Properties

Label 690.2.i.c.323.3
Level $690$
Weight $2$
Character 690.323
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 323.3
Root \(0.258819 - 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 690.323
Dual form 690.2.i.c.47.3

$q$-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} +(-2.22474 - 0.224745i) q^{10} -5.65685i q^{11} +(0.292893 - 1.70711i) q^{12} +(1.44949 + 1.44949i) q^{13} -3.46410 q^{14} +(3.37101 - 1.90691i) 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} +2.04989i q^{26} +(-4.53553 - 2.53553i) q^{27} +(-2.44949 - 2.44949i) q^{28} +9.12096 q^{29} +(3.73205 + 1.03528i) q^{30} -4.89898 q^{31} +(-0.707107 - 0.707107i) q^{32} +(-1.65685 + 9.65685i) 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} +(5.91359 + 1.01461i) q^{42} +(-6.89898 - 6.89898i) q^{43} +5.65685 q^{44} +(-6.31319 + 2.26795i) q^{45} +1.00000 q^{46} +(-2.04989 - 2.04989i) q^{47} +(1.70711 + 0.292893i) 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} +(0.717439 - 4.18154i) q^{57} +(6.44949 + 6.44949i) q^{58} -8.34242 q^{59} +(1.90691 + 3.37101i) q^{60} -8.89898 q^{61} +(-3.46410 - 3.46410i) q^{62} +(-9.37769 + 4.47871i) 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} +(-2.70711 + 1.29289i) q^{72} +(7.89898 + 7.89898i) q^{73} +3.46410 q^{74} +(-3.14198 + 8.07019i) q^{75} -2.44949 q^{76} +(13.8564 + 13.8564i) q^{77} +(0.600398 - 3.49938i) 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} +(-15.5704 - 2.67147i) q^{87} +(4.00000 + 4.00000i) q^{88} -2.19275 q^{89} +(-6.06778 - 2.86042i) q^{90} -7.10102 q^{91} +(0.707107 + 0.707107i) q^{92} +(8.36308 + 1.43488i) 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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(1\)

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 \(-0.977186\pi\)
0.0716124 + 0.997433i \(0.477186\pi\)
\(8\) −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 \(-0.325099\pi\)
\(12\) 0.292893 1.70711i 0.0845510 0.492799i
\(13\) 1.44949 + 1.44949i 0.402016 + 0.402016i 0.878943 0.476927i \(-0.158249\pi\)
−0.476927 + 0.878943i \(0.658249\pi\)
\(14\) −3.46410 −0.925820
\(15\) 3.37101 1.90691i 0.870391 0.492361i
\(16\) −1.00000 −0.250000
\(17\) −5.19615 5.19615i −1.26025 1.26025i −0.950971 0.309282i \(-0.899911\pi\)
−0.309282 0.950971i \(-0.600089\pi\)
\(18\) 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
\(26\) 2.04989i 0.402016i
\(27\) −4.53553 2.53553i −0.872864 0.487964i
\(28\) −2.44949 2.44949i −0.462910 0.462910i
\(29\) 9.12096 1.69372 0.846859 0.531817i \(-0.178490\pi\)
0.846859 + 0.531817i \(0.178490\pi\)
\(30\) 3.73205 + 1.03528i 0.681376 + 0.189015i
\(31\) −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
\(33\) −1.65685 + 9.65685i −0.288421 + 1.68104i
\(34\) 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 −0.476488 0.879181i \(-0.658090\pi\)
0.879181 + 0.476488i \(0.158090\pi\)
\(38\) −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 \(-0.230542\pi\)
\(42\) 5.91359 + 1.01461i 0.912487 + 0.156558i
\(43\) −6.89898 6.89898i −1.05208 1.05208i −0.998567 0.0535176i \(-0.982957\pi\)
−0.0535176 0.998567i \(-0.517043\pi\)
\(44\) 5.65685 0.852803
\(45\) −6.31319 + 2.26795i −0.941115 + 0.338086i
\(46\) 1.00000 0.147442
\(47\) −2.04989 2.04989i −0.299007 0.299007i 0.541618 0.840625i \(-0.317812\pi\)
−0.840625 + 0.541618i \(0.817812\pi\)
\(48\) 1.70711 + 0.292893i 0.246400 + 0.0422755i
\(49\) 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 −0.365840 + 0.930678i \(0.619218\pi\)
−0.930678 + 0.365840i \(0.880782\pi\)
\(54\) −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
\(58\) 6.44949 + 6.44949i 0.846859 + 0.846859i
\(59\) −8.34242 −1.08609 −0.543045 0.839704i \(-0.682729\pi\)
−0.543045 + 0.839704i \(0.682729\pi\)
\(60\) 1.90691 + 3.37101i 0.246181 + 0.435195i
