Properties

Label 570.2.f.b.341.1
Level $570$
Weight $2$
Character 570.341
Analytic conductor $4.551$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{8})\)
Defining polynomial: \(x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 341.1
Root \(0.707107 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 570.341
Dual form 570.2.f.b.341.4

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +(1.00000 - 1.41421i) q^{3} +1.00000 q^{4} -1.00000i q^{5} +(1.00000 - 1.41421i) q^{6} +3.41421 q^{7} +1.00000 q^{8} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +(1.00000 - 1.41421i) q^{3} +1.00000 q^{4} -1.00000i q^{5} +(1.00000 - 1.41421i) q^{6} +3.41421 q^{7} +1.00000 q^{8} +(-1.00000 - 2.82843i) q^{9} -1.00000i q^{10} +2.58579i q^{11} +(1.00000 - 1.41421i) q^{12} +6.24264i q^{13} +3.41421 q^{14} +(-1.41421 - 1.00000i) q^{15} +1.00000 q^{16} -2.82843i q^{17} +(-1.00000 - 2.82843i) q^{18} +(-4.24264 - 1.00000i) q^{19} -1.00000i q^{20} +(3.41421 - 4.82843i) q^{21} +2.58579i q^{22} -6.00000i q^{23} +(1.00000 - 1.41421i) q^{24} -1.00000 q^{25} +6.24264i q^{26} +(-5.00000 - 1.41421i) q^{27} +3.41421 q^{28} -9.07107 q^{29} +(-1.41421 - 1.00000i) q^{30} -1.17157i q^{31} +1.00000 q^{32} +(3.65685 + 2.58579i) q^{33} -2.82843i q^{34} -3.41421i q^{35} +(-1.00000 - 2.82843i) q^{36} +6.24264i q^{37} +(-4.24264 - 1.00000i) q^{38} +(8.82843 + 6.24264i) q^{39} -1.00000i q^{40} +3.07107 q^{41} +(3.41421 - 4.82843i) q^{42} +9.41421 q^{43} +2.58579i q^{44} +(-2.82843 + 1.00000i) q^{45} -6.00000i q^{46} +8.82843i q^{47} +(1.00000 - 1.41421i) q^{48} +4.65685 q^{49} -1.00000 q^{50} +(-4.00000 - 2.82843i) q^{51} +6.24264i q^{52} -8.82843 q^{53} +(-5.00000 - 1.41421i) q^{54} +2.58579 q^{55} +3.41421 q^{56} +(-5.65685 + 5.00000i) q^{57} -9.07107 q^{58} -7.17157 q^{59} +(-1.41421 - 1.00000i) q^{60} +12.4853 q^{61} -1.17157i q^{62} +(-3.41421 - 9.65685i) q^{63} +1.00000 q^{64} +6.24264 q^{65} +(3.65685 + 2.58579i) q^{66} -2.82843i q^{68} +(-8.48528 - 6.00000i) q^{69} -3.41421i q^{70} +2.82843 q^{71} +(-1.00000 - 2.82843i) q^{72} -14.4853 q^{73} +6.24264i q^{74} +(-1.00000 + 1.41421i) q^{75} +(-4.24264 - 1.00000i) q^{76} +8.82843i q^{77} +(8.82843 + 6.24264i) q^{78} +9.31371i q^{79} -1.00000i q^{80} +(-7.00000 + 5.65685i) q^{81} +3.07107 q^{82} -7.17157i q^{83} +(3.41421 - 4.82843i) q^{84} -2.82843 q^{85} +9.41421 q^{86} +(-9.07107 + 12.8284i) q^{87} +2.58579i q^{88} +13.4142 q^{89} +(-2.82843 + 1.00000i) q^{90} +21.3137i q^{91} -6.00000i q^{92} +(-1.65685 - 1.17157i) q^{93} +8.82843i q^{94} +(-1.00000 + 4.24264i) q^{95} +(1.00000 - 1.41421i) q^{96} -9.41421i q^{97} +4.65685 q^{98} +(7.31371 - 2.58579i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{2} + 4q^{3} + 4q^{4} + 4q^{6} + 8q^{7} + 4q^{8} - 4q^{9} + O(q^{10}) \) \( 4q + 4q^{2} + 4q^{3} + 4q^{4} + 4q^{6} + 8q^{7} + 4q^{8} - 4q^{9} + 4q^{12} + 8q^{14} + 4q^{16} - 4q^{18} + 8q^{21} + 4q^{24} - 4q^{25} - 20q^{27} + 8q^{28} - 8q^{29} + 4q^{32} - 8q^{33} - 4q^{36} + 24q^{39} - 16q^{41} + 8q^{42} + 32q^{43} + 4q^{48} - 4q^{49} - 4q^{50} - 16q^{51} - 24q^{53} - 20q^{54} + 16q^{55} + 8q^{56} - 8q^{58} - 40q^{59} + 16q^{61} - 8q^{63} + 4q^{64} + 8q^{65} - 8q^{66} - 4q^{72} - 24q^{73} - 4q^{75} + 24q^{78} - 28q^{81} - 16q^{82} + 8q^{84} + 32q^{86} - 8q^{87} + 48q^{89} + 16q^{93} - 4q^{95} + 4q^{96} - 4q^{98} - 16q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 1.00000 1.41421i 0.577350 0.816497i
\(4\) 1.00000 0.500000
\(5\) 1.00000i 0.447214i
\(6\) 1.00000 1.41421i 0.408248 0.577350i
\(7\) 3.41421 1.29045 0.645226 0.763992i \(-0.276763\pi\)
0.645226 + 0.763992i \(0.276763\pi\)
\(8\) 1.00000 0.353553
\(9\) −1.00000 2.82843i −0.333333 0.942809i
\(10\) 1.00000i 0.316228i
\(11\) 2.58579i 0.779644i 0.920890 + 0.389822i \(0.127463\pi\)
−0.920890 + 0.389822i \(0.872537\pi\)
\(12\) 1.00000 1.41421i 0.288675 0.408248i
\(13\) 6.24264i 1.73140i 0.500566 + 0.865699i \(0.333125\pi\)
−0.500566 + 0.865699i \(0.666875\pi\)
\(14\) 3.41421 0.912487
\(15\) −1.41421 1.00000i −0.365148 0.258199i
\(16\) 1.00000 0.250000
\(17\) 2.82843i 0.685994i −0.939336 0.342997i \(-0.888558\pi\)
0.939336 0.342997i \(-0.111442\pi\)
\(18\) −1.00000 2.82843i −0.235702 0.666667i
\(19\) −4.24264 1.00000i −0.973329 0.229416i
\(20\) 1.00000i 0.223607i
\(21\) 3.41421 4.82843i 0.745042 1.05365i
\(22\) 2.58579i 0.551292i
\(23\) 6.00000i 1.25109i −0.780189 0.625543i \(-0.784877\pi\)
0.780189 0.625543i \(-0.215123\pi\)
\(24\) 1.00000 1.41421i 0.204124 0.288675i
\(25\) −1.00000 −0.200000
\(26\) 6.24264i 1.22428i
\(27\) −5.00000 1.41421i −0.962250 0.272166i
\(28\) 3.41421 0.645226
\(29\) −9.07107 −1.68446 −0.842228 0.539122i \(-0.818756\pi\)
−0.842228 + 0.539122i \(0.818756\pi\)
\(30\) −1.41421 1.00000i −0.258199 0.182574i
\(31\) 1.17157i 0.210421i −0.994450 0.105210i \(-0.966448\pi\)
0.994450 0.105210i \(-0.0335516\pi\)
\(32\) 1.00000 0.176777
\(33\) 3.65685 + 2.58579i 0.636577 + 0.450128i
\(34\) 2.82843i 0.485071i
\(35\) 3.41421i 0.577107i
