −1.55708 2.20204i −0.0885791 0.125270i
\(310\) 10.8990 1.10102i 0.619020 0.0625338i
\(311\) 34.1482i 1.93637i 0.250241 + 0.968184i \(0.419490\pi\)
−0.250241 + 0.968184i \(0.580510\pi\)
\(312\) −0.600398 + 3.49938i −0.0339909 + 0.198113i
\(313\) 19.1464 19.1464i 1.08222 1.08222i 0.0859179 0.996302i \(-0.472618\pi\)
0.996302 0.0859179i \(-0.0273823\pi\)
\(314\) 5.02118 0.283362
\(315\) −5.50470 + 22.5765i −0.310155 + 1.27204i
\(316\) −0.449490 −0.0252858
\(317\) −6.43539 + 6.43539i −0.361448 + 0.361448i −0.864346 0.502898i \(-0.832267\pi\)
0.502898 + 0.864346i \(0.332267\pi\)
\(318\) 3.90968 22.7873i 0.219244 1.27785i
\(319\) 51.5959i 2.88882i
\(320\) −1.41421 + 1.73205i −0.0790569 + 0.0968246i
\(321\) 1.10102 + 1.55708i 0.0614530 + 0.0869076i
\(322\) −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
\(325\) 8.55051 + 5.65153i 0.474297 + 0.313491i
\(326\) 5.65685i 0.313304i
\(327\) 9.89774 + 1.69818i 0.547346 + 0.0939097i
\(328\) 6.00000 6.00000i 0.331295 0.331295i
\(329\) −10.0424 −0.553653
\(330\) −21.8564 1.51575i −1.20316 0.0834393i
\(331\) 10.6969 0.587957 0.293978 0.955812i \(-0.405021\pi\)
0.293978 + 0.955812i \(0.405021\pi\)
\(332\) 1.41421 1.41421i 0.0776151 0.0776151i
\(333\) −4.47871 9.37769i −0.245432 0.513894i
\(334\) 8.00000i 0.437741i
\(335\) −0.349945 3.46410i −0.0191196 0.189264i
\(336\) −4.89898 + 3.46410i −0.267261 + 0.188982i
\(337\) 9.55051 + 9.55051i 0.520249 + 0.520249i 0.917647 0.397397i \(-0.130086\pi\)
−0.397397 + 0.917647i \(0.630086\pi\)
\(338\) −6.22110 6.22110i −0.338383 0.338383i
\(339\) 4.73545 3.34847i 0.257194 0.181864i
\(340\) −1.65153 16.3485i −0.0895668 0.886620i
\(341\) 27.7128i 1.50073i
\(342\) −3.16693 6.63103i −0.171248 0.358565i
\(343\) −4.89898 + 4.89898i −0.264520 + 0.264520i
\(344\) −9.75663 −0.526042
\(345\) 3.86370 + 0.267949i 0.208015 + 0.0144259i
\(346\) −14.8990 −0.800974
\(347\) −13.9993 + 13.9993i −0.751520 + 0.751520i −0.974763 0.223243i \(-0.928336\pi\)
0.223243 + 0.974763i \(0.428336\pi\)
\(348\) −15.5704 2.67147i −0.834663 0.143206i
\(349\) 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
\(351\) −2.89898 10.2494i −0.154736 0.547075i
\(352\) −4.00000 4.00000i −0.213201 0.213201i
\(353\) 2.33562 + 2.33562i 0.124312 + 0.124312i 0.766526 0.642213i \(-0.221984\pi\)
−0.642213 + 0.766526i \(0.721984\pi\)
\(354\) −8.34242 11.7980i −0.443394 0.627054i
\(355\) 8.69694 10.6515i 0.461586 0.565325i
\(356\) 2.19275i 0.116216i
\(357\) 7.45584 43.4558i 0.394605 2.29993i
\(358\) −8.79796 + 8.79796i −0.464987 + 0.464987i
\(359\) 12.8708 0.679294 0.339647 0.940553i \(-0.389692\pi\)
0.339647 + 0.940553i \(0.389692\pi\)
\(360\) 1.58907 6.51727i 0.0837514 0.343490i
\(361\) 13.0000 0.684211
\(362\) −5.65685 + 5.65685i −0.297318 + 0.297318i
\(363\) 6.15076 35.8492i 0.322831 1.88160i
\(364\) 7.10102i 0.372195i
\(365\) 24.8523 2.51059i 1.30083 0.131410i
\(366\) 8.89898 + 12.5851i 0.465157 + 0.657831i
\(367\) 0.202041 + 0.202041i 0.0105465 + 0.0105465i 0.712360 0.701814i \(-0.247626\pi\)
−0.701814 + 0.712360i \(0.747626\pi\)