\(61\) −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
\(63\) −9.37769 + 4.47871i −1.18148 + 0.564265i
\(64\) 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 −0.771157 0.636646i \(-0.780321\pi\)
0.636646 + 0.771157i \(0.280321\pi\)
\(68\) 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 \(-0.118902\pi\)
\(72\) −2.70711 + 1.29289i −0.319036 + 0.152369i
\(73\) 7.89898 + 7.89898i 0.924506 + 0.924506i 0.997344 0.0728382i \(-0.0232057\pi\)
−0.0728382 + 0.997344i \(0.523206\pi\)
\(74\) 3.46410 0.402694
\(75\) −3.14198 + 8.07019i −0.362805 + 0.931865i
\(76\) −2.44949 −0.280976
\(77\) 13.8564 + 13.8564i 1.57908 + 1.57908i
\(78\) 0.600398 3.49938i 0.0679817 0.396227i
\(79\) 0.449490i 0.0505715i 0.999680 + 0.0252858i \(0.00804957\pi\)
−0.999680 + 0.0252858i \(0.991950\pi\)
\(80\) 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 \(-0.785010\pi\)
0.625219 + 0.780449i \(0.285010\pi\)
\(84\) 3.46410 + 4.89898i 0.377964 + 0.534522i
\(85\) 16.3485 + 1.65153i 1.77324 + 0.179134i
\(86\) 9.75663i 1.05208i
\(87\) −15.5704 2.67147i −1.66933 0.286411i
\(88\) 4.00000 + 4.00000i 0.426401 + 0.426401i
\(89\) −2.19275 −0.232431 −0.116216 0.993224i \(-0.537076\pi\)
−0.116216 + 0.993224i \(0.537076\pi\)
\(90\) −6.06778 2.86042i −0.639601 0.301515i
\(91\) −7.10102 −0.744389
\(92\) 0.707107 + 0.707107i 0.0737210 + 0.0737210i
\(93\) 8.36308 + 1.43488i 0.867211 + 0.148790i
\(94\) 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 −0.444167 0.895944i \(-0.646500\pi\)
0.895944 + 0.444167i \(0.146500\pi\)
\(98\) 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 \(0.898644\pi\)
\(102\) −2.15232 + 12.5446i −0.213111 + 1.24210i
\(103\) −1.10102 1.10102i −0.108487 0.108487i 0.650780 0.759267i \(-0.274442\pi\)
−0.759267 + 0.650780i \(0.774442\pi\)
\(104\) −2.04989 −0.201008
\(105\) −3.58630 + 12.9282i −0.349987 + 1.26166i
\(106\) −13.3485 −1.29652
\(107\) −0.778539 0.778539i −0.0752642 0.0752642i 0.668473 0.743737i \(-0.266948\pi\)
−0.743737 + 0.668473i \(0.766948\pi\)
\(108\) 2.53553 4.53553i 0.243982 0.436432i
\(109\) 5.79796i 0.555344i 0.960676 + 0.277672i \(0.0895628\pi\)
−0.960676 + 0.277672i \(0.910437\pi\)
\(110\) −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 \(-0.699657\pi\)
0.809650 + 0.586913i \(0.199657\pi\)
\(114\) 3.46410 2.44949i 0.324443 0.229416i
\(115\) −0.224745 + 2.22474i −0.0209576 + 0.207459i
\(116\) 9.12096i 0.846859i
\(117\) 2.65029 + 5.54927i 0.245019 + 0.513030i
\(118\) −5.89898 5.89898i −0.543045 0.543045i
\(119\) 25.4558 2.33353
\(120\) −1.03528 + 3.73205i −0.0945074 + 0.340688i
\(121\) −21.0000 −1.90909
\(122\) −6.29253 6.29253i −0.569699 0.569699i
\(123\) −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
\(127\) −8.44949 + 8.44949i −0.749771 + 0.749771i −0.974436 0.224665i \(-0.927871\pi\)
0.224665 + 0.974436i \(0.427871\pi\)
\(128\) 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 \(-0.209458\pi\)
\(132\) −9.65685 1.65685i −0.840521 0.144211i
\(133\) −6.00000 6.00000i −0.520266 0.520266i
\(134\) −1.55708 −0.134511
\(135\) 11.4416 2.02254i 0.984733 0.174073i
\(136\) 7.34847 0.630126
\(137\) 3.28913 + 3.28913i 0.281009 + 0.281009i 0.833511 0.552502i \(-0.186327\pi\)
−0.552502 + 0.833511i \(0.686327\pi\)
\(138\) −1.70711 0.292893i −0.145319 0.0249327i
\(139\) 10.6969i 0.907302i 0.891179 + 0.453651i \(0.149879\pi\)
−0.891179 + 0.453651i \(0.850121\pi\)
\(140\) 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
\(147\) −1.46447 + 8.53553i −0.120787 + 0.703999i
\(148\) 2.44949 + 2.44949i 0.201347 + 0.201347i
\(149\) −16.6848 −1.36687 −0.683437 0.730009i \(-0.739516\pi\)
−0.683437 + 0.730009i \(0.739516\pi\)
\(150\) −7.92820 + 3.48477i −0.647335 + 0.284530i
\(151\) 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
\(153\) −9.50079 19.8931i −0.768093 1.60826i