\(36\) −1.00000 2.82843i −0.166667 0.471405i
\(37\) 6.24264i 1.02628i 0.858304 + 0.513142i \(0.171519\pi\)
−0.858304 + 0.513142i \(0.828481\pi\)
\(38\) −4.24264 1.00000i −0.688247 0.162221i
\(39\) 8.82843 + 6.24264i 1.41368 + 0.999623i
\(40\) 1.00000i 0.158114i
\(41\) 3.07107 0.479620 0.239810 0.970820i \(-0.422915\pi\)
0.239810 + 0.970820i \(0.422915\pi\)
\(42\) 3.41421 4.82843i 0.526825 0.745042i
\(43\) 9.41421 1.43565 0.717827 0.696221i \(-0.245137\pi\)
0.717827 + 0.696221i \(0.245137\pi\)
\(44\) 2.58579i 0.389822i
\(45\) −2.82843 + 1.00000i −0.421637 + 0.149071i
\(46\) 6.00000i 0.884652i
\(47\) 8.82843i 1.28776i 0.765127 + 0.643879i \(0.222676\pi\)
−0.765127 + 0.643879i \(0.777324\pi\)
\(48\) 1.00000 1.41421i 0.144338 0.204124i
\(49\) 4.65685 0.665265
\(50\) −1.00000 −0.141421
\(51\) −4.00000 2.82843i −0.560112 0.396059i
\(52\) 6.24264i 0.865699i
\(53\) −8.82843 −1.21268 −0.606339 0.795206i \(-0.707362\pi\)
−0.606339 + 0.795206i \(0.707362\pi\)
\(54\) −5.00000 1.41421i −0.680414 0.192450i
\(55\) 2.58579 0.348667
\(56\) 3.41421 0.456243
\(57\) −5.65685 + 5.00000i −0.749269 + 0.662266i
\(58\) −9.07107 −1.19109
\(59\) −7.17157 −0.933659 −0.466830 0.884347i \(-0.654604\pi\)
−0.466830 + 0.884347i \(0.654604\pi\)
\(60\) −1.41421 1.00000i −0.182574 0.129099i
\(61\) 12.4853 1.59858 0.799288 0.600948i \(-0.205210\pi\)
0.799288 + 0.600948i \(0.205210\pi\)
\(62\) 1.17157i 0.148790i
\(63\) −3.41421 9.65685i −0.430150 1.21665i
\(64\) 1.00000 0.125000
\(65\) 6.24264 0.774304
\(66\) 3.65685 + 2.58579i 0.450128 + 0.318288i
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 2.82843i 0.342997i
\(69\) −8.48528 6.00000i −1.02151 0.722315i
\(70\) 3.41421i 0.408077i
\(71\) 2.82843 0.335673 0.167836 0.985815i \(-0.446322\pi\)
0.167836 + 0.985815i \(0.446322\pi\)
\(72\) −1.00000 2.82843i −0.117851 0.333333i
\(73\) −14.4853 −1.69537 −0.847687 0.530497i \(-0.822005\pi\)
−0.847687 + 0.530497i \(0.822005\pi\)
\(74\) 6.24264i 0.725692i
\(75\) −1.00000 + 1.41421i −0.115470 + 0.163299i
\(76\) −4.24264 1.00000i −0.486664 0.114708i
\(77\) 8.82843i 1.00609i
\(78\) 8.82843 + 6.24264i 0.999623 + 0.706840i
\(79\) 9.31371i 1.04787i 0.851757 + 0.523937i \(0.175537\pi\)
−0.851757 + 0.523937i \(0.824463\pi\)
\(80\) 1.00000i 0.111803i
\(81\) −7.00000 + 5.65685i −0.777778 + 0.628539i
\(82\) 3.07107 0.339143
\(83\) 7.17157i 0.787182i −0.919286 0.393591i \(-0.871233\pi\)
0.919286 0.393591i \(-0.128767\pi\)
\(84\) 3.41421 4.82843i 0.372521 0.526825i
\(85\) −2.82843 −0.306786
\(86\) 9.41421 1.01516
\(87\) −9.07107 + 12.8284i −0.972521 + 1.37535i
\(88\) 2.58579i 0.275646i
\(89\) 13.4142 1.42190 0.710952 0.703241i \(-0.248264\pi\)
0.710952 + 0.703241i \(0.248264\pi\)
\(90\) −2.82843 + 1.00000i −0.298142 + 0.105409i
\(91\) 21.3137i 2.23428i
\(92\) 6.00000i 0.625543i
\(93\) −1.65685 1.17157i −0.171808 0.121486i
\(94\) 8.82843i 0.910583i
\(95\) −1.00000 + 4.24264i −0.102598 + 0.435286i
\(96\) 1.00000 1.41421i 0.102062 0.144338i
\(97\) 9.41421i 0.955869i −0.878396 0.477934i \(-0.841386\pi\)
0.878396 0.477934i \(-0.158614\pi\)
\(98\) 4.65685 0.470413
\(99\) 7.31371 2.58579i 0.735055 0.259881i
\(100\) −1.00000 −0.100000
\(101\) 3.65685i 0.363871i −0.983311 0.181935i \(-0.941764\pi\)
0.983311 0.181935i \(-0.0582361\pi\)
\(102\) −4.00000 2.82843i −0.396059 0.280056i
\(103\) 15.6569i 1.54272i 0.636402 + 0.771358i \(0.280422\pi\)
−0.636402 + 0.771358i \(0.719578\pi\)
\(104\) 6.24264i 0.612141i
\(105\) −4.82843 3.41421i −0.471206 0.333193i
\(106\) −8.82843 −0.857493
\(107\) −7.65685 −0.740216 −0.370108 0.928989i \(-0.620679\pi\)
−0.370108 + 0.928989i \(0.620679\pi\)
\(108\) −5.00000 1.41421i −0.481125 0.136083i
\(109\) 13.6569i 1.30809i −0.756456 0.654045i \(-0.773071\pi\)
0.756456 0.654045i \(-0.226929\pi\)
\(110\) 2.58579 0.246545
\(111\) 8.82843 + 6.24264i 0.837957 + 0.592525i
\(112\) 3.41421 0.322613
\(113\) 7.17157 0.674645 0.337322 0.941389i \(-0.390479\pi\)
0.337322 + 0.941389i \(0.390479\pi\)
\(114\) −5.65685 + 5.00000i −0.529813 + 0.468293i
\(115\) −6.00000 −0.559503
\(116\) −9.07107 −0.842228
\(117\) 17.6569 6.24264i 1.63238 0.577132i
\(118\) −7.17157 −0.660197
\(119\) 9.65685i 0.885242i
\(120\) −1.41421 1.00000i −0.129099 0.0912871i
\(121\) 4.31371 0.392155
\(122\) 12.4853 1.13036
\(123\) 3.07107 4.34315i 0.276909 0.391608i
\(124\) 1.17157i 0.105210i
\(125\) 1.00000i 0.0894427i
\(126\) −3.41421 9.65685i −0.304162 0.860301i
\(127\) 7.17157i 0.636374i −0.948028 0.318187i \(-0.896926\pi\)
0.948028 0.318187i \(-0.103074\pi\)
\(128\) 1.00000 0.0883883
\(129\) 9.41421 13.3137i 0.828875 1.17221i
\(130\) 6.24264 0.547516
\(131\) 19.0711i 1.66625i 0.553087 + 0.833123i \(0.313450\pi\)
−0.553087 + 0.833123i \(0.686550\pi\)
\(132\) 3.65685 + 2.58579i 0.318288 + 0.225064i
\(133\) −14.4853 3.41421i −1.25603 0.296050i
\(134\) 0 0
\(135\) −1.41421 + 5.00000i −0.121716 + 0.430331i
\(136\) 2.82843i 0.242536i
\(137\) 2.48528i 0.212332i −0.994348 0.106166i \(-0.966143\pi\)