\(368\) 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
\(371\) 46.2405i 2.40068i
\(372\) −8.36308 1.43488i −0.433606 0.0743950i
\(373\) 7.55051 7.55051i 0.390951 0.390951i −0.484076 0.875026i \(-0.660844\pi\)
0.875026 + 0.484076i \(0.160844\pi\)
\(374\) 41.5692 2.14949
\(375\) −15.3776 11.7699i −0.794095 0.607794i
\(376\) 2.89898 0.149503
\(377\) −13.2207 + 13.2207i −0.680902 + 0.680902i
\(378\) 8.78335 15.7116i 0.451767 0.808115i
\(379\) 29.1464i 1.49715i −0.663049 0.748576i \(-0.730738\pi\)
0.663049 0.748576i \(-0.269262\pi\)
\(380\) −4.24264 3.46410i −0.217643 0.177705i
\(381\) 16.8990 11.9494i 0.865761 0.612185i
\(382\) 16.6969 + 16.6969i 0.854290 + 0.854290i
\(383\) 16.0492 + 16.0492i 0.820074 + 0.820074i 0.986118 0.166045i \(-0.0530995\pi\)
−0.166045 + 0.986118i \(0.553100\pi\)
\(384\) 1.41421 1.00000i 0.0721688 0.0510310i
\(385\) −43.5959 + 4.40408i −2.22185 + 0.224453i
\(386\) 11.1708i 0.568581i
\(387\) 26.4122 12.6143i 1.34261 0.641220i
\(388\) 4.44949 4.44949i 0.225889 0.225889i
\(389\) 31.1127 1.57748 0.788738 0.614729i \(-0.210735\pi\)
0.788738 + 0.614729i \(0.210735\pi\)
\(390\) −5.21201 5.98879i −0.263920 0.303254i
\(391\) −7.34847 −0.371628
\(392\) −3.53553 + 3.53553i −0.178571 + 0.178571i
\(393\) 23.8983 + 4.10029i 1.20551 + 0.206832i
\(394\) 1.10102i 0.0554686i
\(395\) 0.635674 0.778539i 0.0319843 0.0391726i
\(396\) 16.0000 + 5.65685i 0.804030 + 0.284268i
\(397\) 13.4495 + 13.4495i 0.675011 + 0.675011i 0.958867 0.283856i \(-0.0916139\pi\)
−0.283856 + 0.958867i \(0.591614\pi\)
\(398\) −8.80312 8.80312i −0.441260 0.441260i
\(399\) −8.48528 12.0000i −0.424795 0.600751i
\(400\) −1.00000 4.89898i −0.0500000 0.244949i
\(401\) 14.7778i 0.737969i −0.929436 0.368984i \(-0.879706\pi\)
0.929436 0.368984i \(-0.120294\pi\)
\(402\) −0.456058 + 2.65810i −0.0227461 + 0.132574i
\(403\) −7.10102 + 7.10102i −0.353727 + 0.353727i
\(404\) 6.29253 0.313065
\(405\) 4.12436 + 19.6975i 0.204941 + 0.978774i
\(406\) −31.5959 −1.56808
\(407\) 13.8564 13.8564i 0.686837 0.686837i
\(408\) −2.15232 + 12.5446i −0.106556 + 0.621051i
\(409\) 5.79796i 0.286691i −0.989673 0.143345i \(-0.954214\pi\)
0.989673 0.143345i \(-0.0457860\pi\)
\(410\) 1.90702 + 18.8776i 0.0941812 + 0.932298i
\(411\) −4.65153 6.57826i −0.229443 0.324482i
\(412\) 1.10102 + 1.10102i 0.0542434 + 0.0542434i
\(413\) −20.4347 20.4347i −1.00552 1.00552i
\(414\) −2.82843 1.00000i −0.139010 0.0491473i
\(415\) 0.449490 + 4.44949i 0.0220646 + 0.218417i
\(416\) 2.04989i 0.100504i
\(417\) 18.2608 + 3.13306i 0.894236 + 0.153427i
\(418\) 9.79796 9.79796i 0.479234 0.479234i
\(419\) −18.2419 −0.891176 −0.445588 0.895238i \(-0.647005\pi\)
−0.445588 + 0.895238i \(0.647005\pi\)
\(420\) 0.928203 13.3843i 0.0452917 0.653085i
\(421\) −8.89898 −0.433710 −0.216855 0.976204i \(-0.569580\pi\)
−0.216855 + 0.976204i \(0.569580\pi\)
\(422\) 7.56388 7.56388i 0.368204 0.368204i
\(423\) −7.84785 + 3.74807i −0.381575 + 0.182237i
\(424\) 13.3485i 0.648259i
\(425\) 30.6520 + 20.2597i 1.48684 + 0.982739i
\(426\) −8.69694 + 6.14966i −0.421368 + 0.297952i
\(427\) 21.7980 + 21.7980i 1.05488 + 1.05488i