\(154\) 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 −0.834448 0.551087i \(-0.814213\pi\)
0.551087 + 0.834448i \(0.314213\pi\)
\(158\) −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
\(162\) 0.949747 + 8.94975i 0.0746192 + 0.703159i
\(163\) −4.00000 4.00000i −0.313304 0.313304i 0.532884 0.846188i \(-0.321108\pi\)
−0.846188 + 0.532884i \(0.821108\pi\)
\(164\) 8.48528 0.662589
\(165\) −10.7871 19.0693i −0.839774 1.48454i
\(166\) −2.00000 −0.155230
\(167\) −5.65685 5.65685i −0.437741 0.437741i 0.453510 0.891251i \(-0.350171\pi\)
−0.891251 + 0.453510i \(0.850171\pi\)
\(168\) −1.01461 + 5.91359i −0.0782790 + 0.456243i
\(169\) 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 \(-0.941654\pi\)
0.182274 + 0.983248i \(0.441654\pi\)
\(174\) −9.12096 12.8990i −0.691458 0.977869i
\(175\) 9.55051 + 14.4495i 0.721951 + 1.09228i
\(176\) 5.65685i 0.426401i
\(177\) 14.2414 + 2.44344i 1.07045 + 0.183660i
\(178\) −1.55051 1.55051i −0.116216 0.116216i
\(179\) −12.4422 −0.929973 −0.464987 0.885318i \(-0.653941\pi\)
−0.464987 + 0.885318i \(0.653941\pi\)
\(180\) −2.26795 6.31319i −0.169043 0.470558i
\(181\) 8.00000 0.594635 0.297318 0.954779i \(-0.403908\pi\)
0.297318 + 0.954779i \(0.403908\pi\)
\(182\) −5.02118 5.02118i −0.372195 0.372195i
\(183\) 15.1915 + 2.60645i 1.12299 + 0.192674i
\(184\) 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 \(-0.326008\pi\)
\(192\) −0.292893 + 1.70711i −0.0211377 + 0.123200i
\(193\) −7.89898 7.89898i −0.568581 0.568581i 0.363150 0.931731i \(-0.381701\pi\)
−0.931731 + 0.363150i \(0.881701\pi\)
\(194\) 6.29253 0.451777
\(195\) 7.65029 + 2.12220i 0.547848 + 0.151974i
\(196\) 5.00000 0.357143
\(197\) 0.778539 + 0.778539i 0.0554686 + 0.0554686i 0.734297 0.678828i \(-0.237512\pi\)
−0.678828 + 0.734297i \(0.737512\pi\)
\(198\) 15.3137 7.31371i 1.08830 0.519763i
\(199\) 12.4495i 0.882521i −0.897379 0.441260i \(-0.854531\pi\)
0.897379 0.441260i \(-0.145469\pi\)
\(200\) 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
\(207\) 2.70711 1.29289i 0.188157 0.0898623i
\(208\) −1.44949 1.44949i −0.100504 0.100504i
\(209\) 13.8564 0.958468
\(210\) −11.6775 + 6.60572i −0.805825 + 0.455838i
\(211\) −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
\(213\) −1.80119 + 10.4981i −0.123416 + 0.719320i
\(214\) 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
\(222\) −5.91359 1.01461i −0.396894 0.0680963i
\(223\) −7.55051 7.55051i −0.505620 0.505620i 0.407559 0.913179i \(-0.366380\pi\)
−0.913179 + 0.407559i \(0.866380\pi\)
\(224\) 3.46410 0.231455
\(225\) 7.72741 12.8564i 0.515160 0.857094i
\(226\) 3.34847 0.222737
\(227\) −7.70674 7.70674i −0.511514 0.511514i 0.403476 0.914990i \(-0.367802\pi\)
−0.914990 + 0.403476i \(0.867802\pi\)
\(228\) 4.18154 + 0.717439i 0.276929 + 0.0475136i
\(229\) 22.6969i 1.49986i −0.661520 0.749928i \(-0.730088\pi\)
0.661520 0.749928i \(-0.269912\pi\)
\(230\) −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 \(-0.587715\pi\)
0.962272 + 0.272090i \(0.0877148\pi\)
\(234\) −2.04989 + 5.79796i −0.134005 + 0.379024i
\(235\) 6.44949 + 0.651531i 0.420718 + 0.0425012i
\(236\) 8.34242i 0.543045i
\(237\) 0.131652 0.767327i 0.00855175 0.0498432i
\(238\) 18.0000 + 18.0000i 1.16677 + 1.16677i
\(239\) −6.43539 −0.416271 −0.208135 0.978100i \(-0.566739\pi\)
−0.208135 + 0.978100i \(0.566739\pi\)
\(240\) −3.37101 + 1.90691i −0.217598 + 0.123090i
\(241\) −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
\(243\) −10.2929 11.7071i −0.660289 0.751011i
\(244\) 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 \(0.680490\pi\)
\(252\) −4.47871 9.37769i −0.282132 0.590739i
\(253\) −4.00000 4.00000i −0.251478 0.251478i
\(254\) −11.9494 −0.749771
\(255\) −27.4249 7.60770i −1.71741 0.476412i
\(256\) 1.00000 0.0625000
\(257\) −18.0990 18.0990i −1.12899 1.12899i −0.990342 0.138645i \(-0.955725\pi\)