0.994348 0.106166i \(-0.0338575\pi\)
\(138\) −8.48528 6.00000i −0.722315 0.510754i
\(139\) −10.1421 −0.860245 −0.430122 0.902771i \(-0.641530\pi\)
−0.430122 + 0.902771i \(0.641530\pi\)
\(140\) 3.41421i 0.288554i
\(141\) 12.4853 + 8.82843i 1.05145 + 0.743488i
\(142\) 2.82843 0.237356
\(143\) −16.1421 −1.34987
\(144\) −1.00000 2.82843i −0.0833333 0.235702i
\(145\) 9.07107i 0.753311i
\(146\) −14.4853 −1.19881
\(147\) 4.65685 6.58579i 0.384091 0.543187i
\(148\) 6.24264i 0.513142i
\(149\) 2.48528i 0.203602i 0.994805 + 0.101801i \(0.0324605\pi\)
−0.994805 + 0.101801i \(0.967539\pi\)
\(150\) −1.00000 + 1.41421i −0.0816497 + 0.115470i
\(151\) 3.51472i 0.286024i 0.989721 + 0.143012i \(0.0456787\pi\)
−0.989721 + 0.143012i \(0.954321\pi\)
\(152\) −4.24264 1.00000i −0.344124 0.0811107i
\(153\) −8.00000 + 2.82843i −0.646762 + 0.228665i
\(154\) 8.82843i 0.711415i
\(155\) −1.17157 −0.0941030
\(156\) 8.82843 + 6.24264i 0.706840 + 0.499811i
\(157\) 15.7990 1.26090 0.630448 0.776231i \(-0.282871\pi\)
0.630448 + 0.776231i \(0.282871\pi\)
\(158\) 9.31371i 0.740959i
\(159\) −8.82843 + 12.4853i −0.700140 + 0.990147i
\(160\) 1.00000i 0.0790569i
\(161\) 20.4853i 1.61447i
\(162\) −7.00000 + 5.65685i −0.549972 + 0.444444i
\(163\) −12.7279 −0.996928 −0.498464 0.866910i \(-0.666102\pi\)
−0.498464 + 0.866910i \(0.666102\pi\)
\(164\) 3.07107 0.239810
\(165\) 2.58579 3.65685i 0.201303 0.284686i
\(166\) 7.17157i 0.556622i
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 3.41421 4.82843i 0.263412 0.372521i
\(169\) −25.9706 −1.99774
\(170\) −2.82843 −0.216930
\(171\) 1.41421 + 13.0000i 0.108148 + 0.994135i
\(172\) 9.41421 0.717827
\(173\) 6.00000 0.456172 0.228086 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) −9.07107 + 12.8284i −0.687676 + 0.972521i
\(175\) −3.41421 −0.258090
\(176\) 2.58579i 0.194911i
\(177\) −7.17157 + 10.1421i −0.539048 + 0.762330i
\(178\) 13.4142 1.00544
\(179\) 17.7990 1.33036 0.665179 0.746684i \(-0.268355\pi\)
0.665179 + 0.746684i \(0.268355\pi\)
\(180\) −2.82843 + 1.00000i −0.210819 + 0.0745356i
\(181\) 5.17157i 0.384400i 0.981356 + 0.192200i \(0.0615622\pi\)
−0.981356 + 0.192200i \(0.938438\pi\)
\(182\) 21.3137i 1.57988i
\(183\) 12.4853 17.6569i 0.922939 1.30523i
\(184\) 6.00000i 0.442326i
\(185\) 6.24264 0.458968
\(186\) −1.65685 1.17157i −0.121486 0.0859039i
\(187\) 7.31371 0.534831
\(188\) 8.82843i 0.643879i
\(189\) −17.0711 4.82843i −1.24174 0.351216i
\(190\) −1.00000 + 4.24264i −0.0725476 + 0.307794i
\(191\) 1.75736i 0.127158i 0.997977 + 0.0635790i \(0.0202515\pi\)
−0.997977 + 0.0635790i \(0.979749\pi\)
\(192\) 1.00000 1.41421i 0.0721688 0.102062i
\(193\) 11.5563i 0.831844i −0.909400 0.415922i \(-0.863459\pi\)
0.909400 0.415922i \(-0.136541\pi\)
\(194\) 9.41421i 0.675901i
\(195\) 6.24264 8.82843i 0.447045 0.632217i
\(196\) 4.65685 0.332632
\(197\) 10.1421i 0.722597i −0.932450 0.361299i \(-0.882333\pi\)
0.932450 0.361299i \(-0.117667\pi\)
\(198\) 7.31371 2.58579i 0.519763 0.183764i
\(199\) 16.9706 1.20301 0.601506 0.798869i \(-0.294568\pi\)
0.601506 + 0.798869i \(0.294568\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 0 0
\(202\) 3.65685i 0.257295i
\(203\) −30.9706 −2.17371
\(204\) −4.00000 2.82843i −0.280056 0.198030i
\(205\) 3.07107i 0.214493i
\(206\) 15.6569i 1.09086i
\(207\) −16.9706 + 6.00000i −1.17954 + 0.417029i
\(208\) 6.24264i 0.432849i
\(209\) 2.58579 10.9706i 0.178863 0.758850i
\(210\) −4.82843 3.41421i −0.333193 0.235603i
\(211\) 2.00000i 0.137686i −0.997628 0.0688428i \(-0.978069\pi\)
0.997628 0.0688428i \(-0.0219307\pi\)
\(212\) −8.82843 −0.606339
\(213\) 2.82843 4.00000i 0.193801 0.274075i
\(214\) −7.65685 −0.523412
\(215\) 9.41421i 0.642044i
\(216\) −5.00000 1.41421i −0.340207 0.0962250i
\(217\) 4.00000i 0.271538i
\(218\) 13.6569i 0.924959i
\(219\) −14.4853 + 20.4853i −0.978825 + 1.38427i
\(220\) 2.58579 0.174334
\(221\) 17.6569 1.18773
\(222\) 8.82843 + 6.24264i 0.592525 + 0.418979i
\(223\) 18.0000i 1.20537i −0.797980 0.602685i \(-0.794098\pi\)
0.797980 0.602685i \(-0.205902\pi\)
\(224\) 3.41421 0.228122
\(225\) 1.00000 + 2.82843i 0.0666667 + 0.188562i
\(226\) 7.17157 0.477046
\(227\) −13.6569 −0.906437 −0.453219 0.891399i \(-0.649724\pi\)
−0.453219 + 0.891399i \(0.649724\pi\)
\(228\) −5.65685 + 5.00000i −0.374634 + 0.331133i
\(229\) −8.48528 −0.560723 −0.280362 0.959894i \(-0.590454\pi\)
−0.280362 + 0.959894i \(0.590454\pi\)
\(230\) −6.00000 −0.395628
\(231\) 12.4853 + 8.82843i 0.821471 + 0.580868i
\(232\) −9.07107 −0.595545
\(233\) 21.7990i 1.42810i −0.700095 0.714050i \(-0.746859\pi\)
0.700095 0.714050i \(-0.253141\pi\)
\(234\) 17.6569 6.24264i 1.15426 0.408094i
\(235\) 8.82843 0.575903
\(236\) −7.17157 −0.466830
\(237\) 13.1716 + 9.31371i 0.855586 + 0.604990i
\(238\) 9.65685i 0.625961i
\(239\) 19.8995i 1.28719i −0.765366 0.643596i \(-0.777442\pi\)
0.765366 0.643596i \(-0.222558\pi\)
\(240\) −1.41421 1.00000i −0.0912871 0.0645497i
\(241\) 8.48528i 0.546585i −0.961931 0.273293i \(-0.911887\pi\)