\(428\) −0.778539 0.778539i −0.0376321 0.0376321i
\(429\) 16.3991 11.5959i 0.791756 0.559856i
\(430\) 13.7980 16.8990i 0.665397 0.814941i
\(431\) 5.37113i 0.258718i −0.991598 0.129359i \(-0.958708\pi\)
0.991598 0.129359i \(-0.0412920\pi\)
\(432\) −2.53553 + 4.53553i −0.121991 + 0.218216i
\(433\) 14.6515 14.6515i 0.704108 0.704108i −0.261182 0.965290i \(-0.584112\pi\)
0.965290 + 0.261182i \(0.0841123\pi\)
\(434\) −16.9706 −0.814613
\(435\) 26.6471 23.1908i 1.27763 1.11191i
\(436\) −5.79796 −0.277672
\(437\) −1.73205 + 1.73205i −0.0828552 + 0.0828552i
\(438\) −19.0698 3.27186i −0.911191 0.156336i
\(439\) 16.0000i 0.763638i −0.924237 0.381819i \(-0.875298\pi\)
0.924237 0.381819i \(-0.124702\pi\)
\(440\) 12.5851 1.27135i 0.599969 0.0606092i
\(441\) 5.00000 14.1421i 0.238095 0.673435i
\(442\) 10.6515 + 10.6515i 0.506642 + 0.506642i
\(443\) 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
\(445\) 3.79796 + 3.10102i 0.180041 + 0.147002i
\(446\) 10.6780i 0.505620i
\(447\) −4.88687 + 28.4828i −0.231141 + 1.34719i
\(448\) 2.44949 2.44949i 0.115728 0.115728i
\(449\) −26.4415 −1.24785 −0.623925 0.781484i \(-0.714463\pi\)
−0.623925 + 0.781484i \(0.714463\pi\)
\(450\) 9.04096 + 11.9692i 0.426195 + 0.564232i
\(451\) −48.0000 −2.26023
\(452\) −2.36773 + 2.36773i −0.111368 + 0.111368i
\(453\) −2.60645 + 15.1915i −0.122462 + 0.713759i
\(454\) 10.8990i 0.511514i
\(455\) −12.2993 10.0424i −0.576601 0.470793i
\(456\) 2.44949 + 3.46410i 0.114708 + 0.162221i
\(457\) 6.44949 + 6.44949i 0.301694 + 0.301694i 0.841677 0.539982i \(-0.181569\pi\)
−0.539982 + 0.841677i \(0.681569\pi\)
\(458\) −16.0492 16.0492i −0.749928 0.749928i
\(459\) −10.3923 36.7423i −0.485071 1.71499i
\(460\) −2.22474 + 0.224745i −0.103729 + 0.0104788i
\(461\) 3.17837i 0.148032i 0.997257 + 0.0740158i \(0.0235815\pi\)
−0.997257 + 0.0740158i \(0.976418\pi\)
\(462\) 33.4523 + 5.73951i 1.55634 + 0.267026i
\(463\) −18.0454 + 18.0454i −0.838641 + 0.838641i −0.988680 0.150039i \(-0.952060\pi\)
0.150039 + 0.988680i \(0.452060\pi\)
\(464\) 9.12096 0.423430
\(465\) 14.3125 12.4561i 0.663725 0.577636i
\(466\) 14.8990 0.690182
\(467\) −10.5352 + 10.5352i −0.487510 + 0.487510i −0.907519 0.420010i \(-0.862027\pi\)
0.420010 + 0.907519i \(0.362027\pi\)
\(468\) 2.65029 + 5.54927i 0.122510 + 0.256515i
\(469\) 5.39388i 0.249066i
\(470\) −4.09978 + 5.02118i −0.189109 + 0.231610i
\(471\) 7.10102 5.02118i 0.327198 0.231364i
\(472\) 5.89898 + 5.89898i 0.271523 + 0.271523i
\(473\) 39.0265 + 39.0265i 1.79444 + 1.79444i
\(474\) −0.635674 + 0.449490i −0.0291975 + 0.0206457i
\(475\) 12.0000 2.44949i 0.550598 0.112390i
\(476\) 25.4558i 1.16677i
\(477\) −17.2581 36.1357i −0.790196 1.65454i
\(478\) −4.55051 + 4.55051i −0.208135 + 0.208135i
\(479\) −15.1278 −0.691205 −0.345602 0.938381i \(-0.612325\pi\)
−0.345602 + 0.938381i \(0.612325\pi\)
\(480\) −0.267949 + 3.86370i −0.0122302 + 0.176353i
\(481\) 7.10102 0.323779
\(482\) 13.3636 13.3636i 0.608695 0.608695i
\(483\) −5.91359 1.01461i −0.269078 0.0461664i
\(484\) 21.0000i 0.954545i
