Properties

Label 462.2.i.f.331.1
Level $462$
Weight $2$
Character 462.331
Analytic conductor $3.689$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.68908857338\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.1156923.1
Defining polynomial: \(x^{6} - 3 x^{5} + 12 x^{4} - 19 x^{3} + 27 x^{2} - 18 x + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 331.1
Root \(0.500000 - 0.0585812i\) of defining polynomial
Character \(\chi\) \(=\) 462.331
Dual form 462.2.i.f.67.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.37328 + 2.37860i) q^{5} +1.00000 q^{6} +(-1.37328 - 2.26144i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.37328 + 2.37860i) q^{5} +1.00000 q^{6} +(-1.37328 - 2.26144i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.37328 - 2.37860i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(-0.500000 + 0.866025i) q^{12} +5.49314 q^{13} +(2.64510 - 0.0585812i) q^{14} +2.74657 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.500000 - 0.866025i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(4.01839 - 6.96005i) q^{19} +2.74657 q^{20} +(-1.27182 + 2.32002i) q^{21} +1.00000 q^{22} +(0.645103 - 1.11735i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-1.27182 - 2.20285i) q^{25} +(-2.74657 + 4.75720i) q^{26} +1.00000 q^{27} +(-1.27182 + 2.32002i) q^{28} +4.54364 q^{29} +(-1.37328 + 2.37860i) q^{30} +(-2.54364 - 4.40571i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.500000 + 0.866025i) q^{33} +1.00000 q^{34} +(7.26496 - 0.160897i) q^{35} +1.00000 q^{36} +(2.01839 - 3.49595i) q^{37} +(4.01839 + 6.96005i) q^{38} +(-2.74657 - 4.75720i) q^{39} +(-1.37328 + 2.37860i) q^{40} +5.54364 q^{41} +(-1.37328 - 2.26144i) q^{42} -4.03677 q^{43} +(-0.500000 + 0.866025i) q^{44} +(-1.37328 - 2.37860i) q^{45} +(0.645103 + 1.11735i) q^{46} +(4.64510 - 8.04555i) q^{47} +1.00000 q^{48} +(-3.22818 + 6.21119i) q^{49} +2.54364 q^{50} +(-0.500000 + 0.866025i) q^{51} +(-2.74657 - 4.75720i) q^{52} +(-2.74657 - 4.75720i) q^{53} +(-0.500000 + 0.866025i) q^{54} +2.74657 q^{55} +(-1.37328 - 2.26144i) q^{56} -8.03677 q^{57} +(-2.27182 + 3.93491i) q^{58} +(4.76496 + 8.25314i) q^{59} +(-1.37328 - 2.37860i) q^{60} +(0.829647 - 1.43699i) q^{61} +5.08727 q^{62} +(2.64510 - 0.0585812i) q^{63} +1.00000 q^{64} +(-7.54364 + 13.0660i) q^{65} +(-0.500000 - 0.866025i) q^{66} +(-1.77182 - 3.06888i) q^{67} +(-0.500000 + 0.866025i) q^{68} -1.29021 q^{69} +(-3.49314 + 6.37208i) q^{70} +2.54364 q^{71} +(-0.500000 + 0.866025i) q^{72} +(4.29021 + 7.43085i) q^{73} +(2.01839 + 3.49595i) q^{74} +(-1.27182 + 2.20285i) q^{75} -8.03677 q^{76} +(-1.27182 + 2.32002i) q^{77} +5.49314 q^{78} +(-6.11985 + 10.5999i) q^{79} +(-1.37328 - 2.37860i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.77182 + 4.80093i) q^{82} -14.5299 q^{83} +(2.64510 - 0.0585812i) q^{84} +2.74657 q^{85} +(2.01839 - 3.49595i) q^{86} +(-2.27182 - 3.93491i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(3.25343 - 5.63511i) q^{89} +2.74657 q^{90} +(-7.54364 - 12.4224i) q^{91} -1.29021 q^{92} +(-2.54364 + 4.40571i) q^{93} +(4.64510 + 8.04555i) q^{94} +(11.0368 + 19.1163i) q^{95} +(-0.500000 + 0.866025i) q^{96} -0.0872743 q^{97} +(-3.76496 - 5.90128i) q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 3q^{2} - 3q^{3} - 3q^{4} + 6q^{6} + 6q^{8} - 3q^{9} + O(q^{10}) \) \( 6q - 3q^{2} - 3q^{3} - 3q^{4} + 6q^{6} + 6q^{8} - 3q^{9} - 3q^{11} - 3q^{12} + 3q^{14} - 3q^{16} - 3q^{17} - 3q^{18} + 3q^{19} - 3q^{21} + 6q^{22} - 9q^{23} - 3q^{24} - 3q^{25} + 6q^{27} - 3q^{28} + 18q^{29} - 6q^{31} - 3q^{32} - 3q^{33} + 6q^{34} + 6q^{35} + 6q^{36} - 9q^{37} + 3q^{38} + 24q^{41} + 18q^{43} - 3q^{44} - 9q^{46} + 15q^{47} + 6q^{48} - 24q^{49} + 6q^{50} - 3q^{51} - 3q^{54} - 6q^{57} - 9q^{58} - 9q^{59} + 6q^{61} + 12q^{62} + 3q^{63} + 6q^{64} - 36q^{65} - 3q^{66} - 6q^{67} - 3q^{68} + 18q^{69} + 12q^{70} + 6q^{71} - 3q^{72} - 9q^{74} - 3q^{75} - 6q^{76} - 3q^{77} - 12q^{79} - 3q^{81} - 12q^{82} - 12q^{83} + 3q^{84} - 9q^{86} - 9q^{87} - 3q^{88} + 36q^{89} - 36q^{91} + 18q^{92} - 6q^{93} + 15q^{94} + 24q^{95} - 3q^{96} + 18q^{97} + 15q^{98} + 6q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −1.37328 + 2.37860i −0.614151 + 1.06374i 0.376381 + 0.926465i \(0.377168\pi\)
−0.990533 + 0.137277i \(0.956165\pi\)
\(6\) 1.00000 0.408248
\(7\) −1.37328 2.26144i −0.519053 0.854742i
\(8\) 1.00000 0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −1.37328 2.37860i −0.434271 0.752179i
\(11\) −0.500000 0.866025i −0.150756 0.261116i
\(12\) −0.500000 + 0.866025i −0.144338 + 0.250000i
\(13\) 5.49314 1.52352 0.761761 0.647858i \(-0.224335\pi\)
0.761761 + 0.647858i \(0.224335\pi\)
\(14\) 2.64510 0.0585812i 0.706933 0.0156565i
\(15\) 2.74657 0.709161
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −0.500000 0.866025i −0.121268 0.210042i 0.799000 0.601331i \(-0.205363\pi\)
−0.920268 + 0.391289i \(0.872029\pi\)
\(18\) −0.500000 0.866025i −0.117851 0.204124i
\(19\) 4.01839 6.96005i 0.921881 1.59675i 0.125379 0.992109i \(-0.459985\pi\)
0.796502 0.604636i \(-0.206681\pi\)
\(20\) 2.74657 0.614151
\(21\) −1.27182 + 2.32002i −0.277534 + 0.506269i
\(22\) 1.00000 0.213201
\(23\) 0.645103 1.11735i 0.134513 0.232984i −0.790898 0.611948i \(-0.790386\pi\)
0.925411 + 0.378964i \(0.123720\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) −1.27182 2.20285i −0.254364 0.440571i
\(26\) −2.74657 + 4.75720i −0.538646 + 0.932963i
\(27\) 1.00000 0.192450
\(28\) −1.27182 + 2.32002i −0.240351 + 0.438442i
\(29\) 4.54364 0.843732 0.421866 0.906658i \(-0.361375\pi\)
0.421866 + 0.906658i \(0.361375\pi\)
\(30\) −1.37328 + 2.37860i −0.250726 + 0.434271i
\(31\) −2.54364 4.40571i −0.456851 0.791289i 0.541942 0.840416i \(-0.317689\pi\)
−0.998793 + 0.0491274i \(0.984356\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −0.500000 + 0.866025i −0.0870388 + 0.150756i