−0.138645 0.990342i \(-0.544275\pi\)
\(258\) −2.85765 + 16.6556i −0.177910 + 1.03693i
\(259\) 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 \(-0.670670\pi\)
0.859669 + 0.510852i \(0.170670\pi\)
\(264\) −5.65685 8.00000i −0.348155 0.492366i
\(265\) 3.00000 29.6969i 0.184289 1.82427i
\(266\) 8.48528i 0.520266i
\(267\) 3.74326 + 0.642242i 0.229084 + 0.0393046i
\(268\) −1.10102 1.10102i −0.0672555 0.0672555i
\(269\) 0.635674 0.0387578 0.0193789 0.999812i \(-0.493831\pi\)
0.0193789 + 0.999812i \(0.493831\pi\)
\(270\) 9.52056 + 6.66025i 0.579403 + 0.405330i
\(271\) 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
\(273\) 12.1222 + 2.07984i 0.733669 + 0.125878i
\(274\) 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 −0.830473 0.557059i \(-0.811930\pi\)
0.557059 + 0.830473i \(0.311930\pi\)
\(278\) −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 \(0.946033\pi\)
\(282\) −0.849091 + 4.94887i −0.0505627 + 0.294701i
\(283\) −9.34847 9.34847i −0.555709 0.555709i 0.372374 0.928083i \(-0.378544\pi\)
−0.928083 + 0.372374i \(0.878544\pi\)
\(284\) 6.14966 0.364915
\(285\) 4.67095 + 8.25725i 0.276683 + 0.489117i
\(286\) 11.5959 0.685681
\(287\) 20.7846 + 20.7846i 1.22688 + 1.22688i
\(288\) −1.29289 2.70711i −0.0761845 0.159518i
\(289\) 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 \(-0.604116\pi\)
0.946981 + 0.321288i \(0.104116\pi\)
\(294\) −7.07107 + 5.00000i −0.412393 + 0.291606i
\(295\) 14.4495 11.7980i 0.841282 0.686904i
\(296\) 3.46410i 0.201347i
\(297\) −14.3431 + 25.6569i −0.832274 + 1.48876i
\(298\) −11.7980 11.7980i −0.683437 0.683437i
\(299\) 2.04989 0.118548
\(300\) −8.07019 3.14198i −0.465933 0.181403i
\(301\) 33.7980 1.94808
\(302\) 6.29253 + 6.29253i 0.362094 + 0.362094i
\(303\) 1.84304 10.7420i 0.105880 0.617113i
\(304\) 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 −0.489685 0.871899i \(-0.662888\pi\)
0.871899 + 0.489685i \(0.162888\pi\)
\(308\) −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 \(0.580510\pi\)
\(312\) 3.49938 + 0.600398i 0.198113 + 0.0339909i
\(313\) 19.1464 + 19.1464i 1.08222 + 1.08222i 0.996302 + 0.0859179i \(0.0273823\pi\)
0.0859179 + 0.996302i \(0.472618\pi\)
\(314\) −5.02118 −0.283362
\(315\) 9.90878 21.0194i 0.558297 1.18431i
\(316\) −0.449490 −0.0252858
\(317\) 6.43539 + 6.43539i 0.361448 + 0.361448i 0.864346 0.502898i \(-0.167733\pi\)
−0.502898 + 0.864346i \(0.667733\pi\)
\(318\) 22.7873 + 3.90968i 1.27785 + 0.219244i
\(319\) 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
\(327\) 1.69818 9.89774i 0.0939097 0.547346i
\(328\) 6.00000 + 6.00000i 0.331295 + 0.331295i
\(329\) 10.0424 0.553653
\(330\) 5.85641 21.1117i 0.322385 1.16216i
\(331\) 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
\(333\) 9.37769 4.47871i 0.513894 0.245432i
\(334\) 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 −0.397397 0.917647i \(-0.630086\pi\)
0.917647 + 0.397397i \(0.130086\pi\)
\(338\) 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
\(342\) −6.63103 + 3.16693i −0.358565 + 0.171248i
\(343\) −4.89898 4.89898i −0.264520 0.264520i
\(344\) 9.75663 0.526042
\(345\) 1.03528 3.73205i 0.0557374 0.200927i
\(346\) −14.8990 −0.800974
\(347\) 13.9993 + 13.9993i 0.751520 + 0.751520i 0.974763 0.223243i \(-0.0716642\pi\)
−0.223243 + 0.974763i \(0.571664\pi\)
\(348\) 2.67147 15.5704i 0.143206 0.834663i
\(349\) 22.0000i 1.17763i 0.808267 + 0.588817i \(0.200406\pi\)
−0.808267 + 0.588817i \(0.799594\pi\)
\(350\) −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 \(-0.778016\pi\)
0.642213 + 0.766526i \(0.278016\pi\)
\(354\) 8.34242 + 11.7980i 0.443394 + 0.627054i
\(355\) 8.69694 + 10.6515i 0.461586 + 0.565325i
\(356\) 2.19275i 0.116216i
\(357\) −43.4558 7.45584i −2.29993 0.394605i
\(358\) −8.79796 8.79796i −0.464987 0.464987i