\(485\) 1.41421 + 13.9993i 0.0642161 + 0.635674i
\(486\) 1.00000 15.5563i 0.0453609 0.705650i
\(487\) 4.65153 + 4.65153i 0.210781 + 0.210781i 0.804599 0.593818i \(-0.202380\pi\)
−0.593818 + 0.804599i \(0.702380\pi\)
\(488\) −6.29253 6.29253i −0.284849 0.284849i
\(489\) −5.65685 8.00000i −0.255812 0.361773i
\(490\) −1.12372 11.1237i −0.0507647 0.502519i
\(491\) 11.4566i 0.517028i 0.966008 + 0.258514i \(0.0832328\pi\)
−0.966008 + 0.258514i \(0.916767\pi\)
\(492\) 2.48528 14.4853i 0.112045 0.653047i
\(493\) −47.3939 + 47.3939i −2.13451 + 2.13451i
\(494\) 5.02118 0.225914
\(495\) −32.4254 + 19.7128i −1.45741 + 0.886025i
\(496\) 4.89898 0.219971
\(497\) −15.0635 + 15.0635i −0.675692 + 0.675692i
\(498\) 0.585786 3.41421i 0.0262497 0.152995i
\(499\) 14.2020i 0.635771i −0.948129 0.317885i \(-0.897027\pi\)
0.948129 0.317885i \(-0.102973\pi\)
\(500\) 9.89949 + 5.19615i 0.442719 + 0.232379i
\(501\) 8.00000 + 11.3137i 0.357414 + 0.505459i
\(502\) −18.8990 18.8990i −0.843503 0.843503i
\(503\) 18.8776 + 18.8776i 0.841710 + 0.841710i 0.989081 0.147371i \(-0.0470812\pi\)
−0.147371 + 0.989081i \(0.547081\pi\)
\(504\) −3.46410 + 9.79796i −0.154303 + 0.436436i
\(505\) −8.89898 + 10.8990i −0.395999 + 0.484998i
\(506\) 5.65685i 0.251478i
\(507\) −15.0191 2.57686i −0.667020 0.114442i
\(508\) −8.44949 + 8.44949i −0.374885 + 0.374885i
\(509\) 42.4906 1.88336 0.941682 0.336504i \(-0.109245\pi\)
0.941682 + 0.336504i \(0.109245\pi\)
\(510\) −18.6841 21.4687i −0.827345 0.950650i
\(511\) −38.6969 −1.71185
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) −11.1097 6.21076i −0.490507 0.274212i
\(514\) 25.5959i 1.12899i
\(515\) −3.46410 + 0.349945i −0.152647 + 0.0154204i
\(516\) −13.7980 + 9.75663i −0.607421 + 0.429512i
\(517\) −11.5959 11.5959i −0.509988 0.509988i
\(518\) 8.48528 + 8.48528i 0.372822 + 0.372822i
\(519\) −21.0703 + 14.8990i −0.924885 + 0.653993i
\(520\) 3.55051 + 2.89898i 0.155700 + 0.127129i
\(521\) 42.4906i 1.86155i −0.365595 0.930774i \(-0.619134\pi\)
0.365595 0.930774i \(-0.380866\pi\)
\(522\) −24.6914 + 11.7924i −1.08071 + 0.516140i
\(523\) 2.24745 2.24745i 0.0982741 0.0982741i −0.656260 0.754534i \(-0.727863\pi\)
0.754534 + 0.656260i \(0.227863\pi\)
\(524\) −13.9993 −0.611561
\(525\) 21.8695 + 20.5359i 0.954465 + 0.896260i
\(526\) 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
\(530\) −23.1202 18.8776i −1.00428 0.819990i
\(531\) −23.5959 8.34242i −1.02398 0.362030i
\(532\) 6.00000 + 6.00000i 0.260133 + 0.260133i
\(533\) −12.2993 12.2993i −0.532743 0.532743i
\(534\) −2.19275 3.10102i −0.0948897 0.134194i
\(535\) 2.44949 0.247449i 0.105901 0.0106981i
\(536\) 1.55708i 0.0672555i
\(537\) −3.64423 + 21.2402i −0.157260 + 0.916580i
\(538\) 0.449490 0.449490i 0.0193789 0.0193789i
\(539\) 28.2843 1.21829
\(540\) −4.26999 10.8059i −0.183751 0.465011i
\(541\) −10.6969 −0.459897 −0.229949 0.973203i \(-0.573856\pi\)
−0.229949 + 0.973203i \(0.573856\pi\)
\(542\) −17.3205 + 17.3205i −0.743980 + 0.743980i
\(543\) −2.34315 + 13.6569i −0.100554 + 0.586072i
\(544\) 7.34847i 0.315063i
\(545\) 8.19955 10.0424i 0.351230 0.430167i