0.961931 0.273293i \(-0.0881127\pi\)
\(242\) 4.31371 0.277296
\(243\) 1.00000 + 15.5563i 0.0641500 + 0.997940i
\(244\) 12.4853 0.799288
\(245\) 4.65685i 0.297516i
\(246\) 3.07107 4.34315i 0.195804 0.276909i
\(247\) 6.24264 26.4853i 0.397210 1.68522i
\(248\) 1.17157i 0.0743950i
\(249\) −10.1421 7.17157i −0.642732 0.454480i
\(250\) 1.00000i 0.0632456i
\(251\) 19.0711i 1.20376i 0.798588 + 0.601878i \(0.205580\pi\)
−0.798588 + 0.601878i \(0.794420\pi\)
\(252\) −3.41421 9.65685i −0.215075 0.608325i
\(253\) 15.5147 0.975402
\(254\) 7.17157i 0.449985i
\(255\) −2.82843 + 4.00000i −0.177123 + 0.250490i
\(256\) 1.00000 0.0625000
\(257\) −0.142136 −0.00886618 −0.00443309 0.999990i \(-0.501411\pi\)
−0.00443309 + 0.999990i \(0.501411\pi\)
\(258\) 9.41421 13.3137i 0.586103 0.828875i
\(259\) 21.3137i 1.32437i
\(260\) 6.24264 0.387152
\(261\) 9.07107 + 25.6569i 0.561485 + 1.58812i
\(262\) 19.0711i 1.17821i
\(263\) 16.8284i 1.03769i −0.854870 0.518843i \(-0.826363\pi\)
0.854870 0.518843i \(-0.173637\pi\)
\(264\) 3.65685 + 2.58579i 0.225064 + 0.159144i
\(265\) 8.82843i 0.542326i
\(266\) −14.4853 3.41421i −0.888150 0.209339i
\(267\) 13.4142 18.9706i 0.820937 1.16098i
\(268\) 0 0
\(269\) 12.3848 0.755113 0.377557 0.925987i \(-0.376764\pi\)
0.377557 + 0.925987i \(0.376764\pi\)
\(270\) −1.41421 + 5.00000i −0.0860663 + 0.304290i
\(271\) 4.97056 0.301940 0.150970 0.988538i \(-0.451760\pi\)
0.150970 + 0.988538i \(0.451760\pi\)
\(272\) 2.82843i 0.171499i
\(273\) 30.1421 + 21.3137i 1.82429 + 1.28996i
\(274\) 2.48528i 0.150141i
\(275\) 2.58579i 0.155929i
\(276\) −8.48528 6.00000i −0.510754 0.361158i
\(277\) −8.97056 −0.538989 −0.269494 0.963002i \(-0.586857\pi\)
−0.269494 + 0.963002i \(0.586857\pi\)
\(278\) −10.1421 −0.608285
\(279\) −3.31371 + 1.17157i −0.198387 + 0.0701402i
\(280\) 3.41421i 0.204038i
\(281\) −15.0711 −0.899065 −0.449532 0.893264i \(-0.648409\pi\)
−0.449532 + 0.893264i \(0.648409\pi\)
\(282\) 12.4853 + 8.82843i 0.743488 + 0.525725i
\(283\) −12.7279 −0.756596 −0.378298 0.925684i \(-0.623491\pi\)
−0.378298 + 0.925684i \(0.623491\pi\)
\(284\) 2.82843 0.167836
\(285\) 5.00000 + 5.65685i 0.296174 + 0.335083i
\(286\) −16.1421 −0.954504
\(287\) 10.4853 0.618927
\(288\) −1.00000 2.82843i −0.0589256 0.166667i
\(289\) 9.00000 0.529412
\(290\) 9.07107i 0.532671i
\(291\) −13.3137 9.41421i −0.780463 0.551871i
\(292\) −14.4853 −0.847687
\(293\) 8.82843 0.515762 0.257881 0.966177i \(-0.416976\pi\)
0.257881 + 0.966177i \(0.416976\pi\)
\(294\) 4.65685 6.58579i 0.271593 0.384091i
\(295\) 7.17157i 0.417545i
\(296\) 6.24264i 0.362846i
\(297\) 3.65685 12.9289i 0.212192 0.750213i
\(298\) 2.48528i 0.143968i
\(299\) 37.4558 2.16613
\(300\) −1.00000 + 1.41421i −0.0577350 + 0.0816497i
\(301\) 32.1421 1.85264
\(302\) 3.51472i 0.202249i
\(303\) −5.17157 3.65685i −0.297099 0.210081i
\(304\) −4.24264 1.00000i −0.243332 0.0573539i
\(305\) 12.4853i 0.714905i
\(306\) −8.00000 + 2.82843i −0.457330 + 0.161690i
\(307\) 10.1421i 0.578842i 0.957202 + 0.289421i \(0.0934628\pi\)
−0.957202 + 0.289421i \(0.906537\pi\)
\(308\) 8.82843i 0.503046i
\(309\) 22.1421 + 15.6569i 1.25962 + 0.890687i
\(310\) −1.17157 −0.0665409
\(311\) 9.07107i 0.514373i −0.966362 0.257187i \(-0.917205\pi\)
0.966362 0.257187i \(-0.0827955\pi\)
\(312\) 8.82843 + 6.24264i 0.499811 + 0.353420i
\(313\) −11.1716 −0.631455 −0.315727 0.948850i \(-0.602248\pi\)
−0.315727 + 0.948850i \(0.602248\pi\)
\(314\) 15.7990 0.891589
\(315\) −9.65685 + 3.41421i −0.544102 + 0.192369i
\(316\) 9.31371i 0.523937i
\(317\) −11.6569 −0.654714 −0.327357 0.944901i \(-0.606158\pi\)
−0.327357 + 0.944901i \(0.606158\pi\)
\(318\) −8.82843 + 12.4853i −0.495074 + 0.700140i
\(319\) 23.4558i 1.31328i
\(320\) 1.00000i 0.0559017i
\(321\) −7.65685 + 10.8284i −0.427364 + 0.604384i
\(322\) 20.4853i 1.14160i
\(323\) −2.82843 + 12.0000i −0.157378 + 0.667698i
\(324\) −7.00000 + 5.65685i −0.388889 + 0.314270i
\(325\) 6.24264i 0.346279i
\(326\) −12.7279 −0.704934
\(327\) −19.3137 13.6569i −1.06805 0.755226i
\(328\) 3.07107 0.169571
\(329\) 30.1421i 1.66179i
\(330\) 2.58579 3.65685i 0.142343 0.201303i
\(331\) 16.9706i 0.932786i −0.884577 0.466393i \(-0.845553\pi\)
0.884577 0.466393i \(-0.154447\pi\)
\(332\) 7.17157i 0.393591i
\(333\) 17.6569 6.24264i 0.967590 0.342095i
\(334\) 0 0
\(335\) 0 0
\(336\) 3.41421 4.82843i 0.186261 0.263412i
\(337\) 13.2132i 0.719769i −0.932997 0.359885i \(-0.882816\pi\)
0.932997 0.359885i \(-0.117184\pi\)
\(338\) −25.9706 −1.41261
\(339\) 7.17157 10.1421i 0.389506 0.550845i
\(340\) −2.82843 −0.153393
\(341\) 3.02944 0.164053
\(342\) 1.41421 + 13.0000i 0.0764719 + 0.702959i
\(343\) −8.00000 −0.431959
\(344\) 9.41421 0.507580
\(345\) −6.00000 + 8.48528i −0.323029 + 0.456832i
\(346\) 6.00000 0.322562
\(347\) 26.2843i 1.41101i 0.708703 + 0.705507i \(0.249281\pi\)
−0.708703 + 0.705507i \(0.750719\pi\)
\(348\) −9.07107 + 12.8284i −0.486260 + 0.687676i
\(349\) 22.9706 1.22959 0.614793 0.788688i \(-0.289240\pi\)