\(359\) −12.8708 −0.679294 −0.339647 0.940553i \(-0.610308\pi\)
−0.339647 + 0.940553i \(0.610308\pi\)
\(360\) 2.86042 6.06778i 0.150757 0.319800i
\(361\) 13.0000 0.684211
\(362\) 5.65685 + 5.65685i 0.297318 + 0.297318i
\(363\) 35.8492 + 6.15076i 1.88160 + 0.322831i
\(364\) 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 −0.701814 0.712360i \(-0.747626\pi\)
0.712360 + 0.701814i \(0.247626\pi\)
\(368\) −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
\(372\) −1.43488 + 8.36308i −0.0743950 + 0.433606i
\(373\) 7.55051 + 7.55051i 0.390951 + 0.390951i 0.875026 0.484076i \(-0.160844\pi\)
−0.484076 + 0.875026i \(0.660844\pi\)
\(374\) −41.5692 −2.14949
\(375\) −5.97089 18.4214i −0.308336 0.951278i
\(376\) 2.89898 0.149503
\(377\) 13.2207 + 13.2207i 0.680902 + 0.680902i
\(378\) 15.7116 + 8.78335i 0.808115 + 0.451767i
\(379\) 29.1464i 1.49715i 0.663049 + 0.748576i \(0.269262\pi\)
−0.663049 + 0.748576i \(0.730738\pi\)
\(380\) 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 \(-0.946900\pi\)
0.166045 + 0.986118i \(0.446900\pi\)
\(384\) −1.41421 + 1.00000i −0.0721688 + 0.0510310i
\(385\) −43.5959 4.40408i −2.22185 0.224453i
\(386\) 11.1708i 0.568581i
\(387\) −12.6143 26.4122i −0.641220 1.34261i
\(388\) 4.44949 + 4.44949i 0.225889 + 0.225889i
\(389\) −31.1127 −1.57748 −0.788738 0.614729i \(-0.789265\pi\)
−0.788738 + 0.614729i \(0.789265\pi\)
\(390\) 3.90895 + 6.91019i 0.197937 + 0.349911i
\(391\) −7.34847 −0.371628
\(392\) 3.53553 + 3.53553i 0.178571 + 0.178571i
\(393\) −4.10029 + 23.8983i −0.206832 + 1.20551i
\(394\) 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 −0.283856 0.958867i \(-0.591614\pi\)
0.958867 + 0.283856i \(0.0916139\pi\)
\(398\) 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 \(-0.120294\pi\)
\(402\) 2.65810 + 0.456058i 0.132574 + 0.0227461i
\(403\) −7.10102 7.10102i −0.353727 0.353727i
\(404\) −6.29253 −0.313065
\(405\) −20.1244 + 0.101536i −0.999987 + 0.00504536i
\(406\) −31.5959 −1.56808
\(407\) −13.8564 13.8564i −0.686837 0.686837i
\(408\) −12.5446 2.15232i −0.621051 0.106556i
\(409\) 5.79796i 0.286691i 0.989673 + 0.143345i \(0.0457860\pi\)
−0.989673 + 0.143345i \(0.954214\pi\)
\(410\) −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
\(417\) 3.13306 18.2608i 0.153427 0.894236i
\(418\) 9.79796 + 9.79796i 0.479234 + 0.479234i
\(419\) 18.2419 0.891176 0.445588 0.895238i \(-0.352995\pi\)
0.445588 + 0.895238i \(0.352995\pi\)
\(420\) −12.9282 3.58630i −0.630832 0.174994i
\(421\) −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
\(423\) −3.74807 7.84785i −0.182237 0.381575i
\(424\) 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 \(-0.0412920\pi\)
\(432\) 4.53553 + 2.53553i 0.218216 + 0.121991i
\(433\) 14.6515 + 14.6515i 0.704108 + 0.704108i 0.965290 0.261182i \(-0.0841123\pi\)
−0.261182 + 0.965290i \(0.584112\pi\)
\(434\) 16.9706 0.814613
\(435\) 30.7468 17.3928i 1.47420 0.833922i
\(436\) −5.79796 −0.277672
\(437\) 1.73205 + 1.73205i 0.0828552 + 0.0828552i
\(438\) 3.27186 19.0698i 0.156336 0.911191i
\(439\) 16.0000i 0.763638i 0.924237 + 0.381819i \(0.124702\pi\)
−0.924237 + 0.381819i \(0.875298\pi\)
\(440\) −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 \(-0.874107\pi\)
0.385272 + 0.922803i \(0.374107\pi\)
\(444\) −3.46410 4.89898i −0.164399 0.232495i
\(445\) 3.79796 3.10102i 0.180041 0.147002i
\(446\) 10.6780i 0.505620i
\(447\) 28.4828 + 4.88687i 1.34719 + 0.231141i
\(448\) 2.44949 + 2.44949i 0.115728 + 0.115728i
\(449\) 26.4415 1.24785 0.623925 0.781484i \(-0.285537\pi\)
0.623925 + 0.781484i \(0.285537\pi\)
\(450\) 14.5550 3.62675i 0.686127 0.170967i
\(451\) −48.0000 −2.26023
\(452\) 2.36773 + 2.36773i 0.111368 + 0.111368i
\(453\) −15.1915 2.60645i −0.713759 0.122462i
\(454\) 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 −0.539982 0.841677i \(-0.681569\pi\)