\(546\) 7.10102 + 10.0424i 0.303896 + 0.429773i
\(547\) 27.5959 + 27.5959i 1.17992 + 1.17992i 0.979765 + 0.200151i \(0.0641433\pi\)
0.200151 + 0.979765i \(0.435857\pi\)
\(548\) 3.28913 + 3.28913i 0.140505 + 0.140505i
\(549\) 25.1701 + 8.89898i 1.07423 + 0.379799i
\(550\) −15.5959 + 23.5959i −0.665012 + 1.00613i
\(551\) 22.3417i 0.951788i
\(552\) 1.70711 + 0.292893i 0.0726593 + 0.0124664i
\(553\) −1.10102 + 1.10102i −0.0468202 + 0.0468202i
\(554\) 6.43539 0.273414
\(555\) −13.3843 0.928203i −0.568130 0.0394000i
\(556\) −10.6969 −0.453651
\(557\) −23.9309 + 23.9309i −1.01398 + 1.01398i −0.0140828 + 0.999901i \(0.504483\pi\)
−0.999901 + 0.0140828i \(0.995517\pi\)
\(558\) −13.2621 + 6.33386i −0.561428 + 0.268134i
\(559\) 20.0000i 0.845910i
\(560\) 0.778539 + 7.70674i 0.0328993 + 0.325669i
\(561\) 58.7878 41.5692i 2.48202 1.75505i
\(562\) −4.00000 4.00000i −0.168730 0.168730i
\(563\) 1.12848 + 1.12848i 0.0475599 + 0.0475599i 0.730487 0.682927i \(-0.239293\pi\)
−0.682927 + 0.730487i \(0.739293\pi\)
\(564\) 4.09978 2.89898i 0.172632 0.122069i
\(565\) −0.752551 7.44949i −0.0316601 0.313402i
\(566\) 13.2207i 0.555709i
\(567\) −3.29002 31.0028i −0.138168 1.30200i
\(568\) 4.34847 4.34847i 0.182458 0.182458i
\(569\) −10.0424 −0.420998 −0.210499 0.977594i \(-0.567509\pi\)
−0.210499 + 0.977594i \(0.567509\pi\)
\(570\) −9.46410 0.656339i −0.396408 0.0274910i
\(571\) 26.4495 1.10688 0.553438 0.832890i \(-0.313315\pi\)
0.553438 + 0.832890i \(0.313315\pi\)
\(572\) −8.19955 + 8.19955i −0.342841 + 0.342841i
\(573\) 40.3100 + 6.91610i 1.68397 + 0.288924i
\(574\) 29.3939i 1.22688i
\(575\) 2.75699 4.17121i 0.114975 0.173951i
\(576\) 1.00000 2.82843i 0.0416667 0.117851i
\(577\) 18.7980 + 18.7980i 0.782569 + 0.782569i 0.980264 0.197694i \(-0.0633454\pi\)
−0.197694 + 0.980264i \(0.563345\pi\)
\(578\) 26.1630 + 26.1630i 1.08824 + 1.08824i
\(579\) −11.1708 15.7980i −0.464244 0.656541i
\(580\) −12.8990 + 15.7980i −0.535601 + 0.655975i
\(581\) 6.92820i 0.287430i
\(582\) 1.84304 10.7420i 0.0763964 0.445271i
\(583\) 53.3939 53.3939i 2.21135 2.21135i
\(584\) 11.1708 0.462253
\(585\) −13.3597 3.25742i −0.552355 0.134678i
\(586\) 15.1464 0.625693
\(587\) 0.142865 0.142865i 0.00589665 0.00589665i −0.704152 0.710049i \(-0.748673\pi\)
0.710049 + 0.704152i \(0.248673\pi\)
\(588\) −1.46447 + 8.53553i −0.0603936 + 0.351999i
\(589\) 12.0000i 0.494451i
\(590\) −18.5597 + 1.87492i −0.764093 + 0.0771890i
\(591\) −1.10102 1.55708i −0.0452899 0.0640496i
\(592\) −2.44949 2.44949i −0.100673 0.100673i
\(593\) 2.68556 + 2.68556i 0.110283 + 0.110283i 0.760095 0.649812i \(-0.225152\pi\)
−0.649812 + 0.760095i \(0.725152\pi\)
\(594\) 28.2843 8.00000i 1.16052 0.328244i
\(595\) −44.0908 36.0000i −1.80755 1.47586i
\(596\) 16.6848i 0.683437i
\(597\) −21.2526 3.64637i −0.869811 0.149236i
\(598\) 1.44949 1.44949i 0.0592740 0.0592740i
\(599\) −17.4634 −0.713534 −0.356767 0.934193i \(-0.616121\pi\)
−0.356767 + 0.934193i \(0.616121\pi\)
\(600\) −6.31319 5.92820i −0.257735 0.242018i
\(601\) −35.7980 −1.46023 −0.730115 0.683325i \(-0.760533\pi\)
