Properties

Label 690.2.i.c.47.3
Level $690$
Weight $2$
Character 690.47
Analytic conductor $5.510$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

Related objects

Downloads

Learn more about

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 47.3
Root \(0.258819 + 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 690.47
Dual form 690.2.i.c.323.3

$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 0.707107i 0.500000 0.500000i
\(3\) −1.70711 + 0.292893i −0.985599 + 0.169102i
\(4\) 1.00000i 0.500000i
\(5\) −1.73205 1.41421i −0.774597 0.632456i
\(6\) −1.00000 + 1.41421i −0.408248 + 0.577350i
\(7\) −2.44949 2.44949i −0.925820 0.925820i 0.0716124 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 \(0.325099\pi\)
−0.522233 + 0.852803i \(0.674901\pi\)
\(12\) 0.292893 + 1.70711i 0.0845510 + 0.492799i
\(13\) 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
\(15\) 3.37101 + 1.90691i 0.870391 + 0.492361i
\(16\) −1.00000 −0.250000
\(17\) −5.19615 + 5.19615i −1.26025 + 1.26025i −0.309282 + 0.950971i \(0.600089\pi\)
−0.950971 + 0.309282i \(0.899911\pi\)
\(18\) 1.29289 2.70711i 0.304738 0.638071i
\(19\) 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
\(27\) −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 0.879181 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 \(0.230542\pi\)
−0.748983 + 0.662589i \(0.769458\pi\)
\(42\) 5.91359 1.01461i 0.912487 0.156558i
\(43\) −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
\(45\) −6.31319 2.26795i −0.941115 0.338086i
\(46\) 1.00000 0.147442
\(47\) −2.04989 + 2.04989i −0.299007 + 0.299007i −0.840625 0.541618i \(-0.817812\pi\)
0.541618 + 0.840625i \(0.317812\pi\)
\(48\) 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 −0.930678 0.365840i \(-0.880782\pi\)
−0.365840 0.930678i \(-0.619218\pi\)
\(54\) −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 0.636646 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 \(0.118902\pi\)
−0.931041 + 0.364915i \(0.881098\pi\)
\(72\) −2.70711 1.29289i −0.319036 0.152369i
\(73\) 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
\(75\) −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 \(-0.991950\pi\)
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 0.625219 0.780449i \(-0.285010\pi\)
−0.780449 + 0.625219i \(0.785010\pi\)
\(84\) 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 0.895944 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 \(-0.898644\pi\)
0.949732 0.313065i \(-0.101356\pi\)
\(102\) −2.15232 12.5446i −0.213111 1.24210i
\(103\) −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
\(105\) −3.58630 12.9282i −0.349987 1.26166i
\(106\) −13.3485 −1.29652
\(107\) −0.778539 + 0.778539i −0.0752642 + 0.0752642i −0.743737 0.668473i \(-0.766948\pi\)
0.668473 + 0.743737i \(0.266948\pi\)
\(108\) 2.53553 + 4.53553i 0.243982 + 0.436432i
\(109\) 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 0.809650 0.586913i \(-0.199657\pi\)
−0.586913 + 0.809650i \(0.699657\pi\)
\(114\) 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 0.224665 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 \(0.209458\pi\)
−0.791197 + 0.611561i \(0.790542\pi\)
\(132\) −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 −0.552502 0.833511i \(-0.686327\pi\)
0.833511 + 0.552502i \(0.186327\pi\)
\(138\) −1.70711 + 0.292893i −0.145319 + 0.0249327i
\(139\) 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
\(147\) −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 0.551087 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
\(162\) 0.949747 8.94975i 0.0746192 0.703159i
\(163\) −4.00000 + 4.00000i −0.313304 + 0.313304i −0.846188 0.532884i \(-0.821108\pi\)
0.532884 + 0.846188i \(0.321108\pi\)
\(164\) 8.48528 0.662589
\(165\) −10.7871 + 19.0693i −0.839774 + 1.48454i
\(166\) −2.00000 −0.155230
\(167\) −5.65685 + 5.65685i −0.437741 + 0.437741i −0.891251 0.453510i \(-0.850171\pi\)
0.453510 + 0.891251i \(0.350171\pi\)
\(168\) −1.01461 5.91359i −0.0782790 0.456243i
\(169\) 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 0.182274 0.983248i \(-0.441654\pi\)
−0.983248 + 0.182274i \(0.941654\pi\)
\(174\) −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 \(0.326008\pi\)
−0.519797 + 0.854290i \(0.673992\pi\)