0.841677 + 0.539982i \(0.181569\pi\)
\(458\) 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 \(0.976418\pi\)
\(462\) 5.73951 33.4523i 0.267026 1.55634i
\(463\) −18.0454 18.0454i −0.838641 0.838641i 0.150039 0.988680i \(-0.452060\pi\)
−0.988680 + 0.150039i \(0.952060\pi\)
\(464\) −9.12096 −0.423430
\(465\) −16.5145 + 9.34190i −0.765842 + 0.433220i
\(466\) 14.8990 0.690182
\(467\) 10.5352 + 10.5352i 0.487510 + 0.487510i 0.907519 0.420010i \(-0.137973\pi\)
−0.420010 + 0.907519i \(0.637973\pi\)
\(468\) −5.54927 + 2.65029i −0.256515 + 0.122510i
\(469\) 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
\(477\) −36.1357 + 17.2581i −1.65454 + 0.790196i
\(478\) −4.55051 4.55051i −0.208135 0.208135i
\(479\) 15.1278 0.691205 0.345602 0.938381i \(-0.387675\pi\)
0.345602 + 0.938381i \(0.387675\pi\)
\(480\) −3.73205 1.03528i −0.170344 0.0472537i
\(481\) 7.10102 0.323779
\(482\) −13.3636 13.3636i −0.608695 0.608695i
\(483\) 1.01461 5.91359i 0.0461664 0.269078i
\(484\) 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 −0.593818 0.804599i \(-0.702380\pi\)
0.804599 + 0.593818i \(0.202380\pi\)
\(488\) 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 \(0.916767\pi\)
\(492\) −14.4853 2.48528i −0.653047 0.112045i
\(493\) −47.3939 47.3939i −2.13451 2.13451i
\(494\) −5.02118 −0.225914
\(495\) 12.8295 + 35.7128i 0.576641 + 1.60517i
\(496\) 4.89898 0.219971
\(497\) 15.0635 + 15.0635i 0.675692 + 0.675692i
\(498\) 3.41421 + 0.585786i 0.152995 + 0.0262497i
\(499\) 14.2020i 0.635771i 0.948129 + 0.317885i \(0.102973\pi\)
−0.948129 + 0.317885i \(0.897027\pi\)
\(500\) −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 \(-0.952919\pi\)
0.147371 + 0.989081i \(0.452919\pi\)
\(504\) 3.46410 9.79796i 0.154303 0.436436i
\(505\) −8.89898 10.8990i −0.395999 0.484998i
\(506\) 5.65685i 0.251478i
\(507\) −2.57686 + 15.0191i −0.114442 + 0.667020i
\(508\) −8.44949 8.44949i −0.374885 0.374885i
\(509\) −42.4906 −1.88336 −0.941682 0.336504i \(-0.890755\pi\)
−0.941682 + 0.336504i \(0.890755\pi\)
\(510\) −14.0129 24.7718i −0.620500 1.09691i
\(511\) −38.6969 −1.71185
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) 6.21076 11.1097i 0.274212 0.490507i
\(514\) 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 \(-0.380866\pi\)
\(522\) 11.7924 + 24.6914i 0.516140 + 1.08071i
\(523\) 2.24745 + 2.24745i 0.0982741 + 0.0982741i 0.754534 0.656260i \(-0.227863\pi\)
−0.656260 + 0.754534i \(0.727863\pi\)
\(524\) 13.9993 0.611561
\(525\) −12.0716 27.4641i −0.526847 1.19863i
\(526\) 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
\(530\) 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
\(537\) 21.2402 + 3.64423i 0.916580 + 0.157260i
\(538\) 0.449490 + 0.449490i 0.0193789 + 0.0193789i
\(539\) −28.2843 −1.21829
\(540\) 2.02254 + 11.4416i 0.0870363 + 0.492366i
\(541\) −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
\(543\) −13.6569 2.34315i −0.586072 0.100554i
\(544\) 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 0.200151 0.979765i \(-0.435857\pi\)
0.979765 0.200151i \(-0.0641433\pi\)
\(548\) −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
\(552\) 0.292893 1.70711i 0.0124664 0.0726593i
\(553\) −1.10102 1.10102i −0.0468202 0.0468202i
\(554\) −6.43539 −0.273414
\(555\) 3.58630 12.9282i 0.152230 0.548772i
\(556\) −10.6969 −0.453651
\(557\) 23.9309 + 23.9309i 1.01398 + 1.01398i 0.999901 + 0.0140828i \(0.00448286\pi\)
0.0140828 + 0.999901i \(0.495517\pi\)
\(558\) −6.33386 13.2621i −0.268134 0.561428i
\(559\) 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 \(-0.760707\pi\)
0.682927 + 0.730487i \(0.260707\pi\)
\(564\) −4.09978 + 2.89898i −0.172632 + 0.122069i
\(565\) −0.752551 + 7.44949i −0.0316601 + 0.313402i
\(566\) 13.2207i 0.555709i
\(567\) −31.0028 + 3.29002i −1.30200 + 0.138168i