−0.730115 + 0.683325i \(0.760533\pi\)
\(602\) −23.8988 + 23.8988i −0.974041 + 0.974041i
\(603\) 2.01314 + 4.21518i 0.0819812 + 0.171655i
\(604\) 8.89898i 0.362094i
\(605\) −36.3731 29.6985i −1.47878 1.20742i
\(606\) 8.89898 6.29253i 0.361496 0.255617i
\(607\) 7.34847 + 7.34847i 0.298265 + 0.298265i 0.840334 0.542069i \(-0.182359\pi\)
−0.542069 + 0.840334i \(0.682359\pi\)
\(608\) −1.73205 1.73205i −0.0702439 0.0702439i
\(609\) −44.6834 + 31.5959i −1.81066 + 1.28033i
\(610\) 19.7980 2.00000i 0.801596 0.0809776i
\(611\) 5.94258i 0.240411i
\(612\) 9.50079 + 19.8931i 0.384047 + 0.804131i
\(613\) −11.3485 + 11.3485i −0.458360 + 0.458360i −0.898117 0.439757i \(-0.855065\pi\)
0.439757 + 0.898117i \(0.355065\pi\)
\(614\) −9.47090 −0.382214
\(615\) 21.5745 + 24.7899i 0.869969 + 0.999626i
\(616\) −19.5959 −0.789542
\(617\) −12.7600 + 12.7600i −0.513699 + 0.513699i −0.915658 0.401958i \(-0.868330\pi\)
0.401958 + 0.915658i \(0.368330\pi\)
\(618\) 2.65810 + 0.456058i 0.106924 + 0.0183453i
\(619\) 14.0454i 0.564533i −0.959336 0.282266i \(-0.908914\pi\)
0.959336 0.282266i \(-0.0910862\pi\)
\(620\) −6.92820 + 8.48528i −0.278243 + 0.340777i
\(621\) −5.00000 + 1.41421i −0.200643 + 0.0567504i
\(622\) −24.1464 24.1464i −0.968184 0.968184i
\(623\) −5.37113 5.37113i −0.215190 0.215190i
\(624\) −2.04989 2.89898i −0.0820612 0.116052i
\(625\) −23.0000 + 9.79796i −0.920000 + 0.391918i
\(626\) 27.0771i 1.08222i
\(627\) 4.05845 23.6544i 0.162079 0.944664i
\(628\) −3.55051 + 3.55051i −0.141681 + 0.141681i
\(629\) 25.4558 1.01499
\(630\) −12.0716 19.8564i −0.480943 0.791098i
\(631\) 19.5505 0.778294 0.389147 0.921176i \(-0.372770\pi\)
0.389147 + 0.921176i \(0.372770\pi\)
\(632\) 0.317837 0.317837i 0.0126429 0.0126429i
\(633\) 3.13306 18.2608i 0.124528 0.725802i
\(634\) 9.10102i 0.361448i
\(635\) −2.68556 26.5843i −0.106573 1.05497i
\(636\) 13.3485 + 18.8776i 0.529301 + 0.748545i
\(637\) 7.24745 + 7.24745i 0.287154 + 0.287154i
\(638\) −36.4838 36.4838i −1.44441 1.44441i
\(639\) −6.14966 + 17.3939i −0.243277 + 0.688091i
\(640\) −0.224745 2.22474i −0.00888382 0.0879408i
\(641\) 13.5065i 0.533473i 0.963769 + 0.266737i \(0.0859454\pi\)
−0.963769 + 0.266737i \(0.914055\pi\)
\(642\) −1.87956 0.322481i −0.0741803 0.0127273i
\(643\) −13.1010 + 13.1010i −0.516654 + 0.516654i −0.916557 0.399903i \(-0.869044\pi\)
0.399903 + 0.916557i \(0.369044\pi\)
\(644\) 3.46410 0.136505
\(645\) 2.61428 37.6967i 0.102937 1.48431i
\(646\) 18.0000 0.708201
\(647\) −13.6493 + 13.6493i −0.536610 + 0.536610i −0.922532 0.385921i \(-0.873884\pi\)
0.385921 + 0.922532i \(0.373884\pi\)
\(648\) 0.949747 + 8.94975i 0.0373096 + 0.351579i
\(649\) 47.1918i 1.85244i
\(650\) −10.0424 + 2.04989i −0.393894 + 0.0804032i
\(651\) −24.0000 + 16.9706i −0.940634 + 0.665129i
\(652\) 4.00000 + 4.00000i 0.156652 + 0.156652i
\(653\) −9.26382 9.26382i −0.362521 0.362521i 0.502219 0.864740i \(-0.332517\pi\)
−0.864740 + 0.502219i \(0.832517\pi\)
\(654\) −8.19955 + 5.79796i −0.320628 + 0.226718i
\(655\) 19.7980 24.2474i 0.773570 0.947426i
\(656\) 8.48528i 0.331295i