\(34\) 1.00000 0.171499
\(35\) 7.26496 0.160897i 1.22800 0.0271966i
\(36\) 1.00000 0.166667
\(37\) 2.01839 3.49595i 0.331821 0.574730i −0.651048 0.759036i \(-0.725670\pi\)
0.982869 + 0.184306i \(0.0590038\pi\)
\(38\) 4.01839 + 6.96005i 0.651868 + 1.12907i
\(39\) −2.74657 4.75720i −0.439803 0.761761i
\(40\) −1.37328 + 2.37860i −0.217135 + 0.376089i
\(41\) 5.54364 0.865771 0.432885 0.901449i \(-0.357495\pi\)
0.432885 + 0.901449i \(0.357495\pi\)
\(42\) −1.37328 2.26144i −0.211902 0.348947i
\(43\) −4.03677 −0.615602 −0.307801 0.951451i \(-0.599593\pi\)
−0.307801 + 0.951451i \(0.599593\pi\)
\(44\) −0.500000 + 0.866025i −0.0753778 + 0.130558i
\(45\) −1.37328 2.37860i −0.204717 0.354580i
\(46\) 0.645103 + 1.11735i 0.0951152 + 0.164744i
\(47\) 4.64510 8.04555i 0.677558 1.17356i −0.298156 0.954517i \(-0.596372\pi\)
0.975714 0.219048i \(-0.0702950\pi\)
\(48\) 1.00000 0.144338
\(49\) −3.22818 + 6.21119i −0.461169 + 0.887312i
\(50\) 2.54364 0.359725
\(51\) −0.500000 + 0.866025i −0.0700140 + 0.121268i
\(52\) −2.74657 4.75720i −0.380880 0.659704i
\(53\) −2.74657 4.75720i −0.377270 0.653451i 0.613394 0.789777i \(-0.289804\pi\)
−0.990664 + 0.136326i \(0.956471\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) 2.74657 0.370347
\(56\) −1.37328 2.26144i −0.183513 0.302197i
\(57\) −8.03677 −1.06450
\(58\) −2.27182 + 3.93491i −0.298304 + 0.516678i
\(59\) 4.76496 + 8.25314i 0.620344 + 1.07447i 0.989422 + 0.145069i \(0.0463405\pi\)
−0.369077 + 0.929399i \(0.620326\pi\)
\(60\) −1.37328 2.37860i −0.177290 0.307076i
\(61\) 0.829647 1.43699i 0.106225 0.183988i −0.808013 0.589165i \(-0.799457\pi\)
0.914238 + 0.405177i \(0.132790\pi\)
\(62\) 5.08727 0.646084
\(63\) 2.64510 0.0585812i 0.333252 0.00738053i
\(64\) 1.00000 0.125000
\(65\) −7.54364 + 13.0660i −0.935673 + 1.62063i
\(66\) −0.500000 0.866025i −0.0615457 0.106600i
\(67\) −1.77182 3.06888i −0.216462 0.374923i 0.737262 0.675607i \(-0.236118\pi\)
−0.953724 + 0.300684i \(0.902785\pi\)
\(68\) −0.500000 + 0.866025i −0.0606339 + 0.105021i
\(69\) −1.29021 −0.155322
\(70\) −3.49314 + 6.37208i −0.417510 + 0.761610i
\(71\) 2.54364 0.301874 0.150937 0.988543i \(-0.451771\pi\)
0.150937 + 0.988543i \(0.451771\pi\)
\(72\) −0.500000 + 0.866025i −0.0589256 + 0.102062i
\(73\) 4.29021 + 7.43085i 0.502131 + 0.869716i 0.999997 + 0.00246191i \(0.000783650\pi\)
−0.497866 + 0.867254i \(0.665883\pi\)
\(74\) 2.01839 + 3.49595i 0.234633 + 0.406396i
\(75\) −1.27182 + 2.20285i −0.146857 + 0.254364i
\(76\) −8.03677 −0.921881
\(77\) −1.27182 + 2.32002i −0.144937 + 0.264390i
\(78\) 5.49314 0.621975
\(79\) −6.11985 + 10.5999i −0.688537 + 1.19258i 0.283774 + 0.958891i \(0.408413\pi\)
−0.972311 + 0.233690i \(0.924920\pi\)
\(80\) −1.37328 2.37860i −0.153538 0.265935i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −2.77182 + 4.80093i −0.306096 + 0.530174i
\(83\) −14.5299 −1.59486 −0.797432 0.603408i \(-0.793809\pi\)
−0.797432 + 0.603408i \(0.793809\pi\)
\(84\) 2.64510 0.0585812i 0.288604 0.00639173i
\(85\) 2.74657 0.297907
\(86\) 2.01839 3.49595i 0.217648 0.376978i
\(87\) −2.27182 3.93491i −0.243565 0.421866i
\(88\) −0.500000 0.866025i −0.0533002 0.0923186i
\(89\) 3.25343 5.63511i 0.344863 0.597320i −0.640466 0.767987i \(-0.721259\pi\)
0.985329 + 0.170666i \(0.0545920\pi\)
\(90\) 2.74657 0.289514
\(91\) −7.54364 12.4224i −0.790788 1.30222i
\(92\) −1.29021 −0.134513
\(93\) −2.54364 + 4.40571i −0.263763 + 0.456851i
\(94\) 4.64510 + 8.04555i 0.479106 + 0.829836i
\(95\) 11.0368 + 19.1163i 1.13235 + 1.96129i
\(96\) −0.500000 + 0.866025i −0.0510310 + 0.0883883i
\(97\) −0.0872743 −0.00886136 −0.00443068 0.999990i \(-0.501410\pi\)
−0.00443068 + 0.999990i \(0.501410\pi\)
\(98\) −3.76496 5.90128i −0.380318 0.596119i
\(99\) 1.00000 0.100504
\(100\) −1.27182 + 2.20285i −0.127182 + 0.220285i
\(101\) −6.51152 11.2783i −0.647921 1.12223i −0.983619 0.180262i \(-0.942305\pi\)
0.335698 0.941970i \(-0.391028\pi\)
\(102\) −0.500000 0.866025i −0.0495074 0.0857493i
\(103\) 9.03677 15.6522i 0.890420 1.54225i 0.0510469 0.998696i \(-0.483744\pi\)
0.839373 0.543556i \(-0.182922\pi\)
\(104\) 5.49314 0.538646
\(105\) −3.77182 6.21119i −0.368092 0.606150i
\(106\) 5.49314 0.533541
\(107\) −8.72132 + 15.1058i −0.843122 + 1.46033i 0.0441209 + 0.999026i \(0.485951\pi\)
−0.887243 + 0.461303i \(0.847382\pi\)
\(108\) −0.500000 0.866025i −0.0481125 0.0833333i
\(109\) −0.829647 1.43699i −0.0794658 0.137639i 0.823554 0.567238i \(-0.191988\pi\)
−0.903020 + 0.429599i \(0.858655\pi\)
\(110\) −1.37328 + 2.37860i −0.130938 + 0.226790i
\(111\) −4.03677 −0.383154
\(112\) 2.64510 0.0585812i 0.249939 0.00553540i
\(113\) −7.08727 −0.666715 −0.333357 0.942801i \(-0.608182\pi\)
−0.333357 + 0.942801i \(0.608182\pi\)
\(114\) 4.01839 6.96005i 0.376356 0.651868i
\(115\) 1.77182 + 3.06888i 0.165223 + 0.286175i
\(116\) −2.27182 3.93491i −0.210933 0.365347i
\(117\) −2.74657 + 4.75720i −0.253920 + 0.439803i
\(118\) −9.52991 −0.877299
\(119\) −1.27182 + 2.32002i −0.116587 + 0.212676i
\(120\) 2.74657 0.250726
\(121\) −0.500000 + 0.866025i −0.0454545 + 0.0787296i
\(122\) 0.829647 + 1.43699i 0.0751127 + 0.130099i
\(123\) −2.77182 4.80093i −0.249926 0.432885i
\(124\) −2.54364 + 4.40571i −0.228425 + 0.395644i
\(125\) −6.74657 −0.603431
\(126\) −1.27182 + 2.32002i −0.113303 + 0.206684i
\(127\) −6.78334 −0.601924 −0.300962 0.953636i \(-0.597308\pi\)
−0.300962 + 0.953636i \(0.597308\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 2.01839 + 3.49595i 0.177709 + 0.307801i
\(130\) −7.54364 13.0660i −0.661621 1.14596i
\(131\) 6.94950 12.0369i 0.607181 1.05167i −0.384522 0.923116i \(-0.625634\pi\)
0.991703 0.128552i \(-0.0410329\pi\)
\(132\) 1.00000 0.0870388
\(133\) −21.2581 + 0.470804i −1.84331 + 0.0408238i
\(134\) 3.54364 0.306124