0.614793 + 0.788688i \(0.289240\pi\)
\(350\) −3.41421 −0.182497
\(351\) 8.82843 31.2132i 0.471227 1.66604i
\(352\) 2.58579i 0.137823i
\(353\) 3.17157i 0.168806i 0.996432 + 0.0844029i \(0.0268983\pi\)
−0.996432 + 0.0844029i \(0.973102\pi\)
\(354\) −7.17157 + 10.1421i −0.381165 + 0.539048i
\(355\) 2.82843i 0.150117i
\(356\) 13.4142 0.710952
\(357\) −13.6569 9.65685i −0.722797 0.511095i
\(358\) 17.7990 0.940706
\(359\) 16.5858i 0.875364i 0.899130 + 0.437682i \(0.144200\pi\)
−0.899130 + 0.437682i \(0.855800\pi\)
\(360\) −2.82843 + 1.00000i −0.149071 + 0.0527046i
\(361\) 17.0000 + 8.48528i 0.894737 + 0.446594i
\(362\) 5.17157i 0.271812i
\(363\) 4.31371 6.10051i 0.226411 0.320193i
\(364\) 21.3137i 1.11714i
\(365\) 14.4853i 0.758194i
\(366\) 12.4853 17.6569i 0.652616 0.922939i
\(367\) −5.75736 −0.300532 −0.150266 0.988646i \(-0.548013\pi\)
−0.150266 + 0.988646i \(0.548013\pi\)
\(368\) 6.00000i 0.312772i
\(369\) −3.07107 8.68629i −0.159873 0.452190i
\(370\) 6.24264 0.324539
\(371\) −30.1421 −1.56490
\(372\) −1.65685 1.17157i −0.0859039 0.0607432i
\(373\) 34.0416i 1.76261i −0.472549 0.881304i \(-0.656666\pi\)
0.472549 0.881304i \(-0.343334\pi\)
\(374\) 7.31371 0.378183
\(375\) 1.41421 + 1.00000i 0.0730297 + 0.0516398i
\(376\) 8.82843i 0.455291i
\(377\) 56.6274i 2.91646i
\(378\) −17.0711 4.82843i −0.878041 0.248347i
\(379\) 8.00000i 0.410932i 0.978664 + 0.205466i \(0.0658711\pi\)
−0.978664 + 0.205466i \(0.934129\pi\)
\(380\) −1.00000 + 4.24264i −0.0512989 + 0.217643i
\(381\) −10.1421 7.17157i −0.519597 0.367411i
\(382\) 1.75736i 0.0899143i
\(383\) 3.85786 0.197128 0.0985638 0.995131i \(-0.468575\pi\)
0.0985638 + 0.995131i \(0.468575\pi\)
\(384\) 1.00000 1.41421i 0.0510310 0.0721688i
\(385\) 8.82843 0.449938
\(386\) 11.5563i 0.588203i
\(387\) −9.41421 26.6274i −0.478551 1.35355i
\(388\) 9.41421i 0.477934i
\(389\) 31.6569i 1.60507i −0.596608 0.802533i \(-0.703485\pi\)
0.596608 0.802533i \(-0.296515\pi\)
\(390\) 6.24264 8.82843i 0.316108 0.447045i
\(391\) −16.9706 −0.858238
\(392\) 4.65685 0.235207
\(393\) 26.9706 + 19.0711i 1.36048 + 0.962008i
\(394\) 10.1421i 0.510953i
\(395\) 9.31371 0.468624
\(396\) 7.31371 2.58579i 0.367528 0.129941i
\(397\) −16.9706 −0.851728 −0.425864 0.904787i \(-0.640030\pi\)
−0.425864 + 0.904787i \(0.640030\pi\)
\(398\) 16.9706 0.850657
\(399\) −19.3137 + 17.0711i −0.966895 + 0.854622i
\(400\) −1.00000 −0.0500000
\(401\) 18.3848 0.918092 0.459046 0.888413i \(-0.348191\pi\)
0.459046 + 0.888413i \(0.348191\pi\)
\(402\) 0 0
\(403\) 7.31371 0.364322
\(404\) 3.65685i 0.181935i
\(405\) 5.65685 + 7.00000i 0.281091 + 0.347833i
\(406\) −30.9706 −1.53704
\(407\) −16.1421 −0.800136
\(408\) −4.00000 2.82843i −0.198030 0.140028i
\(409\) 12.4853i 0.617357i −0.951166 0.308679i \(-0.900113\pi\)
0.951166 0.308679i \(-0.0998868\pi\)
\(410\) 3.07107i 0.151669i
\(411\) −3.51472 2.48528i −0.173368 0.122590i
\(412\) 15.6569i 0.771358i
\(413\) −24.4853 −1.20484
\(414\) −16.9706 + 6.00000i −0.834058 + 0.294884i
\(415\) −7.17157 −0.352039
\(416\) 6.24264i 0.306071i
\(417\) −10.1421 + 14.3431i −0.496663 + 0.702387i
\(418\) 2.58579 10.9706i 0.126475 0.536588i
\(419\) 30.3848i 1.48439i 0.670182 + 0.742197i \(0.266216\pi\)
−0.670182 + 0.742197i \(0.733784\pi\)
\(420\) −4.82843 3.41421i −0.235603 0.166597i
\(421\) 32.2843i 1.57344i −0.617311 0.786720i \(-0.711778\pi\)
0.617311 0.786720i \(-0.288222\pi\)
\(422\) 2.00000i 0.0973585i
\(423\) 24.9706 8.82843i 1.21411 0.429253i
\(424\) −8.82843 −0.428746
\(425\) 2.82843i 0.137199i
\(426\) 2.82843 4.00000i 0.137038 0.193801i
\(427\) 42.6274 2.06289
\(428\) −7.65685 −0.370108
\(429\) −16.1421 + 22.8284i −0.779350 + 1.10217i
\(430\) 9.41421i 0.453994i
\(431\) 3.31371 0.159616 0.0798079 0.996810i \(-0.474569\pi\)
0.0798079 + 0.996810i \(0.474569\pi\)
\(432\) −5.00000 1.41421i −0.240563 0.0680414i
\(433\) 22.3848i 1.07574i 0.843027 + 0.537872i \(0.180772\pi\)
−0.843027 + 0.537872i \(0.819228\pi\)
\(434\) 4.00000i 0.192006i
\(435\) 12.8284 + 9.07107i 0.615076 + 0.434924i
\(436\) 13.6569i 0.654045i
\(437\) −6.00000 + 25.4558i −0.287019 + 1.21772i
\(438\) −14.4853 + 20.4853i −0.692134 + 0.978825i
\(439\) 27.9411i 1.33356i −0.745256 0.666779i \(-0.767673\pi\)
0.745256 0.666779i \(-0.232327\pi\)
\(440\) 2.58579 0.123273
\(441\) −4.65685 13.1716i −0.221755 0.627218i
\(442\) 17.6569 0.839851
\(443\) 18.0000i 0.855206i 0.903967 + 0.427603i \(0.140642\pi\)
−0.903967 + 0.427603i \(0.859358\pi\)
\(444\) 8.82843 + 6.24264i 0.418979 + 0.296263i
\(445\) 13.4142i 0.635895i
\(446\) 18.0000i 0.852325i
\(447\) 3.51472 + 2.48528i 0.166240 + 0.117550i
\(448\) 3.41421 0.161306
\(449\) −7.75736 −0.366092 −0.183046 0.983104i \(-0.558596\pi\)
−0.183046 + 0.983104i \(0.558596\pi\)
\(450\) 1.00000 + 2.82843i 0.0471405 + 0.133333i
\(451\) 7.94113i 0.373933i
\(452\) 7.17157 0.337322
\(453\) 4.97056 + 3.51472i 0.233537 + 0.165136i
\(454\) −13.6569 −0.640948
\(455\) 21.3137 0.999202
\(456\) −5.65685 + 5.00000i −0.264906 + 0.234146i