\(657\) −30.2407 + 14.4427i −1.17980 + 0.563464i
\(658\) 7.10102 7.10102i 0.276827 0.276827i
\(659\) 4.09978 0.159705 0.0798523 0.996807i \(-0.474555\pi\)
0.0798523 + 0.996807i \(0.474555\pi\)
\(660\) 16.5266 14.3830i 0.643297 0.559858i
\(661\) 7.10102 0.276198 0.138099 0.990418i \(-0.455901\pi\)
0.138099 + 0.990418i \(0.455901\pi\)
\(662\) −7.56388 + 7.56388i −0.293978 + 0.293978i
\(663\) 25.7151 + 4.41201i 0.998691 + 0.171348i
\(664\) 2.00000i 0.0776151i
\(665\) −18.8776 + 1.90702i −0.732041 + 0.0739512i
\(666\) 9.79796 + 3.46410i 0.379663 + 0.134231i
\(667\) 6.44949 + 6.44949i 0.249725 + 0.249725i
\(668\) −5.65685 5.65685i −0.218870 0.218870i
\(669\) −10.6780 15.1010i −0.412837 0.583839i
\(670\) 2.69694 + 2.20204i 0.104192 + 0.0850723i
\(671\) 50.3402i 1.94336i
\(672\) 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 \(0.223942\pi\)
\(674\) −13.5065 −0.520249
\(675\) 24.7550 + 7.88599i 0.952821 + 0.303532i
\(676\) 8.79796 0.338383
\(677\) 22.6595 22.6595i 0.870876 0.870876i −0.121692 0.992568i \(-0.538832\pi\)
0.992568 + 0.121692i \(0.0388319\pi\)
\(678\) −0.980744 + 5.71619i −0.0376652 + 0.219529i
\(679\) 21.7980i 0.836529i
\(680\) 12.7279 + 10.3923i 0.488094 + 0.398527i
\(681\) 10.8990 + 15.4135i 0.417650 + 0.590646i
\(682\) −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
\(685\) −10.3485 + 1.04541i −0.395395 + 0.0399430i
\(686\) 6.92820i 0.264520i
\(687\) −38.7461 6.64778i −1.47826 0.253629i
\(688\) 6.89898 6.89898i 0.263021 0.263021i
\(689\) 27.3629 1.04244
\(690\) −2.92152 + 2.54258i −0.111220 + 0.0967944i
\(691\) −28.0000 −1.06517 −0.532585 0.846376i \(-0.678779\pi\)
−0.532585 + 0.846376i \(0.678779\pi\)
\(692\) 10.5352 10.5352i 0.400487 0.400487i
\(693\) 53.0482 25.3354i 2.01514 0.962413i
\(694\) 19.7980i 0.751520i
\(695\) 15.1278 18.5276i 0.573828 0.702793i
\(696\) 12.8990 9.12096i 0.488935 0.345729i
\(697\) −44.0908 44.0908i −1.67006 1.67006i
\(698\) 15.5563 + 15.5563i 0.588817 + 0.588817i
\(699\) 21.0703 14.8990i 0.796953 0.563531i
\(700\) −14.4495 9.55051i −0.546139 0.360975i
\(701\) 43.0621i 1.62643i 0.581962 + 0.813216i \(0.302285\pi\)
−0.581962 + 0.813216i \(0.697715\pi\)
\(702\) 9.29734 + 5.19756i 0.350905 + 0.196169i
\(703\) 6.00000 6.00000i 0.226294 0.226294i
\(704\) 5.65685 0.213201
\(705\) −0.776779 + 11.2008i −0.0292552 + 0.421846i
\(706\) −3.30306 −0.124312
\(707\) 15.4135 15.4135i 0.579684 0.579684i
\(708\) 14.2414 + 2.44344i 0.535224 + 0.0918300i
\(709\) 7.10102i 0.266684i −0.991070 0.133342i \(-0.957429\pi\)
0.991070 0.133342i \(-0.0425709\pi\)
\(710\) 1.38211 + 13.6814i 0.0518695 + 0.513455i
\(711\) −0.449490 + 1.27135i −0.0168572 + 0.0476793i
\(712\) 1.55051 + 1.55051i 0.0581078 + 0.0581078i
\(713\) 3.46410 + 3.46410i 0.129732 + 0.129732i
\(714\) 25.4558 + 36.0000i 0.952661 + 1.34727i
\(715\) −2.60612 25.7980i −0.0974635 0.964789i
\(716\) 12.4422i 0.464987i
\(717\) −1.88488 + 10.9859i −0.0703922 + 0.410276i
\(718\) −9.10102 + 9.10102i −0.339647 + 0.339647i
\(719\) −32.8769 −1.22610 −0.613050 0.790044i \(-0.710058\pi\)
−0.613050 + 0.790044i \(0.710058\pi\)