\(135\) −1.37328 + 2.37860i −0.118193 + 0.204717i
\(136\) −0.500000 0.866025i −0.0428746 0.0742611i
\(137\) −2.74657 4.75720i −0.234655 0.406435i 0.724517 0.689257i \(-0.242063\pi\)
−0.959172 + 0.282822i \(0.908729\pi\)
\(138\) 0.645103 1.11735i 0.0549148 0.0951152i
\(139\) 13.6309 1.15616 0.578079 0.815981i \(-0.303802\pi\)
0.578079 + 0.815981i \(0.303802\pi\)
\(140\) −3.77182 6.21119i −0.318777 0.524941i
\(141\) −9.29021 −0.782376
\(142\) −1.27182 + 2.20285i −0.106729 + 0.184859i
\(143\) −2.74657 4.75720i −0.229680 0.397817i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) −6.23970 + 10.8075i −0.518179 + 0.897513i
\(146\) −8.58041 −0.710120
\(147\) 6.99314 0.309906i 0.576784 0.0255606i
\(148\) −4.03677 −0.331821
\(149\) −8.01839 + 13.8883i −0.656892 + 1.13777i 0.324524 + 0.945877i \(0.394796\pi\)
−0.981416 + 0.191893i \(0.938537\pi\)
\(150\) −1.27182 2.20285i −0.103844 0.179862i
\(151\) 2.84803 + 4.93294i 0.231770 + 0.401437i 0.958329 0.285667i \(-0.0922151\pi\)
−0.726559 + 0.687104i \(0.758882\pi\)
\(152\) 4.01839 6.96005i 0.325934 0.564535i
\(153\) 1.00000 0.0808452
\(154\) −1.37328 2.26144i −0.110662 0.182232i
\(155\) 13.9725 1.12230
\(156\) −2.74657 + 4.75720i −0.219901 + 0.380880i
\(157\) −9.05516 15.6840i −0.722680 1.25172i −0.959922 0.280269i \(-0.909576\pi\)
0.237241 0.971451i \(-0.423757\pi\)
\(158\) −6.11985 10.5999i −0.486869 0.843282i
\(159\) −2.74657 + 4.75720i −0.217817 + 0.377270i
\(160\) 2.74657 0.217135
\(161\) −3.41273 + 0.0755817i −0.268960 + 0.00595668i
\(162\) 1.00000 0.0785674
\(163\) 6.72132 11.6417i 0.526454 0.911846i −0.473071 0.881024i \(-0.656854\pi\)
0.999525 0.0308210i \(-0.00981219\pi\)
\(164\) −2.77182 4.80093i −0.216443 0.374890i
\(165\) −1.37328 2.37860i −0.106910 0.185174i
\(166\) 7.26496 12.5833i 0.563870 0.976651i
\(167\) 23.5667 1.82364 0.911822 0.410585i \(-0.134675\pi\)
0.911822 + 0.410585i \(0.134675\pi\)
\(168\) −1.27182 + 2.32002i −0.0981229 + 0.178993i
\(169\) 17.1745 1.32112
\(170\) −1.37328 + 2.37860i −0.105326 + 0.182430i
\(171\) 4.01839 + 6.96005i 0.307294 + 0.532248i
\(172\) 2.01839 + 3.49595i 0.153901 + 0.266564i
\(173\) 5.45636 9.45070i 0.414840 0.718523i −0.580572 0.814209i \(-0.697171\pi\)
0.995412 + 0.0956857i \(0.0305044\pi\)
\(174\) 4.54364 0.344452
\(175\) −3.23504 + 5.90128i −0.244546 + 0.446095i
\(176\) 1.00000 0.0753778
\(177\) 4.76496 8.25314i 0.358156 0.620344i
\(178\) 3.25343 + 5.63511i 0.243855 + 0.422369i
\(179\) 6.47475 + 11.2146i 0.483946 + 0.838218i 0.999830 0.0184400i \(-0.00586995\pi\)
−0.515884 + 0.856658i \(0.672537\pi\)
\(180\) −1.37328 + 2.37860i −0.102359 + 0.177290i
\(181\) 7.59414 0.564468 0.282234 0.959346i \(-0.408925\pi\)
0.282234 + 0.959346i \(0.408925\pi\)
\(182\) 14.5299 0.321794i 1.07703 0.0238530i
\(183\) −1.65929 −0.122659
\(184\) 0.645103 1.11735i 0.0475576 0.0823722i
\(185\) 5.54364 + 9.60186i 0.407576 + 0.705943i
\(186\) −2.54364 4.40571i −0.186509 0.323042i
\(187\) −0.500000 + 0.866025i −0.0365636 + 0.0633300i
\(188\) −9.29021 −0.677558
\(189\) −1.37328 2.26144i −0.0998917 0.164495i
\(190\) −22.0735 −1.60138
\(191\) −9.49314 + 16.4426i −0.686899 + 1.18974i 0.285937 + 0.958249i \(0.407695\pi\)
−0.972836 + 0.231496i \(0.925638\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) 10.7833 + 18.6773i 0.776202 + 1.34442i 0.934116 + 0.356968i \(0.116190\pi\)
−0.157915 + 0.987453i \(0.550477\pi\)
\(194\) 0.0436371 0.0755817i 0.00313296 0.00542645i
\(195\) 15.0873 1.08042
\(196\) 6.99314 0.309906i 0.499510 0.0221362i
\(197\) −3.12405 −0.222579 −0.111290 0.993788i \(-0.535498\pi\)
−0.111290 + 0.993788i \(0.535498\pi\)
\(198\) −0.500000 + 0.866025i −0.0355335 + 0.0615457i
\(199\) 13.0368 + 22.5804i 0.924152 + 1.60068i 0.792919 + 0.609327i \(0.208560\pi\)
0.131234 + 0.991351i \(0.458106\pi\)
\(200\) −1.27182 2.20285i −0.0899312 0.155765i
\(201\) −1.77182 + 3.06888i −0.124974 + 0.216462i
\(202\) 13.0230 0.916298
\(203\) −6.23970 10.2751i −0.437941 0.721174i
\(204\) 1.00000 0.0700140
\(205\) −7.61299 + 13.1861i −0.531714 + 0.920956i
\(206\) 9.03677 + 15.6522i 0.629622 + 1.09054i
\(207\) 0.645103 + 1.11735i 0.0448377 + 0.0776612i
\(208\) −2.74657 + 4.75720i −0.190440 + 0.329852i
\(209\) −8.03677 −0.555915
\(210\) 7.26496 0.160897i 0.501330 0.0111030i
\(211\) 15.6677 1.07861 0.539304 0.842111i \(-0.318687\pi\)
0.539304 + 0.842111i \(0.318687\pi\)
\(212\) −2.74657 + 4.75720i −0.188635 + 0.326726i
\(213\) −1.27182 2.20285i −0.0871436 0.150937i
\(214\) −8.72132 15.1058i −0.596177 1.03261i
\(215\) 5.54364 9.60186i 0.378073 0.654841i
\(216\) 1.00000 0.0680414
\(217\) −6.47009 + 11.8026i −0.439218 + 0.801210i
\(218\) 1.65929 0.112382
\(219\) 4.29021 7.43085i 0.289905 0.502131i
\(220\) −1.37328 2.37860i −0.0925868 0.160365i
\(221\) −2.74657 4.75720i −0.184754 0.320004i
\(222\) 2.01839 3.49595i 0.135465 0.234633i
\(223\) 2.40586 0.161108 0.0805542 0.996750i \(-0.474331\pi\)
0.0805542 + 0.996750i \(0.474331\pi\)
\(224\) −1.27182 + 2.32002i −0.0849770 + 0.155013i
\(225\) 2.54364 0.169576
\(226\) 3.54364 6.13776i 0.235719 0.408278i
\(227\) −1.22818 2.12727i −0.0815173 0.141192i 0.822385 0.568932i \(-0.192643\pi\)
−0.903902 + 0.427740i \(0.859310\pi\)
\(228\) 4.01839 + 6.96005i 0.266124 + 0.460941i
\(229\) 5.29021 9.16290i 0.349587 0.605502i −0.636589 0.771203i \(-0.719655\pi\)
0.986176 + 0.165701i \(0.0529887\pi\)
\(230\) −3.54364 −0.233661
\(231\) 2.64510 0.0585812i 0.174035 0.00385436i
\(232\) 4.54364 0.298304
\(233\) 3.53677 6.12587i 0.231702 0.401319i −0.726607 0.687053i \(-0.758904\pi\)
0.958309 + 0.285734i \(0.0922373\pi\)
\(234\) −2.74657 4.75720i −0.179549 0.310988i
\(235\) 12.7581 + 22.0977i 0.832246 + 1.44149i
\(236\) 4.76496 8.25314i 0.310172 0.537234i
\(237\) 12.2397 0.795054
\(238\) −1.37328 2.26144i −0.0890168 0.146587i