\(457\) 4.82843 0.225864 0.112932 0.993603i \(-0.463976\pi\)
0.112932 + 0.993603i \(0.463976\pi\)
\(458\) −8.48528 −0.396491
\(459\) −4.00000 + 14.1421i −0.186704 + 0.660098i
\(460\) −6.00000 −0.279751
\(461\) 0.142136i 0.00661992i 0.999995 + 0.00330996i \(0.00105359\pi\)
−0.999995 + 0.00330996i \(0.998946\pi\)
\(462\) 12.4853 + 8.82843i 0.580868 + 0.410736i
\(463\) −23.2132 −1.07881 −0.539405 0.842047i \(-0.681351\pi\)
−0.539405 + 0.842047i \(0.681351\pi\)
\(464\) −9.07107 −0.421114
\(465\) −1.17157 + 1.65685i −0.0543304 + 0.0768348i
\(466\) 21.7990i 1.00982i
\(467\) 13.7990i 0.638541i 0.947664 + 0.319271i \(0.103438\pi\)
−0.947664 + 0.319271i \(0.896562\pi\)
\(468\) 17.6569 6.24264i 0.816188 0.288566i
\(469\) 0 0
\(470\) 8.82843 0.407225
\(471\) 15.7990 22.3431i 0.727979 1.02952i
\(472\) −7.17157 −0.330098
\(473\) 24.3431i 1.11930i
\(474\) 13.1716 + 9.31371i 0.604990 + 0.427793i
\(475\) 4.24264 + 1.00000i 0.194666 + 0.0458831i
\(476\) 9.65685i 0.442621i
\(477\) 8.82843 + 24.9706i 0.404226 + 1.14332i
\(478\) 19.8995i 0.910182i
\(479\) 0.585786i 0.0267653i −0.999910 0.0133826i \(-0.995740\pi\)
0.999910 0.0133826i \(-0.00425995\pi\)
\(480\) −1.41421 1.00000i −0.0645497 0.0456435i
\(481\) −38.9706 −1.77690
\(482\) 8.48528i 0.386494i
\(483\) −28.9706 20.4853i −1.31821 0.932113i
\(484\) 4.31371 0.196078
\(485\) −9.41421 −0.427477
\(486\) 1.00000 + 15.5563i 0.0453609 + 0.705650i
\(487\) 7.85786i 0.356074i 0.984024 + 0.178037i \(0.0569746\pi\)
−0.984024 + 0.178037i \(0.943025\pi\)
\(488\) 12.4853 0.565182
\(489\) −12.7279 + 18.0000i −0.575577 + 0.813988i
\(490\) 4.65685i 0.210375i
\(491\) 12.4437i 0.561574i −0.959770 0.280787i \(-0.909405\pi\)
0.959770 0.280787i \(-0.0905955\pi\)
\(492\) 3.07107 4.34315i 0.138454 0.195804i
\(493\) 25.6569i 1.15553i
\(494\) 6.24264 26.4853i 0.280870 1.19163i
\(495\) −2.58579 7.31371i −0.116222 0.328727i
\(496\) 1.17157i 0.0526052i
\(497\) 9.65685 0.433169
\(498\) −10.1421 7.17157i −0.454480 0.321366i
\(499\) −14.3431 −0.642087 −0.321044 0.947064i \(-0.604034\pi\)
−0.321044 + 0.947064i \(0.604034\pi\)
\(500\) 1.00000i 0.0447214i
\(501\) 0 0
\(502\) 19.0711i 0.851183i
\(503\) 42.2843i 1.88536i 0.333695 + 0.942681i \(0.391705\pi\)
−0.333695 + 0.942681i \(0.608295\pi\)
\(504\) −3.41421 9.65685i −0.152081 0.430150i
\(505\) −3.65685 −0.162728
\(506\) 15.5147 0.689713
\(507\) −25.9706 + 36.7279i −1.15339 + 1.63114i
\(508\) 7.17157i 0.318187i
\(509\) 23.8995 1.05933 0.529663 0.848208i \(-0.322318\pi\)
0.529663 + 0.848208i \(0.322318\pi\)
\(510\) −2.82843 + 4.00000i −0.125245 + 0.177123i
\(511\) −49.4558 −2.18780
\(512\) 1.00000 0.0441942
\(513\) 19.7990 + 11.0000i 0.874147 + 0.485662i
\(514\) −0.142136 −0.00626933
\(515\) 15.6569 0.689923
\(516\) 9.41421 13.3137i 0.414438 0.586103i
\(517\) −22.8284 −1.00399
\(518\) 21.3137i 0.936471i
\(519\) 6.00000 8.48528i 0.263371 0.372463i
\(520\) 6.24264 0.273758
\(521\) −22.3848 −0.980695 −0.490347 0.871527i \(-0.663130\pi\)
−0.490347 + 0.871527i \(0.663130\pi\)
\(522\) 9.07107 + 25.6569i 0.397030 + 1.12297i
\(523\) 24.9706i 1.09189i 0.837822 + 0.545943i \(0.183829\pi\)
−0.837822 + 0.545943i \(0.816171\pi\)
\(524\) 19.0711i 0.833123i
\(525\) −3.41421 + 4.82843i −0.149008 + 0.210730i
\(526\) 16.8284i 0.733754i
\(527\) −3.31371 −0.144347
\(528\) 3.65685 + 2.58579i 0.159144 + 0.112532i
\(529\) −13.0000 −0.565217
\(530\) 8.82843i 0.383482i
\(531\) 7.17157 + 20.2843i 0.311220 + 0.880262i
\(532\) −14.4853 3.41421i −0.628017 0.148025i
\(533\) 19.1716i 0.830413i
\(534\) 13.4142 18.9706i 0.580490 0.820937i
\(535\) 7.65685i 0.331035i
\(536\) 0 0
\(537\) 17.7990 25.1716i 0.768083 1.08623i
\(538\) 12.3848 0.533946
\(539\) 12.0416i 0.518670i
\(540\) −1.41421 + 5.00000i −0.0608581 + 0.215166i
\(541\) −9.02944 −0.388206 −0.194103 0.980981i \(-0.562180\pi\)
−0.194103 + 0.980981i \(0.562180\pi\)
\(542\) 4.97056 0.213504
\(543\) 7.31371 + 5.17157i 0.313861 + 0.221933i
\(544\) 2.82843i 0.121268i
\(545\) −13.6569 −0.584995
\(546\) 30.1421 + 21.3137i 1.28996 + 0.912143i
\(547\) 18.8284i 0.805045i −0.915410 0.402523i \(-0.868133\pi\)
0.915410 0.402523i \(-0.131867\pi\)
\(548\) 2.48528i 0.106166i
\(549\) −12.4853 35.3137i −0.532859 1.50715i
\(550\) 2.58579i 0.110258i
\(551\) 38.4853 + 9.07107i 1.63953 + 0.386440i
\(552\) −8.48528 6.00000i −0.361158 0.255377i
\(553\) 31.7990i 1.35223i
\(554\) −8.97056 −0.381123
\(555\) 6.24264 8.82843i 0.264985 0.374746i
\(556\) −10.1421 −0.430122
\(557\) 16.6274i 0.704526i −0.935901 0.352263i \(-0.885412\pi\)
0.935901 0.352263i \(-0.114588\pi\)
\(558\) −3.31371 + 1.17157i −0.140280 + 0.0495966i
\(559\) 58.7696i 2.48569i
\(560\) 3.41421i 0.144277i
\(561\) 7.31371 10.3431i 0.308785 0.436688i
\(562\) −15.0711 −0.635735
\(563\) −2.34315 −0.0987518 −0.0493759 0.998780i \(-0.515723\pi\)
−0.0493759 + 0.998780i \(0.515723\pi\)
\(564\) 12.4853 + 8.82843i 0.525725 + 0.371744i
\(565\) 7.17157i 0.301710i
\(566\) −12.7279 −0.534994
\(567\) −23.8995 + 19.3137i −1.00368 + 0.811100i