\(720\) 3.48477 + 5.73205i 0.129870 + 0.213621i
\(721\) 5.39388 0.200878
\(722\) −9.19239 + 9.19239i −0.342105 + 0.342105i
\(723\) 5.53538 32.2626i 0.205863 1.19986i
\(724\) 8.00000i 0.297318i
\(725\) −9.12096 44.6834i −0.338744 1.65950i
\(726\) 21.0000 + 29.6985i 0.779383 + 1.10221i
\(727\) −0.247449 0.247449i −0.00917736 0.00917736i 0.702503 0.711681i \(-0.252066\pi\)
−0.711681 + 0.702503i \(0.752066\pi\)
\(728\) −5.02118 5.02118i −0.186097 0.186097i
\(729\) −14.1421 23.0000i −0.523783 0.851852i
\(730\) −15.7980 + 19.3485i −0.584709 + 0.716119i
\(731\) 71.6963i 2.65178i
\(732\) −15.1915 2.60645i −0.561494 0.0963372i
\(733\) 9.14643 9.14643i 0.337831 0.337831i −0.517719 0.855550i \(-0.673219\pi\)
0.855550 + 0.517719i \(0.173219\pi\)
\(734\) −0.285729 −0.0105465
\(735\) −12.7129 14.6076i −0.468923 0.538809i
\(736\) −1.00000 −0.0368605
\(737\) −6.22831 + 6.22831i −0.229423 + 0.229423i
\(738\) −10.9706 22.9706i −0.403832 0.845558i
\(739\) 1.30306i 0.0479339i 0.999713 + 0.0239669i \(0.00762965\pi\)
−0.999713 + 0.0239669i \(0.992370\pi\)
\(740\) 7.70674 0.778539i 0.283305 0.0286197i
\(741\) 7.10102 5.02118i 0.260863 0.184458i
\(742\) 32.6969 + 32.6969i 1.20034 + 1.20034i
\(743\) 17.6062 + 17.6062i 0.645910 + 0.645910i 0.952002 0.306092i \(-0.0990215\pi\)
−0.306092 + 0.952002i \(0.599021\pi\)
\(744\) 6.92820 4.89898i 0.254000 0.179605i
\(745\) 28.8990 + 23.5959i 1.05878 + 0.864488i
\(746\) 10.6780i 0.390951i
\(747\) −2.58579 5.41421i −0.0946090 0.198096i
\(748\) −29.3939 + 29.3939i −1.07475 + 1.07475i
\(749\) −3.81405 −0.139362
\(750\) 19.1962 2.55103i 0.700944 0.0931503i
\(751\) −17.7526 −0.647800 −0.323900 0.946091i \(-0.604994\pi\)
−0.323900 + 0.946091i \(0.604994\pi\)
\(752\) −2.04989 + 2.04989i −0.0747517 + 0.0747517i
\(753\) −45.6262 7.82821i −1.66271 0.285276i
\(754\) 18.6969i 0.680902i
\(755\) 15.4135 + 12.5851i 0.560954 + 0.458017i
\(756\) 4.89898 + 17.3205i 0.178174 + 0.629941i
\(757\) −10.6515 10.6515i −0.387136 0.387136i 0.486528 0.873665i \(-0.338263\pi\)
−0.873665 + 0.486528i \(0.838263\pi\)
\(758\) 20.6096 + 20.6096i 0.748576 + 0.748576i
\(759\) −5.65685 8.00000i −0.205331 0.290382i
\(760\) 5.44949 0.550510i 0.197674 0.0199691i
\(761\) 14.4279i 0.523010i −0.965202 0.261505i \(-0.915781\pi\)
0.965202 0.261505i \(-0.0842187\pi\)
\(762\) −3.49989 + 20.3989i −0.126788 + 0.738973i
\(763\) −14.2020 + 14.2020i −0.514148 + 0.514148i
\(764\) −23.6130 −0.854290
\(765\) −47.8920 11.6772i −1.73154 0.422191i
\(766\) −22.6969 −0.820074
\(767\) 12.0922 12.0922i 0.436626 0.436626i
\(768\) −0.292893 + 1.70711i −0.0105689 + 0.0615999i
\(769\) 0.696938i 0.0251322i −0.999921 0.0125661i \(-0.996000\pi\)
0.999921 0.0125661i \(-0.00400003\pi\)
\(770\) 27.7128 33.9411i 0.998700 1.22315i
\(771\) 25.5959 + 36.1981i 0.921814 + 1.30364i
\(772\) 7.89898 + 7.89898i 0.284290 + 0.284290i
\(773\) −18.2740 18.2740i −0.657271 0.657271i 0.297463 0.954733i \(-0.403860\pi\)
−0.954733 + 0.297463i \(0.903860\pi\)
\(774\) −9.75663 + 27.5959i −0.350695 + 0.991915i
\(775\) −4.89898 24.0000i −0.175977