\(239\) 7.66769 0.495981 0.247991 0.968762i \(-0.420230\pi\)
0.247991 + 0.968762i \(0.420230\pi\)
\(240\) −1.37328 + 2.37860i −0.0886451 + 0.153538i
\(241\) 12.5299 + 21.7024i 0.807122 + 1.39798i 0.914849 + 0.403797i \(0.132310\pi\)
−0.107726 + 0.994181i \(0.534357\pi\)
\(242\) −0.500000 0.866025i −0.0321412 0.0556702i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) −1.65929 −0.106225
\(245\) −10.3407 16.2083i −0.660643 1.03551i
\(246\) 5.54364 0.353449
\(247\) 22.0735 38.2325i 1.40451 2.43268i
\(248\) −2.54364 4.40571i −0.161521 0.279763i
\(249\) 7.26496 + 12.5833i 0.460398 + 0.797432i
\(250\) 3.37328 5.84270i 0.213345 0.369525i
\(251\) −25.0230 −1.57944 −0.789720 0.613467i \(-0.789774\pi\)
−0.789720 + 0.613467i \(0.789774\pi\)
\(252\) −1.37328 2.26144i −0.0865088 0.142457i
\(253\) −1.29021 −0.0811145
\(254\) 3.39167 5.87455i 0.212812 0.368602i
\(255\) −1.37328 2.37860i −0.0859984 0.148954i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 5.25343 9.09921i 0.327700 0.567593i −0.654355 0.756187i \(-0.727060\pi\)
0.982055 + 0.188594i \(0.0603931\pi\)
\(258\) −4.03677 −0.251319
\(259\) −10.6777 + 0.236479i −0.663479 + 0.0146941i
\(260\) 15.0873 0.935673
\(261\) −2.27182 + 3.93491i −0.140622 + 0.243565i
\(262\) 6.94950 + 12.0369i 0.429342 + 0.743641i
\(263\) −11.8201 20.4730i −0.728860 1.26242i −0.957366 0.288879i \(-0.906717\pi\)
0.228506 0.973543i \(-0.426616\pi\)
\(264\) −0.500000 + 0.866025i −0.0307729 + 0.0533002i
\(265\) 15.0873 0.926804
\(266\) 10.2213 18.6454i 0.626709 1.14323i
\(267\) −6.50686 −0.398214
\(268\) −1.77182 + 3.06888i −0.108231 + 0.187462i
\(269\) 7.57622 + 13.1224i 0.461930 + 0.800086i 0.999057 0.0434151i \(-0.0138238\pi\)
−0.537127 + 0.843501i \(0.680490\pi\)
\(270\) −1.37328 2.37860i −0.0835754 0.144757i
\(271\) −9.49314 + 16.4426i −0.576667 + 0.998816i 0.419191 + 0.907898i \(0.362314\pi\)
−0.995858 + 0.0909186i \(0.971020\pi\)
\(272\) 1.00000 0.0606339
\(273\) −6.98627 + 12.7442i −0.422828 + 0.771312i
\(274\) 5.49314 0.331853
\(275\) −1.27182 + 2.20285i −0.0766935 + 0.132837i
\(276\) 0.645103 + 1.11735i 0.0388306 + 0.0672566i
\(277\) −12.2397 21.1998i −0.735413 1.27377i −0.954542 0.298076i \(-0.903655\pi\)
0.219130 0.975696i \(-0.429678\pi\)
\(278\) −6.81546 + 11.8047i −0.408764 + 0.708000i
\(279\) 5.08727 0.304567
\(280\) 7.26496 0.160897i 0.434164 0.00961545i
\(281\) −12.0873 −0.721066 −0.360533 0.932746i \(-0.617405\pi\)
−0.360533 + 0.932746i \(0.617405\pi\)
\(282\) 4.64510 8.04555i 0.276612 0.479106i
\(283\) −2.34071 4.05422i −0.139141 0.240998i 0.788031 0.615636i \(-0.211101\pi\)
−0.927172 + 0.374637i \(0.877767\pi\)
\(284\) −1.27182 2.20285i −0.0754685 0.130715i
\(285\) 11.0368 19.1163i 0.653762 1.13235i
\(286\) 5.49314 0.324816
\(287\) −7.61299 12.5366i −0.449381 0.740011i
\(288\) 1.00000 0.0589256
\(289\) 8.00000 13.8564i 0.470588 0.815083i
\(290\) −6.23970 10.8075i −0.366408 0.634637i
\(291\) 0.0436371 + 0.0755817i 0.00255805 + 0.00443068i
\(292\) 4.29021 7.43085i 0.251065 0.434858i
\(293\) −11.6309 −0.679485 −0.339743 0.940518i \(-0.610340\pi\)
−0.339743 + 0.940518i \(0.610340\pi\)
\(294\) −3.22818 + 6.21119i −0.188271 + 0.362244i
\(295\) −26.1745 −1.52394
\(296\) 2.01839 3.49595i 0.117316 0.203198i
\(297\) −0.500000 0.866025i −0.0290129 0.0502519i
\(298\) −8.01839 13.8883i −0.464493 0.804525i
\(299\) 3.54364 6.13776i 0.204934 0.354956i
\(300\) 2.54364 0.146857
\(301\) 5.54364 + 9.12890i 0.319530 + 0.526181i
\(302\) −5.69607 −0.327772
\(303\) −6.51152 + 11.2783i −0.374077 + 0.647921i
\(304\) 4.01839 + 6.96005i 0.230470 + 0.399186i
\(305\) 2.27868 + 3.94679i 0.130477 + 0.225993i
\(306\) −0.500000 + 0.866025i −0.0285831 + 0.0495074i
\(307\) −14.0735 −0.803220 −0.401610 0.915811i \(-0.631549\pi\)
−0.401610 + 0.915811i \(0.631549\pi\)
\(308\) 2.64510 0.0585812i 0.150719 0.00333797i
\(309\) −18.0735 −1.02817
\(310\) −6.98627 + 12.1006i −0.396794 + 0.687267i
\(311\) −6.13824 10.6317i −0.348068 0.602871i 0.637839 0.770170i \(-0.279829\pi\)
−0.985906 + 0.167299i \(0.946495\pi\)
\(312\) −2.74657 4.75720i −0.155494 0.269323i
\(313\) −11.7282 + 20.3138i −0.662916 + 1.14820i 0.316930 + 0.948449i \(0.397348\pi\)
−0.979846 + 0.199755i \(0.935985\pi\)
\(314\) 18.1103 1.02202
\(315\) −3.49314 + 6.37208i −0.196816 + 0.359026i
\(316\) 12.2397 0.688537
\(317\) 0.286010 0.495384i 0.0160639 0.0278235i −0.857882 0.513847i \(-0.828220\pi\)
0.873946 + 0.486024i \(0.161553\pi\)
\(318\) −2.74657 4.75720i −0.154020 0.266770i
\(319\) −2.27182 3.93491i −0.127197 0.220312i
\(320\) −1.37328 + 2.37860i −0.0767689 + 0.132968i
\(321\) 17.4426 0.973553
\(322\) 1.64091 2.99330i 0.0914442 0.166810i
\(323\) −8.03677 −0.447178
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) −6.98627 12.1006i −0.387529 0.671219i
\(326\) 6.72132 + 11.6417i 0.372259 + 0.644772i
\(327\) −0.829647 + 1.43699i −0.0458796 + 0.0794658i
\(328\) 5.54364 0.306096
\(329\) −24.5735 + 0.544231i −1.35478 + 0.0300044i
\(330\) 2.74657 0.151194
\(331\) −3.85909 + 6.68414i −0.212115 + 0.367394i −0.952376 0.304925i \(-0.901368\pi\)
0.740261 + 0.672319i \(0.234702\pi\)
\(332\) 7.26496 + 12.5833i 0.398716 + 0.690597i
\(333\) 2.01839 + 3.49595i 0.110607 + 0.191577i
\(334\) −11.7833 + 20.4093i −0.644756 + 1.11675i
\(335\) 9.73284 0.531762
\(336\) −1.37328 2.26144i −0.0749188 0.123371i
\(337\) 28.5530 1.55538 0.777689 0.628649i \(-0.216392\pi\)
0.777689 + 0.628649i \(0.216392\pi\)
\(338\) −8.58727 + 14.8736i −0.467086 + 0.809017i
\(339\) 3.54364 + 6.13776i 0.192464 + 0.333357i
\(340\) −1.37328 2.37860i −0.0744768 0.128998i
\(341\) −2.54364 + 4.40571i −0.137746 + 0.238583i
\(342\) −8.03677 −0.434579
\(343\) 18.4794 1.22940i 0.997794 0.0663814i
\(344\) −4.03677 −0.217648
\(345\) 1.77182 3.06888i 0.0953915 0.165223i
\(346\) 5.45636 + 9.45070i 0.293336 + 0.508073i