\(568\) 4.34847 + 4.34847i 0.182458 + 0.182458i
\(569\) 10.0424 0.420998 0.210499 0.977594i \(-0.432491\pi\)
0.210499 + 0.977594i \(0.432491\pi\)
\(570\) −2.53590 + 9.14162i −0.106217 + 0.382900i
\(571\) 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
\(573\) −6.91610 + 40.3100i −0.288924 + 1.68397i
\(574\) 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 −0.197694 0.980264i \(-0.563345\pi\)
0.980264 + 0.197694i \(0.0633454\pi\)
\(578\) −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
\(582\) −10.7420 1.84304i −0.445271 0.0763964i
\(583\) 53.3939 + 53.3939i 2.21135 + 2.21135i
\(584\) −11.1708 −0.462253
\(585\) −12.4383 5.86354i −0.514259 0.242428i
\(586\) 15.1464 0.625693
\(587\) −0.142865 0.142865i −0.00589665 0.00589665i 0.704152 0.710049i \(-0.251327\pi\)
−0.710049 + 0.704152i \(0.751327\pi\)
\(588\) −8.53553 1.46447i −0.351999 0.0603936i
\(589\) 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 \(-0.774848\pi\)
0.649812 + 0.760095i \(0.274848\pi\)
\(594\) −28.2843 + 8.00000i −1.16052 + 0.328244i
\(595\) −44.0908 + 36.0000i −1.80755 + 1.47586i
\(596\) 16.6848i 0.683437i
\(597\) −3.64637 + 21.2526i −0.149236 + 0.869811i
\(598\) 1.44949 + 1.44949i 0.0592740 + 0.0592740i
\(599\) 17.4634 0.713534 0.356767 0.934193i \(-0.383879\pi\)
0.356767 + 0.934193i \(0.383879\pi\)
\(600\) −3.48477 7.92820i −0.142265 0.323668i
\(601\) −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
\(603\) −4.21518 + 2.01314i −0.171655 + 0.0819812i
\(604\) 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 −0.542069 0.840334i \(-0.682359\pi\)
0.840334 + 0.542069i \(0.182359\pi\)
\(608\) 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
\(612\) 19.8931 9.50079i 0.804131 0.384047i
\(613\) −11.3485 11.3485i −0.458360 0.458360i 0.439757 0.898117i \(-0.355065\pi\)
−0.898117 + 0.439757i \(0.855065\pi\)
\(614\) 9.47090 0.382214
\(615\) −16.1806 28.6040i −0.652467 1.15342i
\(616\) −19.5959 −0.789542
\(617\) 12.7600 + 12.7600i 0.513699 + 0.513699i 0.915658 0.401958i \(-0.131670\pi\)
−0.401958 + 0.915658i \(0.631670\pi\)
\(618\) −0.456058 + 2.65810i −0.0183453 + 0.106924i
\(619\) 14.0454i 0.564533i 0.959336 + 0.282266i \(0.0910862\pi\)
−0.959336 + 0.282266i \(0.908914\pi\)
\(620\) 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
\(627\) −23.6544 4.05845i −0.944664 0.162079i
\(628\) −3.55051 3.55051i −0.141681 0.141681i
\(629\) −25.4558 −1.01499
\(630\) 21.8695 7.85641i 0.871303 0.313007i
\(631\) 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
\(633\) 18.2608 + 3.13306i 0.725802 + 0.124528i
\(634\) 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 \(0.914055\pi\)
\(642\) −0.322481 + 1.87956i −0.0127273 + 0.0741803i
\(643\) −13.1010 13.1010i −0.516654 0.516654i 0.399903 0.916557i \(-0.369044\pi\)
−0.916557 + 0.399903i \(0.869044\pi\)
\(644\) −3.46410 −0.136505
\(645\) −36.4122 10.1008i −1.43373 0.397719i
\(646\) 18.0000 0.708201
\(647\) 13.6493 + 13.6493i 0.536610 + 0.536610i 0.922532 0.385921i \(-0.126116\pi\)
−0.385921 + 0.922532i \(0.626116\pi\)
\(648\) −8.94975 + 0.949747i −0.351579 + 0.0373096i
\(649\) 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 \(-0.667483\pi\)
0.864740 + 0.502219i \(0.167483\pi\)
\(654\) 8.19955 5.79796i 0.320628 0.226718i
\(655\) 19.7980 + 24.2474i 0.773570 + 0.947426i
\(656\) 8.48528i 0.331295i
\(657\) 14.4427 + 30.2407i 0.563464 + 1.17980i
\(658\) 7.10102 + 7.10102i 0.276827 + 0.276827i
\(659\) −4.09978 −0.159705 −0.0798523 0.996807i \(-0.525445\pi\)
−0.0798523 + 0.996807i \(0.525445\pi\)
\(660\) 19.0693 10.7871i 0.742272 0.419887i
\(661\) 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
\(663\) −4.41201 + 25.7151i −0.171348 + 0.998691i
\(664\) 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
\(672\) −5.91359 1.01461i −0.228122 0.0391395i