\(568\) 2.82843 0.118678
\(569\) −43.0711 −1.80563 −0.902817 0.430026i \(-0.858504\pi\)
−0.902817 + 0.430026i \(0.858504\pi\)
\(570\) 5.00000 + 5.65685i 0.209427 + 0.236940i
\(571\) 9.65685 0.404127 0.202063 0.979372i \(-0.435235\pi\)
0.202063 + 0.979372i \(0.435235\pi\)
\(572\) −16.1421 −0.674937
\(573\) 2.48528 + 1.75736i 0.103824 + 0.0734147i
\(574\) 10.4853 0.437647
\(575\) 6.00000i 0.250217i
\(576\) −1.00000 2.82843i −0.0416667 0.117851i
\(577\) −24.8284 −1.03362 −0.516810 0.856100i \(-0.672881\pi\)
−0.516810 + 0.856100i \(0.672881\pi\)
\(578\) 9.00000 0.374351
\(579\) −16.3431 11.5563i −0.679198 0.480265i
\(580\) 9.07107i 0.376656i
\(581\) 24.4853i 1.01582i
\(582\) −13.3137 9.41421i −0.551871 0.390232i
\(583\) 22.8284i 0.945457i
\(584\) −14.4853 −0.599405
\(585\) −6.24264 17.6569i −0.258101 0.730021i
\(586\) 8.82843 0.364699
\(587\) 8.82843i 0.364388i −0.983263 0.182194i \(-0.941680\pi\)
0.983263 0.182194i \(-0.0583199\pi\)
\(588\) 4.65685 6.58579i 0.192045 0.271593i
\(589\) −1.17157 + 4.97056i −0.0482738 + 0.204808i
\(590\) 7.17157i 0.295249i
\(591\) −14.3431 10.1421i −0.589998 0.417192i
\(592\) 6.24264i 0.256571i
\(593\) 16.1421i 0.662878i 0.943477 + 0.331439i \(0.107534\pi\)
−0.943477 + 0.331439i \(0.892466\pi\)
\(594\) 3.65685 12.9289i 0.150043 0.530481i
\(595\) −9.65685 −0.395892
\(596\) 2.48528i 0.101801i
\(597\) 16.9706 24.0000i 0.694559 0.982255i
\(598\) 37.4558 1.53168
\(599\) 26.8284 1.09618 0.548090 0.836419i \(-0.315355\pi\)
0.548090 + 0.836419i \(0.315355\pi\)
\(600\) −1.00000 + 1.41421i −0.0408248 + 0.0577350i
\(601\) 4.00000i 0.163163i 0.996667 + 0.0815817i \(0.0259972\pi\)
−0.996667 + 0.0815817i \(0.974003\pi\)
\(602\) 32.1421 1.31002
\(603\) 0 0
\(604\) 3.51472i 0.143012i
\(605\) 4.31371i 0.175377i
\(606\) −5.17157 3.65685i −0.210081 0.148550i
\(607\) 18.4853i 0.750294i −0.926965 0.375147i \(-0.877592\pi\)
0.926965 0.375147i \(-0.122408\pi\)
\(608\) −4.24264 1.00000i −0.172062 0.0405554i
\(609\) −30.9706 + 43.7990i −1.25499 + 1.77482i
\(610\) 12.4853i 0.505514i
\(611\) −55.1127 −2.22962
\(612\) −8.00000 + 2.82843i −0.323381 + 0.114332i
\(613\) 39.1127 1.57975 0.789874 0.613270i \(-0.210146\pi\)
0.789874 + 0.613270i \(0.210146\pi\)
\(614\) 10.1421i 0.409303i
\(615\) −4.34315 3.07107i −0.175133 0.123837i
\(616\) 8.82843i 0.355707i
\(617\) 13.1716i 0.530268i −0.964212 0.265134i \(-0.914584\pi\)
0.964212 0.265134i \(-0.0854161\pi\)
\(618\) 22.1421 + 15.6569i 0.890687 + 0.629811i
\(619\) −9.45584 −0.380062 −0.190031 0.981778i \(-0.560859\pi\)
−0.190031 + 0.981778i \(0.560859\pi\)
\(620\) −1.17157 −0.0470515
\(621\) −8.48528 + 30.0000i −0.340503 + 1.20386i
\(622\) 9.07107i 0.363717i
\(623\) 45.7990 1.83490
\(624\) 8.82843 + 6.24264i 0.353420 + 0.249906i
\(625\) 1.00000 0.0400000
\(626\) −11.1716 −0.446506
\(627\) −12.9289 14.6274i −0.516332 0.584163i
\(628\) 15.7990 0.630448
\(629\) 17.6569 0.704025
\(630\) −9.65685 + 3.41421i −0.384738 + 0.136026i
\(631\) 40.4853 1.61169 0.805847 0.592124i \(-0.201710\pi\)
0.805847 + 0.592124i \(0.201710\pi\)
\(632\) 9.31371i 0.370479i
\(633\) −2.82843 2.00000i −0.112420 0.0794929i
\(634\) −11.6569 −0.462953
\(635\) −7.17157 −0.284595
\(636\) −8.82843 + 12.4853i −0.350070 + 0.495074i
\(637\) 29.0711i 1.15184i
\(638\) 23.4558i 0.928626i
\(639\) −2.82843 8.00000i −0.111891 0.316475i
\(640\) 1.00000i 0.0395285i
\(641\) −36.7279 −1.45067 −0.725333 0.688398i \(-0.758314\pi\)
−0.725333 + 0.688398i \(0.758314\pi\)
\(642\) −7.65685 + 10.8284i −0.302192 + 0.427364i
\(643\) 4.72792 0.186451 0.0932255 0.995645i \(-0.470282\pi\)
0.0932255 + 0.995645i \(0.470282\pi\)
\(644\) 20.4853i 0.807233i
\(645\) −13.3137 9.41421i −0.524227 0.370684i
\(646\) −2.82843 + 12.0000i −0.111283 + 0.472134i
\(647\) 25.3137i 0.995185i 0.867411 + 0.497592i \(0.165782\pi\)
−0.867411 + 0.497592i \(0.834218\pi\)
\(648\) −7.00000 + 5.65685i −0.274986 + 0.222222i
\(649\) 18.5442i 0.727922i
\(650\) 6.24264i 0.244857i
\(651\) −5.65685 4.00000i −0.221710 0.156772i
\(652\) −12.7279 −0.498464
\(653\) 47.1127i 1.84366i 0.387592 + 0.921831i \(0.373307\pi\)
−0.387592 + 0.921831i \(0.626693\pi\)
\(654\) −19.3137 13.6569i −0.755226 0.534025i
\(655\) 19.0711 0.745168
\(656\) 3.07107 0.119905
\(657\) 14.4853 + 40.9706i 0.565125 + 1.59841i
\(658\) 30.1421i 1.17506i
\(659\) −3.17157 −0.123547 −0.0617735 0.998090i \(-0.519676\pi\)
−0.0617735 + 0.998090i \(0.519676\pi\)
\(660\) 2.58579 3.65685i 0.100652 0.142343i
\(661\) 20.4853i 0.796785i 0.917215 + 0.398393i \(0.130432\pi\)
−0.917215 + 0.398393i \(0.869568\pi\)
\(662\) 16.9706i 0.659580i
\(663\) 17.6569 24.9706i 0.685735 0.969776i
\(664\) 7.17157i 0.278311i
\(665\) −3.41421 + 14.4853i −0.132398 + 0.561715i
\(666\) 17.6569 6.24264i 0.684189 0.241897i
\(667\) 54.4264i 2.10740i
\(668\) 0 0
\(669\) −25.4558 18.0000i −0.984180 0.695920i
\(670\) 0 0
\(671\) 32.2843i 1.24632i
\(672\) 3.41421 4.82843i 0.131706 0.186261i
\(673\) 21.6985i 0.836415i −0.908351 0.418208i \(-0.862658\pi\)