\(347\) 11.7213 + 20.3019i 0.629233 + 1.08986i 0.987706 + 0.156324i \(0.0499643\pi\)
−0.358473 + 0.933540i \(0.616702\pi\)
\(348\) −2.27182 + 3.93491i −0.121782 + 0.210933i
\(349\) 25.7328 1.37745 0.688724 0.725024i \(-0.258171\pi\)
0.688724 + 0.725024i \(0.258171\pi\)
\(350\) −3.49314 5.75227i −0.186716 0.307472i
\(351\) 5.49314 0.293202
\(352\) −0.500000 + 0.866025i −0.0266501 + 0.0461593i
\(353\) 9.20293 + 15.9399i 0.489823 + 0.848398i 0.999931 0.0117122i \(-0.00372821\pi\)
−0.510109 + 0.860110i \(0.670395\pi\)
\(354\) 4.76496 + 8.25314i 0.253255 + 0.438650i
\(355\) −3.49314 + 6.05029i −0.185396 + 0.321116i
\(356\) −6.50686 −0.344863
\(357\) 2.64510 0.0585812i 0.139994 0.00310044i
\(358\) −12.9495 −0.684402
\(359\) 15.9863 27.6890i 0.843723 1.46137i −0.0430022 0.999075i \(-0.513692\pi\)
0.886725 0.462297i \(-0.152974\pi\)
\(360\) −1.37328 2.37860i −0.0723784 0.125363i
\(361\) −22.7949 39.4819i −1.19973 2.07799i
\(362\) −3.79707 + 6.57672i −0.199570 + 0.345665i
\(363\) 1.00000 0.0524864
\(364\) −6.98627 + 12.7442i −0.366180 + 0.667976i
\(365\) −23.5667 −1.23354
\(366\) 0.829647 1.43699i 0.0433663 0.0751127i
\(367\) −18.2397 31.5921i −0.952105 1.64909i −0.740859 0.671661i \(-0.765581\pi\)
−0.211246 0.977433i \(-0.567752\pi\)
\(368\) 0.645103 + 1.11735i 0.0336283 + 0.0582459i
\(369\) −2.77182 + 4.80093i −0.144295 + 0.249926i
\(370\) −11.0873 −0.576400
\(371\) −6.98627 + 12.7442i −0.362709 + 0.661644i
\(372\) 5.08727 0.263763
\(373\) 10.1566 17.5918i 0.525890 0.910868i −0.473655 0.880710i \(-0.657066\pi\)
0.999545 0.0301580i \(-0.00960104\pi\)
\(374\) −0.500000 0.866025i −0.0258544 0.0447811i
\(375\) 3.37328 + 5.84270i 0.174196 + 0.301716i
\(376\) 4.64510 8.04555i 0.239553 0.414918i
\(377\) 24.9588 1.28544
\(378\) 2.64510 0.0585812i 0.136049 0.00301309i
\(379\) 9.44264 0.485036 0.242518 0.970147i \(-0.422027\pi\)
0.242518 + 0.970147i \(0.422027\pi\)
\(380\) 11.0368 19.1163i 0.566175 0.980643i
\(381\) 3.39167 + 5.87455i 0.173761 + 0.300962i
\(382\) −9.49314 16.4426i −0.485711 0.841276i
\(383\) −11.8522 + 20.5287i −0.605621 + 1.04897i 0.386332 + 0.922360i \(0.373742\pi\)
−0.991953 + 0.126606i \(0.959592\pi\)
\(384\) 1.00000 0.0510310
\(385\) −3.77182 6.21119i −0.192230 0.316551i
\(386\) −21.5667 −1.09772
\(387\) 2.01839 3.49595i 0.102600 0.177709i
\(388\) 0.0436371 + 0.0755817i 0.00221534 + 0.00383708i
\(389\) 0.626716 + 1.08550i 0.0317758 + 0.0550372i 0.881476 0.472229i \(-0.156550\pi\)
−0.849700 + 0.527266i \(0.823217\pi\)
\(390\) −7.54364 + 13.0660i −0.381987 + 0.661621i
\(391\) −1.29021 −0.0652485
\(392\) −3.22818 + 6.21119i −0.163048 + 0.313712i
\(393\) −13.8990 −0.701112
\(394\) 1.56202 2.70550i 0.0786936 0.136301i
\(395\) −16.8086 29.1133i −0.845732 1.46485i
\(396\) −0.500000 0.866025i −0.0251259 0.0435194i
\(397\) −14.3086 + 24.7832i −0.718128 + 1.24383i 0.243613 + 0.969872i \(0.421667\pi\)
−0.961741 + 0.273961i \(0.911666\pi\)
\(398\) −26.0735 −1.30695
\(399\) 11.0368 + 18.1746i 0.552530 + 0.909870i
\(400\) 2.54364 0.127182
\(401\) −0.202931 + 0.351487i −0.0101339 + 0.0175524i −0.871048 0.491198i \(-0.836559\pi\)
0.860914 + 0.508751i \(0.169892\pi\)
\(402\) −1.77182 3.06888i −0.0883703 0.153062i
\(403\) −13.9725 24.2012i −0.696022 1.20555i
\(404\) −6.51152 + 11.2783i −0.323960 + 0.561116i
\(405\) 2.74657 0.136478
\(406\) 12.0184 0.266172i 0.596463 0.0132099i
\(407\) −4.03677 −0.200095
\(408\) −0.500000 + 0.866025i −0.0247537 + 0.0428746i
\(409\) 16.3775 + 28.3666i 0.809814 + 1.40264i 0.912992 + 0.407977i \(0.133765\pi\)
−0.103178 + 0.994663i \(0.532901\pi\)
\(410\) −7.61299 13.1861i −0.375979 0.651214i
\(411\) −2.74657 + 4.75720i −0.135478 + 0.234655i
\(412\) −18.0735 −0.890420
\(413\) 12.1203 22.1096i 0.596402 1.08794i
\(414\) −1.29021 −0.0634101
\(415\) 19.9537 34.5608i 0.979488 1.69652i
\(416\) −2.74657 4.75720i −0.134662 0.233241i
\(417\) −6.81546 11.8047i −0.333754 0.578079i
\(418\) 4.01839 6.96005i 0.196546 0.340427i
\(419\) −15.9358 −0.778513 −0.389257 0.921129i \(-0.627268\pi\)
−0.389257 + 0.921129i \(0.627268\pi\)
\(420\) −3.49314 + 6.37208i −0.170448 + 0.310926i
\(421\) −27.1240 −1.32195 −0.660973 0.750410i \(-0.729856\pi\)
−0.660973 + 0.750410i \(0.729856\pi\)
\(422\) −7.83384 + 13.5686i −0.381345 + 0.660510i
\(423\) 4.64510 + 8.04555i 0.225853 + 0.391188i
\(424\) −2.74657 4.75720i −0.133385 0.231030i
\(425\) −1.27182 + 2.20285i −0.0616923 + 0.106854i
\(426\) 2.54364 0.123240
\(427\) −4.38900 + 0.0972034i −0.212399 + 0.00470400i
\(428\) 17.4426 0.843122
\(429\) −2.74657 + 4.75720i −0.132606 + 0.229680i
\(430\) 5.54364 + 9.60186i 0.267338 + 0.463043i
\(431\) 20.3133 + 35.1836i 0.978455 + 1.69473i 0.668028 + 0.744137i \(0.267139\pi\)
0.310427 + 0.950597i \(0.399528\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) 1.10100 0.0529107 0.0264554 0.999650i \(-0.491578\pi\)
0.0264554 + 0.999650i \(0.491578\pi\)
\(434\) −6.98627 11.5045i −0.335352 0.552236i
\(435\) 12.4794 0.598342
\(436\) −0.829647 + 1.43699i −0.0397329 + 0.0688194i
\(437\) −5.18454 8.97989i −0.248010 0.429567i
\(438\) 4.29021 + 7.43085i 0.204994 + 0.355060i
\(439\) −11.4284 + 19.7946i −0.545450 + 0.944747i 0.453129 + 0.891445i \(0.350308\pi\)
−0.998578 + 0.0533018i \(0.983025\pi\)
\(440\) 2.74657 0.130938
\(441\) −3.76496 5.90128i −0.179284 0.281013i
\(442\) 5.49314 0.261282
\(443\) 4.77868 8.27692i 0.227042 0.393248i −0.729888 0.683567i \(-0.760428\pi\)
0.956930 + 0.290318i \(0.0937612\pi\)
\(444\) 2.01839 + 3.49595i 0.0957884 + 0.165910i
\(445\) 8.93577 + 15.4772i 0.423596 + 0.733690i
\(446\) −1.20293 + 2.08354i −0.0569604 + 0.0986584i
\(447\) 16.0368 0.758513
\(448\) −1.37328 2.26144i −0.0648816 0.106843i
\(449\) 0.681412 0.0321578 0.0160789 0.999871i \(-0.494882\pi\)
0.0160789 + 0.999871i \(0.494882\pi\)
\(450\) −1.27182 + 2.20285i −0.0599541 + 0.103844i