\(673\) 3.00000 + 3.00000i 0.115642 + 0.115642i 0.762560 0.646918i \(-0.223942\pi\)
−0.646918 + 0.762560i \(0.723942\pi\)
\(674\) 13.5065 0.520249
\(675\) −16.9571 + 19.6840i −0.652678 + 0.757636i
\(676\) 8.79796 0.338383
\(677\) −22.6595 22.6595i −0.870876 0.870876i 0.121692 0.992568i \(-0.461168\pi\)
−0.992568 + 0.121692i \(0.961168\pi\)
\(678\) −5.71619 0.980744i −0.219529 0.0376652i
\(679\) 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 \(-0.786620\pi\)
0.621262 + 0.783603i \(0.286620\pi\)
\(684\) −6.92820 2.44949i −0.264906 0.0936586i
\(685\) −10.3485 1.04541i −0.395395 0.0399430i
\(686\) 6.92820i 0.264520i
\(687\) −6.64778 + 38.7461i −0.253629 + 1.47826i
\(688\) 6.89898 + 6.89898i 0.263021 + 0.263021i
\(689\) −27.3629 −1.04244
\(690\) 3.37101 1.90691i 0.128332 0.0725947i
\(691\) −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
\(693\) 25.3354 + 53.0482i 0.962413 + 2.01514i
\(694\) 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 \(0.697715\pi\)
\(702\) 5.19756 9.29734i 0.196169 0.350905i
\(703\) 6.00000 + 6.00000i 0.226294 + 0.226294i
\(704\) −5.65685 −0.213201
\(705\) −10.8191 3.00124i −0.407472 0.113033i
\(706\) −3.30306 −0.124312
\(707\) −15.4135 15.4135i −0.579684 0.579684i
\(708\) −2.44344 + 14.2414i −0.0918300 + 0.535224i
\(709\) 7.10102i 0.266684i 0.991070 + 0.133342i \(0.0425709\pi\)
−0.991070 + 0.133342i \(0.957429\pi\)
\(710\) −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
\(717\) 10.9859 + 1.88488i 0.410276 + 0.0703922i
\(718\) −9.10102 9.10102i −0.339647 0.339647i
\(719\) 32.8769 1.22610 0.613050 0.790044i \(-0.289942\pi\)
0.613050 + 0.790044i \(0.289942\pi\)
\(720\) 6.31319 2.26795i 0.235279 0.0845215i
\(721\) 5.39388 0.200878
\(722\) 9.19239 + 9.19239i 0.342105 + 0.342105i
\(723\) 32.2626 + 5.53538i 1.19986 + 0.205863i
\(724\) 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 −0.711681 0.702503i \(-0.752066\pi\)
0.702503 + 0.711681i \(0.252066\pi\)
\(728\) 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
\(732\) −2.60645 + 15.1915i −0.0963372 + 0.561494i
\(733\) 9.14643 + 9.14643i 0.337831 + 0.337831i 0.855550 0.517719i \(-0.173219\pi\)
−0.517719 + 0.855550i \(0.673219\pi\)
\(734\) 0.285729 0.0105465
\(735\) −9.53454 16.8550i −0.351687 0.621708i
\(736\) −1.00000 −0.0368605
\(737\) 6.22831 + 6.22831i 0.229423 + 0.229423i
\(738\) 22.9706 10.9706i 0.845558 0.403832i
\(739\) 1.30306i 0.0479339i −0.999713 0.0239669i \(-0.992370\pi\)
0.999713 0.0239669i \(-0.00762965\pi\)
\(740\) −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 \(-0.900979\pi\)
0.306092 + 0.952002i \(0.400979\pi\)
\(744\) −6.92820 + 4.89898i −0.254000 + 0.179605i
\(745\) 28.8990 23.5959i 1.05878 0.864488i
\(746\) 10.6780i 0.390951i
\(747\) −5.41421 + 2.58579i −0.198096 + 0.0946090i
\(748\) −29.3939 29.3939i −1.07475 1.07475i
\(749\) 3.81405 0.139362
\(750\) 8.80385 17.2480i 0.321471 0.629807i
\(751\) −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
\(753\) 7.82821 45.6262i 0.285276 1.66271i
\(754\) 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 −0.873665 0.486528i \(-0.838263\pi\)
0.486528 + 0.873665i \(0.338263\pi\)
\(758\) −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 \(-0.0842187\pi\)
\(762\) 20.3989 + 3.49989i 0.738973 + 0.126788i
\(763\) −14.2020 14.2020i −0.514148 0.514148i
\(764\) 23.6130 0.854290
\(765\) 44.5889 + 21.0197i 1.61212 + 0.759969i
\(766\) −22.6969 −0.820074
\(767\) −12.0922 12.0922i −0.436626 0.436626i
\(768\) −1.70711 0.292893i −0.0615999 0.0105689i
\(769\) 0.696938i 0.0251322i 0.999921 + 0.0125661i \(0.00400003\pi\)
−0.999921 + 0.0125661i \(0.996000\pi\)
\(770\) −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 \(-0.596140\pi\)
0.954733 + 0.297463i \(0.0961404\pi\)
\(774\) 9.75663 27.5959i 0.350695 0.991915i
\(775\) −4.89898 + 24.0000i −0.175977 + 0.862105i