\(192\) −0.292893 1.70711i −0.0211377 0.123200i
\(193\) −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
\(195\) 7.65029 2.12220i 0.547848 0.151974i
\(196\) 5.00000 0.357143
\(197\) 0.778539 0.778539i 0.0554686 0.0554686i −0.678828 0.734297i \(-0.737512\pi\)
0.734297 + 0.678828i \(0.237512\pi\)
\(198\) 15.3137 + 7.31371i 1.08830 + 0.519763i
\(199\) 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
\(207\) 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 −0.913179 0.407559i \(-0.866380\pi\)
0.407559 + 0.913179i \(0.366380\pi\)
\(224\) 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 −0.914990 0.403476i \(-0.867802\pi\)
0.403476 + 0.914990i \(0.367802\pi\)
\(228\) 4.18154 0.717439i 0.276929 0.0475136i
\(229\) 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 0.962272 0.272090i \(-0.0877148\pi\)
−0.272090 + 0.962272i \(0.587715\pi\)
\(234\) −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 \(-0.680490\pi\)
0.537125 0.843503i \(-0.319510\pi\)
\(252\) −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 −0.138645 + 0.990342i \(0.544275\pi\)
−0.990342 + 0.138645i \(0.955725\pi\)
\(258\) −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 0.859669 0.510852i \(-0.170670\pi\)
−0.510852 + 0.859669i \(0.670670\pi\)
\(264\) −5.65685 + 8.00000i −0.348155 + 0.492366i
\(265\) 3.00000 + 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 0.557059 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 \(-0.946033\pi\)
0.985662 0.168730i \(-0.0539665\pi\)
\(282\) −0.849091 4.94887i −0.0505627 0.294701i
\(283\) −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
\(285\) 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 0.946981 0.321288i \(-0.104116\pi\)
−0.321288 + 0.946981i \(0.604116\pi\)
\(294\) −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 0.871899 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 \(-0.580510\pi\)
0.250241 0.968184i \(-0.419490\pi\)
\(312\) 3.49938 0.600398i 0.198113 0.0339909i
\(313\) 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
\(315\) 9.90878 + 21.0194i 0.558297 + 1.18431i
\(316\) −0.449490 −0.0252858
\(317\) 6.43539 6.43539i 0.361448 0.361448i −0.502898 0.864346i \(-0.667733\pi\)
0.864346 + 0.502898i \(0.167733\pi\)
\(318\) 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 0.917647 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
\(342\) −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 −0.223243 0.974763i \(-0.571664\pi\)
0.974763 + 0.223243i \(0.0716642\pi\)
\(348\) 2.67147 + 15.5704i 0.143206 + 0.834663i
\(349\) 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 0.642213 0.766526i \(-0.278016\pi\)
−0.766526 + 0.642213i \(0.778016\pi\)
\(354\) 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 0.712360 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
\(372\) −1.43488 8.36308i −0.0743950 0.433606i
\(373\) 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
\(375\) −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 \(-0.730738\pi\)
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 0.166045 0.986118i \(-0.446900\pi\)
−0.986118 + 0.166045i \(0.946900\pi\)
\(384\) −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 0.958867 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 \(0.120294\pi\)
−0.929436 + 0.368984i \(0.879706\pi\)
\(402\) 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 \(-0.954214\pi\)
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
\(417\) 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 \(0.0412920\pi\)
−0.991598 + 0.129359i \(0.958708\pi\)
\(432\) 4.53553 2.53553i 0.218216 0.121991i
\(433\) 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
\(435\) 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 \(-0.875298\pi\)
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 0.385272 0.922803i \(-0.374107\pi\)
−0.922803 + 0.385272i \(0.874107\pi\)
\(444\) −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 0.841677 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 \(-0.976418\pi\)
0.997257 0.0740158i \(-0.0235815\pi\)
\(462\) 5.73951 + 33.4523i 0.267026 + 1.55634i
\(463\) −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
\(465\) −16.5145 9.34190i −0.765842 0.433220i