\(451\) −2.77182 4.80093i −0.130520 0.226067i
\(452\) 3.54364 + 6.13776i 0.166679 + 0.288696i
\(453\) 2.84803 4.93294i 0.133812 0.231770i
\(454\) 2.45636 0.115283
\(455\) 39.9074 0.883830i 1.87089 0.0414346i
\(456\) −8.03677 −0.376356
\(457\) −9.07355 + 15.7158i −0.424443 + 0.735156i −0.996368 0.0851493i \(-0.972863\pi\)
0.571926 + 0.820306i \(0.306197\pi\)
\(458\) 5.29021 + 9.16290i 0.247195 + 0.428154i
\(459\) −0.500000 0.866025i −0.0233380 0.0404226i
\(460\) 1.77182 3.06888i 0.0826115 0.143087i
\(461\) −41.7045 −1.94237 −0.971185 0.238326i \(-0.923401\pi\)
−0.971185 + 0.238326i \(0.923401\pi\)
\(462\) −1.27182 + 2.32002i −0.0591704 + 0.107937i
\(463\) −28.5804 −1.32824 −0.664122 0.747624i \(-0.731195\pi\)
−0.664122 + 0.747624i \(0.731195\pi\)
\(464\) −2.27182 + 3.93491i −0.105467 + 0.182673i
\(465\) −6.98627 12.1006i −0.323981 0.561151i
\(466\) 3.53677 + 6.12587i 0.163838 + 0.283776i
\(467\) −2.69141 + 4.66166i −0.124544 + 0.215716i −0.921554 0.388249i \(-0.873080\pi\)
0.797011 + 0.603965i \(0.206413\pi\)
\(468\) 5.49314 0.253920
\(469\) −4.50686 + 8.22130i −0.208108 + 0.379624i
\(470\) −25.5162 −1.17697
\(471\) −9.05516 + 15.6840i −0.417240 + 0.722680i
\(472\) 4.76496 + 8.25314i 0.219325 + 0.379882i
\(473\) 2.01839 + 3.49595i 0.0928055 + 0.160744i
\(474\) −6.11985 + 10.5999i −0.281094 + 0.486869i
\(475\) −20.4426 −0.937972
\(476\) 2.64510 0.0585812i 0.121238 0.00268506i
\(477\) 5.49314 0.251513
\(478\) −3.83384 + 6.64041i −0.175356 + 0.303725i
\(479\) −7.23970 12.5395i −0.330791 0.572946i 0.651877 0.758325i \(-0.273982\pi\)
−0.982667 + 0.185379i \(0.940649\pi\)
\(480\) −1.37328 2.37860i −0.0626816 0.108568i
\(481\) 11.0873 19.2037i 0.505536 0.875614i
\(482\) −25.0598 −1.14144
\(483\) 1.77182 + 2.91772i 0.0806205 + 0.132761i
\(484\) 1.00000 0.0454545
\(485\) 0.119852 0.207590i 0.00544222 0.00942619i
\(486\) −0.500000 0.866025i −0.0226805 0.0392837i
\(487\) 4.21666 + 7.30347i 0.191075 + 0.330952i 0.945607 0.325312i \(-0.105469\pi\)
−0.754532 + 0.656264i \(0.772136\pi\)
\(488\) 0.829647 1.43699i 0.0375564 0.0650495i
\(489\) −13.4426 −0.607897
\(490\) 19.2071 0.851179i 0.867690 0.0384524i
\(491\) −38.6770 −1.74547 −0.872734 0.488195i \(-0.837655\pi\)
−0.872734 + 0.488195i \(0.837655\pi\)
\(492\) −2.77182 + 4.80093i −0.124963 + 0.216443i
\(493\) −2.27182 3.93491i −0.102318 0.177219i
\(494\) 22.0735 + 38.2325i 0.993136 + 1.72016i
\(495\) −1.37328 + 2.37860i −0.0617245 + 0.106910i
\(496\) 5.08727 0.228425
\(497\) −3.49314 5.75227i −0.156689 0.258025i
\(498\) −14.5299 −0.651101
\(499\) −19.0230 + 32.9489i −0.851589 + 1.47499i 0.0281856 + 0.999603i \(0.491027\pi\)
−0.879774 + 0.475392i \(0.842306\pi\)
\(500\) 3.37328 + 5.84270i 0.150858 + 0.261293i
\(501\) −11.7833 20.4093i −0.526441 0.911822i
\(502\) 12.5115 21.6706i 0.558417 0.967206i
\(503\) 21.5667 0.961611 0.480805 0.876827i \(-0.340344\pi\)
0.480805 + 0.876827i \(0.340344\pi\)
\(504\) 2.64510 0.0585812i 0.117822 0.00260941i
\(505\) 35.7687 1.59169
\(506\) 0.645103 1.11735i 0.0286783 0.0496723i
\(507\) −8.58727 14.8736i −0.381374 0.660560i
\(508\) 3.39167 + 5.87455i 0.150481 + 0.260641i
\(509\) 13.3270 23.0830i 0.590708 1.02314i −0.403429 0.915011i \(-0.632182\pi\)
0.994137 0.108125i \(-0.0344848\pi\)
\(510\) 2.74657 0.121620
\(511\) 10.9127 19.9067i 0.482751 0.880620i
\(512\) 1.00000 0.0441942
\(513\) 4.01839 6.96005i 0.177416 0.307294i
\(514\) 5.25343 + 9.09921i 0.231719 + 0.401349i
\(515\) 24.8201 + 42.9897i 1.09370 + 1.89435i
\(516\) 2.01839 3.49595i 0.0888545 0.153901i
\(517\) −9.29021 −0.408583
\(518\) 5.13404 9.36538i 0.225577 0.411491i
\(519\) −10.9127 −0.479015
\(520\) −7.54364 + 13.0660i −0.330810 + 0.572980i
\(521\) 11.9863 + 20.7608i 0.525128 + 0.909549i 0.999572 + 0.0292627i \(0.00931595\pi\)
−0.474444 + 0.880286i \(0.657351\pi\)
\(522\) −2.27182 3.93491i −0.0994348 0.172226i
\(523\) −10.3407 + 17.9106i −0.452168 + 0.783177i −0.998520 0.0543780i \(-0.982682\pi\)
0.546353 + 0.837555i \(0.316016\pi\)
\(524\) −13.8990 −0.607181
\(525\) 6.72818 0.149009i 0.293642 0.00650330i
\(526\) 23.6402 1.03076
\(527\) −2.54364 + 4.40571i −0.110803 + 0.191916i
\(528\) −0.500000 0.866025i −0.0217597 0.0376889i
\(529\) 10.6677 + 18.4770i 0.463812 + 0.803347i
\(530\) −7.54364 + 13.0660i −0.327675 + 0.567549i
\(531\) −9.52991 −0.413563
\(532\) 11.0368 + 18.1746i 0.478505 + 0.787971i
\(533\) 30.4520 1.31902
\(534\) 3.25343 5.63511i 0.140790 0.243855i
\(535\) −23.9537 41.4890i −1.03561 1.79373i
\(536\) −1.77182 3.06888i −0.0765309 0.132555i
\(537\) 6.47475 11.2146i 0.279406 0.483946i
\(538\) −15.1524 −0.653268
\(539\) 6.99314 0.309906i 0.301216 0.0133486i
\(540\) 2.74657 0.118193
\(541\) −17.9537 + 31.0967i −0.771890 + 1.33695i 0.164637 + 0.986354i \(0.447355\pi\)
−0.936526 + 0.350598i \(0.885978\pi\)
\(542\) −9.49314 16.4426i −0.407765 0.706270i
\(543\) −3.79707 6.57672i −0.162948 0.282234i
\(544\) −0.500000 + 0.866025i −0.0214373 + 0.0371305i
\(545\) 4.55736 0.195216
\(546\) −7.54364 12.4224i −0.322838 0.531629i
\(547\) −5.12405 −0.219088 −0.109544 0.993982i \(-0.534939\pi\)
−0.109544 + 0.993982i \(0.534939\pi\)
\(548\) −2.74657 + 4.75720i −0.117328 + 0.203217i
\(549\) 0.829647 + 1.43699i 0.0354085 + 0.0613293i
\(550\) −1.27182 2.20285i −0.0542305 0.0939300i
\(551\) 18.2581 31.6239i 0.777821 1.34723i
\(552\) −1.29021 −0.0549148
\(553\) 32.3753 0.717016i 1.37674 0.0304906i
\(554\) 24.4794 1.04003
\(555\) 5.54364 9.60186i 0.235314 0.407576i
\(556\) −6.81546 11.8047i −0.289040 0.500631i
\(557\) 6.43798 + 11.1509i 0.272786 + 0.472479i 0.969574 0.244798i \(-0.0787216\pi\)
−0.696788 + 0.717277i \(0.745388\pi\)
\(558\) −2.54364 + 4.40571i −0.107681 + 0.186509i
\(559\) −22.1745 −0.937883
\(560\) −3.49314 + 6.37208i −0.147612 + 0.269270i
\(561\) 1.00000 0.0422200