0.908351 0.418208i \(-0.137342\pi\)
\(674\) 13.2132i 0.508954i
\(675\) 5.00000 + 1.41421i 0.192450 + 0.0544331i
\(676\) −25.9706 −0.998868
\(677\) 41.5980 1.59874 0.799370 0.600839i \(-0.205167\pi\)
0.799370 + 0.600839i \(0.205167\pi\)
\(678\) 7.17157 10.1421i 0.275423 0.389506i
\(679\) 32.1421i 1.23350i
\(680\) −2.82843 −0.108465
\(681\) −13.6569 + 19.3137i −0.523332 + 0.740103i
\(682\) 3.02944 0.116003
\(683\) −51.2548 −1.96121 −0.980606 0.195990i \(-0.937208\pi\)
−0.980606 + 0.195990i \(0.937208\pi\)
\(684\) 1.41421 + 13.0000i 0.0540738 + 0.497067i
\(685\) −2.48528 −0.0949577
\(686\) −8.00000 −0.305441
\(687\) −8.48528 + 12.0000i −0.323734 + 0.457829i
\(688\) 9.41421 0.358914
\(689\) 55.1127i 2.09963i
\(690\) −6.00000 + 8.48528i −0.228416 + 0.323029i
\(691\) 3.02944 0.115245 0.0576226 0.998338i \(-0.481648\pi\)
0.0576226 + 0.998338i \(0.481648\pi\)
\(692\) 6.00000 0.228086
\(693\) 24.9706 8.82843i 0.948553 0.335364i
\(694\) 26.2843i 0.997737i
\(695\) 10.1421i 0.384713i
\(696\) −9.07107 + 12.8284i −0.343838 + 0.486260i
\(697\) 8.68629i 0.329017i
\(698\) 22.9706 0.869449
\(699\) −30.8284 21.7990i −1.16604 0.824514i
\(700\) −3.41421 −0.129045
\(701\) 14.4853i 0.547102i −0.961858 0.273551i \(-0.911802\pi\)
0.961858 0.273551i \(-0.0881982\pi\)
\(702\) 8.82843 31.2132i 0.333208 1.17807i
\(703\) 6.24264 26.4853i 0.235446 0.998911i
\(704\) 2.58579i 0.0974555i
\(705\) 8.82843 12.4853i 0.332498 0.470223i
\(706\) 3.17157i 0.119364i
\(707\) 12.4853i 0.469557i
\(708\) −7.17157 + 10.1421i −0.269524 + 0.381165i
\(709\) 36.4853 1.37023 0.685117 0.728433i \(-0.259751\pi\)
0.685117 + 0.728433i \(0.259751\pi\)
\(710\) 2.82843i 0.106149i
\(711\) 26.3431 9.31371i 0.987945 0.349291i
\(712\) 13.4142 0.502719
\(713\) −7.02944 −0.263254
\(714\) −13.6569 9.65685i −0.511095 0.361399i
\(715\) 16.1421i 0.603682i
\(716\) 17.7990 0.665179
\(717\) −28.1421 19.8995i −1.05099 0.743160i
\(718\) 16.5858i 0.618976i
\(719\) 5.27208i 0.196615i −0.995156 0.0983077i \(-0.968657\pi\)
0.995156 0.0983077i \(-0.0313429\pi\)
\(720\) −2.82843 + 1.00000i −0.105409 + 0.0372678i
\(721\) 53.4558i 1.99080i
\(722\) 17.0000 + 8.48528i 0.632674 + 0.315789i
\(723\) −12.0000 8.48528i −0.446285 0.315571i
\(724\) 5.17157i 0.192200i
\(725\) 9.07107 0.336891
\(726\) 4.31371 6.10051i 0.160097 0.226411i
\(727\) −5.55635 −0.206074 −0.103037 0.994678i \(-0.532856\pi\)
−0.103037 + 0.994678i \(0.532856\pi\)
\(728\) 21.3137i 0.789939i
\(729\) 23.0000 + 14.1421i 0.851852 + 0.523783i
\(730\) 14.4853i 0.536124i
\(731\) 26.6274i 0.984851i
\(732\) 12.4853 17.6569i 0.461469 0.652616i
\(733\) −32.4853 −1.19987 −0.599936 0.800048i \(-0.704807\pi\)
−0.599936 + 0.800048i \(0.704807\pi\)
\(734\) −5.75736 −0.212508
\(735\) −6.58579 4.65685i −0.242920 0.171771i
\(736\) 6.00000i 0.221163i
\(737\) 0 0
\(738\) −3.07107 8.68629i −0.113048 0.319747i
\(739\) −3.51472 −0.129291 −0.0646455 0.997908i \(-0.520592\pi\)
−0.0646455 + 0.997908i \(0.520592\pi\)
\(740\) 6.24264 0.229484
\(741\) −31.2132 35.3137i −1.14665 1.29728i
\(742\) −30.1421 −1.10655
\(743\) −48.8284 −1.79134 −0.895671 0.444718i \(-0.853304\pi\)
−0.895671 + 0.444718i \(0.853304\pi\)
\(744\) −1.65685 1.17157i −0.0607432 0.0429519i
\(745\) 2.48528 0.0910537
\(746\) 34.0416i 1.24635i
\(747\) −20.2843 + 7.17157i −0.742163 + 0.262394i
\(748\) 7.31371 0.267416
\(749\) −26.1421 −0.955213
\(750\) 1.41421 + 1.00000i 0.0516398 + 0.0365148i
\(751\) 31.5147i 1.14999i 0.818157 + 0.574994i \(0.194996\pi\)
−0.818157 + 0.574994i \(0.805004\pi\)
\(752\) 8.82843i 0.321940i
\(753\) 26.9706 + 19.0711i 0.982862 + 0.694988i
\(754\) 56.6274i 2.06225i
\(755\) 3.51472 0.127914
\(756\) −17.0711 4.82843i −0.620869 0.175608i
\(757\) 38.3431 1.39361 0.696803 0.717263i \(-0.254605\pi\)
0.696803 + 0.717263i \(0.254605\pi\)
\(758\) 8.00000i 0.290573i
\(759\) 15.5147 21.9411i 0.563149 0.796412i
\(760\) −1.00000 + 4.24264i −0.0362738 + 0.153897i
\(761\) 6.82843i 0.247530i −0.992312 0.123765i \(-0.960503\pi\)
0.992312 0.123765i \(-0.0394969\pi\)
\(762\) −10.1421 7.17157i −0.367411 0.259799i
\(763\) 46.6274i 1.68803i
\(764\) 1.75736i 0.0635790i
\(765\) 2.82843 + 8.00000i 0.102262 + 0.289241i
\(766\) 3.85786 0.139390
\(767\) 44.7696i 1.61653i
\(768\) 1.00000 1.41421i 0.0360844 0.0510310i
\(769\) 9.31371 0.335861 0.167930 0.985799i \(-0.446292\pi\)
0.167930 + 0.985799i \(0.446292\pi\)
\(770\) 8.82843 0.318154
\(771\) −0.142136 + 0.201010i −0.00511889 + 0.00723920i
\(772\) 11.5563i 0.415922i
\(773\) 11.6569 0.419268 0.209634 0.977780i \(-0.432773\pi\)
0.209634 + 0.977780i \(0.432773\pi\)
\(774\) −9.41421 26.6274i −0.338387 0.957103i
\(775\) 1.17157i 0.0420841i
\(776\) 9.41421i 0.337951i
\(777\) 30.1421 + 21.3137i 1.08134 + 0.764625i
\(778\) 31.6569i 1.13495i
\(779\) −13.0294 3.07107i −0.466828 0.110032i
\(780\) 6.24264 8.82843i 0.223522 0.316108i
\(781\) 7.31371i 0.261705i
\(782\) −16.9706 −0.606866
\(783\) 45.3553 + 12.8284i 1.62087 + 0.458451i
\(784\) 4.65685 0.166316