\(466\) 14.8990 0.690182
\(467\) 10.5352 10.5352i 0.487510 0.487510i −0.420010 0.907519i \(-0.637973\pi\)
0.907519 + 0.420010i \(0.137973\pi\)
\(468\) −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 0.804599 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 \(-0.916767\pi\)
0.966008 0.258514i \(-0.0832328\pi\)
\(492\) −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 \(-0.897027\pi\)
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 0.147371 0.989081i \(-0.452919\pi\)
−0.989081 + 0.147371i \(0.952919\pi\)
\(504\) 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 \(0.380866\pi\)
−0.365595 + 0.930774i \(0.619134\pi\)
\(522\) 11.7924 24.6914i 0.516140 1.08071i
\(523\) 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
\(525\) −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 0.979765 + 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
\(552\) 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 0.0140828 0.999901i \(-0.495517\pi\)
0.999901 0.0140828i \(-0.00448286\pi\)
\(558\) −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 0.682927 0.730487i \(-0.260707\pi\)
−0.730487 + 0.682927i \(0.760707\pi\)
\(564\) −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 0.980264 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
\(582\) −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 −0.710049 0.704152i \(-0.751327\pi\)
0.704152 + 0.710049i \(0.251327\pi\)
\(588\) −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 0.649812 0.760095i \(-0.274848\pi\)
−0.760095 + 0.649812i \(0.774848\pi\)
\(594\) −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 0.840334 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
\(612\) 19.8931 + 9.50079i 0.804131 + 0.384047i
\(613\) −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
\(615\) −16.1806 + 28.6040i −0.652467 + 1.15342i
\(616\) −19.5959 −0.789542
\(617\) 12.7600 12.7600i 0.513699 0.513699i −0.401958 0.915658i \(-0.631670\pi\)
0.915658 + 0.401958i \(0.131670\pi\)
\(618\) −0.456058 2.65810i −0.0183453 0.106924i
\(619\) 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
\(627\) −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 \(-0.914055\pi\)
0.963769 0.266737i \(-0.0859454\pi\)
\(642\) −0.322481 1.87956i −0.0127273 0.0741803i
\(643\) −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
\(645\) −36.4122 + 10.1008i −1.43373 + 0.397719i
\(646\) 18.0000 0.708201
\(647\) 13.6493 13.6493i 0.536610 0.536610i −0.385921 0.922532i \(-0.626116\pi\)
0.922532 + 0.385921i \(0.126116\pi\)
\(648\) −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 0.864740 0.502219i \(-0.167483\pi\)
−0.502219 + 0.864740i \(0.667483\pi\)
\(654\) 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 −0.646918 0.762560i \(-0.723942\pi\)
0.762560 + 0.646918i \(0.223942\pi\)
\(674\) 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 −0.992568 0.121692i \(-0.961168\pi\)
0.121692 + 0.992568i \(0.461168\pi\)
\(678\) −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 0.621262 0.783603i \(-0.286620\pi\)
−0.783603 + 0.621262i \(0.786620\pi\)
\(684\) −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 \(-0.697715\pi\)
0.581962 0.813216i \(-0.302285\pi\)
\(702\) 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 \(-0.957429\pi\)
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
\(717\) 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 0.702503 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
\(732\) −2.60645 15.1915i −0.0963372 0.561494i
\(733\) 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
\(735\) −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 \(0.00762965\pi\)
−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 0.306092 0.952002i \(-0.400979\pi\)
−0.952002 + 0.306092i \(0.900979\pi\)
\(744\) −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 0.486528 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 \(0.0842187\pi\)
−0.965202 + 0.261505i \(0.915781\pi\)
\(762\) 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 \(-0.996000\pi\)
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 0.954733 0.297463i \(-0.0961404\pi\)
−0.297463 + 0.954733i \(0.596140\pi\)
\(774\) 9.75663 + 27.5959i 0.350695 + 0.991915i
\(775\)