\(562\) 6.04364 10.4679i 0.254935 0.441561i
\(563\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(564\) 4.64510 + 8.04555i 0.195594 + 0.338779i
\(565\) 9.73284 16.8578i 0.409464 0.709212i
\(566\) 4.68141 0.196774
\(567\) −1.27182 + 2.32002i −0.0534114 + 0.0974315i
\(568\) 2.54364 0.106729
\(569\) −10.6777 + 18.4943i −0.447632 + 0.775321i −0.998231 0.0594486i \(-0.981066\pi\)
0.550600 + 0.834769i \(0.314399\pi\)
\(570\) 11.0368 + 19.1163i 0.462280 + 0.800692i
\(571\) −3.72818 6.45740i −0.156020 0.270234i 0.777410 0.628994i \(-0.216533\pi\)
−0.933430 + 0.358760i \(0.883200\pi\)
\(572\) −2.74657 + 4.75720i −0.114840 + 0.198908i
\(573\) 18.9863 0.793163
\(574\) 14.6635 0.324753i 0.612042 0.0135549i
\(575\) −3.28181 −0.136861
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −2.82232 4.88840i −0.117495 0.203507i 0.801280 0.598290i \(-0.204153\pi\)
−0.918774 + 0.394783i \(0.870820\pi\)
\(578\) 8.00000 + 13.8564i 0.332756 + 0.576351i
\(579\) 10.7833 18.6773i 0.448140 0.776202i
\(580\) 12.4794 0.518179
\(581\) 19.9537 + 32.8585i 0.827819 + 1.36320i
\(582\) −0.0872743 −0.00361763
\(583\) −2.74657 + 4.75720i −0.113751 + 0.197023i
\(584\) 4.29021 + 7.43085i 0.177530 + 0.307491i
\(585\) −7.54364 13.0660i −0.311891 0.540211i
\(586\) 5.81546 10.0727i 0.240234 0.416098i
\(587\) −34.4059 −1.42008 −0.710041 0.704160i \(-0.751324\pi\)
−0.710041 + 0.704160i \(0.751324\pi\)
\(588\) −3.76496 5.90128i −0.155264 0.243365i
\(589\) −40.8853 −1.68465
\(590\) 13.0873 22.6678i 0.538795 0.933220i
\(591\) 1.56202 + 2.70550i 0.0642531 + 0.111290i
\(592\) 2.01839 + 3.49595i 0.0829552 + 0.143683i
\(593\) 9.35909 16.2104i 0.384332 0.665682i −0.607344 0.794439i \(-0.707765\pi\)
0.991676 + 0.128756i \(0.0410985\pi\)
\(594\) 1.00000 0.0410305
\(595\) −3.77182 6.21119i −0.154629 0.254634i
\(596\) 16.0368 0.656892
\(597\) 13.0368 22.5804i 0.533560 0.924152i
\(598\) 3.54364 + 6.13776i 0.144910 + 0.250992i
\(599\) −5.20713 9.01901i −0.212757 0.368507i 0.739819 0.672806i \(-0.234911\pi\)
−0.952577 + 0.304299i \(0.901578\pi\)
\(600\) −1.27182 + 2.20285i −0.0519218 + 0.0899312i
\(601\) 25.0873 1.02333 0.511666 0.859185i \(-0.329029\pi\)
0.511666 + 0.859185i \(0.329029\pi\)
\(602\) −10.6777 + 0.236479i −0.435190 + 0.00963816i
\(603\) 3.54364 0.144308
\(604\) 2.84803 4.93294i 0.115885 0.200718i
\(605\) −1.37328 2.37860i −0.0558319 0.0967038i
\(606\) −6.51152 11.2783i −0.264513 0.458149i
\(607\) −15.9537 + 27.6326i −0.647541 + 1.12157i 0.336168 + 0.941802i \(0.390869\pi\)
−0.983708 + 0.179771i \(0.942464\pi\)
\(608\) −8.03677 −0.325934
\(609\) −5.77868 + 10.5413i −0.234164 + 0.427156i
\(610\) −4.55736 −0.184522
\(611\) 25.5162 44.1953i 1.03227 1.78795i
\(612\) −0.500000 0.866025i −0.0202113 0.0350070i
\(613\) −1.71399 2.96872i −0.0692274 0.119905i 0.829334 0.558753i \(-0.188720\pi\)
−0.898561 + 0.438848i \(0.855387\pi\)
\(614\) 7.03677 12.1880i 0.283981 0.491870i
\(615\) 15.2260 0.613971
\(616\) −1.27182 + 2.32002i −0.0512430 + 0.0934761i
\(617\) 12.7550 0.513495 0.256748 0.966478i \(-0.417349\pi\)
0.256748 + 0.966478i \(0.417349\pi\)
\(618\) 9.03677 15.6522i 0.363512 0.629622i
\(619\) 10.7949 + 18.6973i 0.433882 + 0.751506i 0.997204 0.0747317i \(-0.0238100\pi\)
−0.563321 + 0.826238i \(0.690477\pi\)
\(620\) −6.98627 12.1006i −0.280575 0.485971i
\(621\) 0.645103 1.11735i 0.0258871 0.0448377i
\(622\) 12.2765 0.492242
\(623\) −17.2113 + 0.381180i −0.689557 + 0.0152716i
\(624\) 5.49314 0.219901
\(625\) 15.6240 27.0616i 0.624962 1.08247i
\(626\) −11.7282 20.3138i −0.468752 0.811903i
\(627\) 4.01839 + 6.96005i 0.160479 + 0.277958i
\(628\) −9.05516 + 15.6840i −0.361340 + 0.625860i
\(629\) −4.03677 −0.160957
\(630\) −3.77182 6.21119i −0.150273 0.247460i
\(631\) 4.23131 0.168446 0.0842230 0.996447i \(-0.473159\pi\)
0.0842230 + 0.996447i \(0.473159\pi\)
\(632\) −6.11985 + 10.5999i −0.243435 + 0.421641i
\(633\) −7.83384 13.5686i −0.311367 0.539304i
\(634\) 0.286010 + 0.495384i 0.0113589 + 0.0196742i
\(635\) 9.31546 16.1348i 0.369673 0.640292i
\(636\) 5.49314 0.217817
\(637\) −17.7328 + 34.1189i −0.702601 + 1.35184i
\(638\) 4.54364 0.179884
\(639\) −1.27182 + 2.20285i −0.0503124 + 0.0871436i
\(640\) −1.37328 2.37860i −0.0542838 0.0940223i
\(641\) −2.03677 3.52780i −0.0804477 0.139340i 0.822995 0.568049i \(-0.192302\pi\)
−0.903442 + 0.428710i \(0.858968\pi\)
\(642\) −8.72132 + 15.1058i −0.344203 + 0.596177i
\(643\) −19.2618 −0.759612 −0.379806 0.925066i \(-0.624009\pi\)
−0.379806 + 0.925066i \(0.624009\pi\)
\(644\) 1.77182 + 2.91772i 0.0698194 + 0.114974i
\(645\) −11.0873 −0.436561
\(646\) 4.01839 6.96005i 0.158101 0.273840i
\(647\) 9.44683 + 16.3624i 0.371393 + 0.643272i 0.989780 0.142602i \(-0.0455468\pi\)
−0.618387 + 0.785874i \(0.712214\pi\)
\(648\) −0.500000 0.866025i −0.0196419 0.0340207i
\(649\) 4.76496 8.25314i 0.187041 0.323964i
\(650\) 13.9725 0.548048
\(651\) 13.4564 0.298018i 0.527396 0.0116803i
\(652\) −13.4426 −0.526454
\(653\) 4.46056 7.72591i 0.174555 0.302338i −0.765452 0.643493i \(-0.777485\pi\)
0.940007 + 0.341155i \(0.110818\pi\)
\(654\) −0.829647 1.43699i −0.0324418 0.0561908i
\(655\) 19.0873 + 33.0601i 0.745802 + 1.29177i
\(656\) −2.77182 + 4.80093i −0.108221 + 0.187445i
\(657\) −8.58041 −0.334754
\(658\) 11.8155 21.5534i 0.460614 0.840240i
\(659\) 45.4426 1.77019 0.885097 0.465407i \(-0.154092\pi\)
0.885097 + 0.465407i \(0.154092\pi\)
\(660\) −1.37328 + 2.37860i −0.0534550 + 0.0925868i
\(661\) 14.5115 + 25.1347i 0.564433 + 0.977626i 0.997102 + 0.0760737i \(0.0242384\pi\)
−0.432669 + 0.901553i \(0.642428\pi\)
\(662\) −3.85909 6.68414i −0.149988 0.259787i
\(663\) −2.74657 + 4.75720i −0.106668 + 0.184754i
\(664\) −14.5299 −0.563870
\(665\) 28.0735 51.2110i 1.08865 1.98588i
\(666\) −4.03677 −0.156422
\(667\) 2.93111 5.07684i 0.113493 0.196576i
\(668\) −11.7833 20.4093i −0.455911 0.789661i
\(669\) −1.20293 2.08354i −0.0465080 0.0805542i
\(670\) −4.86642 + 8.42889i −0.188006 + 0.325636i
\(671\) −1.65929 −0.0640563
\(672\) 2.64510 0.0585812i 0.102037 0.00225982i
\(673\) −16.2481 −0.626318 −0.313159 0.949701i \(-0.601387\pi\)
−0.313159 + 0.949701i \(0.601387\pi\)
\(674\) −14.2765 + 24.7276i −0.549909 + 0.952471i
\(675\) −1.27182 2.20285i −0.0489523 0.0847879i
\(676\) −8.58727 14.8736i −0.330280 0.572061i
\(677\) 1.94484 3.36856i 0.0747463 0.129464i −0.826230 0.563333i \(-0.809519\pi\)
0.900976 + 0.433869i \(0.142852\pi\)
\(678\) −7.08727 −0.272185
\(679\) 0.119852 + 0.197365i 0.00459951 + 0.00757418i
\(680\) 2.74657 0.105326
\(681\) −1.22818 + 2.12727i −0.0470640 + 0.0815173i
\(682\) −2.54364 4.40571i −0.0974009 0.168703i
\(683\) −2.90273 5.02768i −0.111070 0.192379i 0.805132 0.593096i \(-0.202094\pi\)
−0.916202 + 0.400717i \(0.868761\pi\)
\(684\) 4.01839 6.96005i 0.153647 0.266124i
\(685\) 15.0873 0.576455
\(686\) −8.17501 + 16.6183i −0.312123 + 0.634491i
\(687\) −10.5804 −0.403668
\(688\) 2.01839 3.49595i 0.0769503 0.133282i
\(689\) −15.0873 26.1319i −0.574779 0.995547i
\(690\) 1.77182 + 3.06888i 0.0674520 + 0.116830i
\(691\) 3.17768 5.50390i 0.120885 0.209378i −0.799232 0.601022i \(-0.794760\pi\)
0.920117 + 0.391644i \(0.128094\pi\)
\(692\) −10.9127 −0.414840
\(693\) −1.37328 2.26144i −0.0521668 0.0859048i
\(694\) −23.4426 −0.889870
\(695\) −18.7191 + 32.4225i −0.710056 + 1.22985i
\(696\) −2.27182 3.93491i −0.0861131 0.149152i
\(697\) −2.77182 4.80093i −0.104990 0.181848i
\(698\) −12.8664 + 22.2853i −0.487001 + 0.843511i
\(699\) −7.07355 −0.267546
\(700\) 6.72818 0.149009i 0.254301 0.00563202i
\(701\) 5.86223 0.221413 0.110707 0.993853i \(-0.464689\pi\)
0.110707 + 0.993853i \(0.464689\pi\)
\(702\) −2.74657 + 4.75720i −0.103663 + 0.179549i
\(703\) −16.2213 28.0961i −0.611799 1.05967i
\(704\) −0.500000 0.866025i −0.0188445 0.0326396i
\(705\) 12.7581 22.0977i 0.480498 0.832246i
\(706\) −18.4059 −0.692714
\(707\) −16.5630 + 30.2137i −0.622914 + 1.13630i
\(708\) −9.52991 −0.358156
\(709\) 6.72818 11.6536i 0.252682 0.437658i −0.711581 0.702604i \(-0.752021\pi\)
0.964263 + 0.264946i \(0.0853540\pi\)
\(710\) −3.49314 6.05029i −0.131095 0.227063i
\(711\) −6.11985 10.5999i −0.229512 0.397527i
\(712\) 3.25343 5.63511i 0.121928 0.211185i
\(713\) −6.56363 −0.245810
\(714\) −1.27182 + 2.32002i −0.0475966 + 0.0868244i
\(715\) 15.0873 0.564232
\(716\) 6.47475 11.2146i 0.241973 0.419109i
\(717\) −3.83384 6.64041i −0.143177 0.247991i
\(718\) 15.9863 + 27.6890i 0.596602 + 1.03335i
\(719\) 12.1382 21.0240i 0.452680 0.784065i −0.545872 0.837869i \(-0.683801\pi\)
0.998552 + 0.0538042i \(0.0171347\pi\)
\(720\) 2.74657 0.102359
\(721\) −47.8064 + 1.05877i −1.78040 + 0.0394306i
\(722\) 45.5897 1.69667
\(723\) 12.5299 21.7024i 0.465992 0.807122i
\(724\) −3.79707 6.57672i −0.141117 0.244422i
\(725\) −5.77868 10.0090i −0.214615 0.371724i
\(726\) −0.500000 + 0.866025i −0.0185567 + 0.0321412i
\(727\) −22.1471 −0.821390 −0.410695 0.911773i \(-0.634714\pi\)
−0.410695 + 0.911773i \(0.634714\pi\)
\(728\) −7.54364 12.4224i −0.279586 0.460404i
\(729\) 1.00000 0.0370370
\(730\) 11.7833 20.4093i 0.436121 0.755384i
\(731\) 2.01839 + 3.49595i 0.0746527 + 0.129302i
\(732\) 0.829647 + 1.43699i 0.0306646 + 0.0531127i
\(733\) 2.66349 4.61330i 0.0983782 0.170396i −0.812635 0.582773i \(-0.801968\pi\)
0.911014 + 0.412377i \(0.135301\pi\)
\(734\) 36.4794 1.34648
\(735\) −8.86642 + 17.0594i −0.327043 + 0.629247i
\(736\) −1.29021 −0.0475576
\(737\) −1.77182 + 3.06888i −0.0652658 + 0.113044i
\(738\) −2.77182 4.80093i −0.102032 0.176725i
\(739\) 12.6309 + 21.8774i 0.464636 + 0.804772i 0.999185 0.0403648i \(-0.0128520\pi\)
−0.534549 + 0.845137i \(0.679519\pi\)
\(740\) 5.54364 9.60186i 0.203788 0.352971i
\(741\) −44.1471 −1.62178
\(742\) −7.54364 12.4224i −0.276936 0.456040i
\(743\) −25.4196 −0.932554 −0.466277 0.884639i \(-0.654405\pi\)
−0.466277 + 0.884639i \(0.654405\pi\)
\(744\) −2.54364 + 4.40571i −0.0932543 + 0.161521i
\(745\) −22.0230 38.1450i −0.806862 1.39753i
\(746\) 10.1566 + 17.5918i 0.371860 + 0.644081i
\(747\) 7.26496 12.5833i 0.265811 0.460398i
\(748\) 1.00000 0.0365636
\(749\) 46.1376 1.02181i 1.68583 0.0373361i
\(750\) −6.74657 −0.246350
\(751\) 20.2765 35.1199i 0.739899 1.28154i −0.212641 0.977130i \(-0.568206\pi\)
0.952540 0.304413i \(-0.0984602\pi\)
\(752\) 4.64510 + 8.04555i 0.169389 + 0.293391i
\(753\) 12.5115 + 21.6706i 0.455945 + 0.789720i
\(754\) −12.4794 + 21.6150i −0.454473 + 0.787171i
\(755\) −15.6446 −0.569367
\(756\) −1.27182 + 2.32002i −0.0462556 + 0.0843782i
\(757\) 13.3554 0.485409 0.242704 0.970100i \(-0.421965\pi\)
0.242704 + 0.970100i \(0.421965\pi\)
\(758\) −4.72132 + 8.17756i −0.171486 + 0.297022i
\(759\) 0.645103 + 1.11735i 0.0234157 + 0.0405573i
\(760\) 11.0368 + 19.1163i 0.400346 + 0.693419i
\(761\) −9.22818 + 15.9837i −0.334521 + 0.579408i −0.983393 0.181490i \(-0.941908\pi\)
0.648871 + 0.760898i \(0.275241\pi\)
\(762\) −6.78334 −0.245735
\(763\) −2.11032 + 3.84959i −0.0763987 + 0.139365i
\(764\) 18.9863 0.686899
\(765\) −1.37328 + 2.37860i −0.0496512 + 0.0859984i
\(766\) −11.8522 20.5287i −0.428238 0.741731i
\(767\) 26.1745 + 45.3356i 0.945108 + 1.63698i
\(768\) −0.500000 + 0.866025i −0.0180422 + 0.0312500i
\(769\) 49.9158 1.80001 0.900005 0.435881i \(-0.143563\pi\)
0.900005 + 0.435881i \(0.143563\pi\)
\(770\) 7.26496 0.160897i 0.261811 0.00579833i
\(771\) −10.5069 −0.378395
\(772\) 10.7833 18.6773i 0.388101 0.672211i
\(773\) 21.0694 + 36.4932i 0.757812 + 1.31257i 0.943964 + 0.330048i \(0.107065\pi\)
−0.186152 + 0.982521i \(0.559602\pi\)
\(774\) 2.01839 + 3.49595i 0.0725494 + 0.125659i
\(775\) −6.47009 + 11.2065i −0.232412 + 0.402550i
\(776\) −0.0872743 −0.00313296
\(777\) 5.54364