Properties

Label 420.2.l.a.239.2
Level $420$
Weight $2$
Character 420.239
Analytic conductor $3.354$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 420.l (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.35371688489\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{8})\)
Defining polynomial: \( x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 239.2
Root \(0.707107 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 420.239
Dual form 420.2.l.a.239.4

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421i q^{2} +(-1.00000 + 1.41421i) q^{3} -2.00000 q^{4} +(2.12132 + 0.707107i) q^{5} +(2.00000 + 1.41421i) q^{6} +1.00000 q^{7} +2.82843i q^{8} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})\) \(q-1.41421i q^{2} +(-1.00000 + 1.41421i) q^{3} -2.00000 q^{4} +(2.12132 + 0.707107i) q^{5} +(2.00000 + 1.41421i) q^{6} +1.00000 q^{7} +2.82843i q^{8} +(-1.00000 - 2.82843i) q^{9} +(1.00000 - 3.00000i) q^{10} -4.24264 q^{11} +(2.00000 - 2.82843i) q^{12} +6.00000i q^{13} -1.41421i q^{14} +(-3.12132 + 2.29289i) q^{15} +4.00000 q^{16} +4.24264 q^{17} +(-4.00000 + 1.41421i) q^{18} +6.00000i q^{19} +(-4.24264 - 1.41421i) q^{20} +(-1.00000 + 1.41421i) q^{21} +6.00000i q^{22} +1.41421i q^{23} +(-4.00000 - 2.82843i) q^{24} +(4.00000 + 3.00000i) q^{25} +8.48528 q^{26} +(5.00000 + 1.41421i) q^{27} -2.00000 q^{28} -2.82843i q^{29} +(3.24264 + 4.41421i) q^{30} -5.65685i q^{32} +(4.24264 - 6.00000i) q^{33} -6.00000i q^{34} +(2.12132 + 0.707107i) q^{35} +(2.00000 + 5.65685i) q^{36} +6.00000i q^{37} +8.48528 q^{38} +(-8.48528 - 6.00000i) q^{39} +(-2.00000 + 6.00000i) q^{40} +1.41421i q^{41} +(2.00000 + 1.41421i) q^{42} +8.00000 q^{43} +8.48528 q^{44} +(-0.121320 - 6.70711i) q^{45} +2.00000 q^{46} -2.82843i q^{47} +(-4.00000 + 5.65685i) q^{48} +1.00000 q^{49} +(4.24264 - 5.65685i) q^{50} +(-4.24264 + 6.00000i) q^{51} -12.0000i q^{52} -8.48528 q^{53} +(2.00000 - 7.07107i) q^{54} +(-9.00000 - 3.00000i) q^{55} +2.82843i q^{56} +(-8.48528 - 6.00000i) q^{57} -4.00000 q^{58} +(6.24264 - 4.58579i) q^{60} -10.0000 q^{61} +(-1.00000 - 2.82843i) q^{63} -8.00000 q^{64} +(-4.24264 + 12.7279i) q^{65} +(-8.48528 - 6.00000i) q^{66} -4.00000 q^{67} -8.48528 q^{68} +(-2.00000 - 1.41421i) q^{69} +(1.00000 - 3.00000i) q^{70} +12.7279 q^{71} +(8.00000 - 2.82843i) q^{72} -6.00000i q^{73} +8.48528 q^{74} +(-8.24264 + 2.65685i) q^{75} -12.0000i q^{76} -4.24264 q^{77} +(-8.48528 + 12.0000i) q^{78} +(8.48528 + 2.82843i) q^{80} +(-7.00000 + 5.65685i) q^{81} +2.00000 q^{82} -2.82843i q^{83} +(2.00000 - 2.82843i) q^{84} +(9.00000 + 3.00000i) q^{85} -11.3137i q^{86} +(4.00000 + 2.82843i) q^{87} -12.0000i q^{88} -7.07107i q^{89} +(-9.48528 + 0.171573i) q^{90} +6.00000i q^{91} -2.82843i q^{92} -4.00000 q^{94} +(-4.24264 + 12.7279i) q^{95} +(8.00000 + 5.65685i) q^{96} -6.00000i q^{97} -1.41421i q^{98} +(4.24264 + 12.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{3} - 8 q^{4} + 8 q^{6} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{3} - 8 q^{4} + 8 q^{6} + 4 q^{7} - 4 q^{9} + 4 q^{10} + 8 q^{12} - 4 q^{15} + 16 q^{16} - 16 q^{18} - 4 q^{21} - 16 q^{24} + 16 q^{25} + 20 q^{27} - 8 q^{28} - 4 q^{30} + 8 q^{36} - 8 q^{40} + 8 q^{42} + 32 q^{43} + 8 q^{45} + 8 q^{46} - 16 q^{48} + 4 q^{49} + 8 q^{54} - 36 q^{55} - 16 q^{58} + 8 q^{60} - 40 q^{61} - 4 q^{63} - 32 q^{64} - 16 q^{67} - 8 q^{69} + 4 q^{70} + 32 q^{72} - 16 q^{75} - 28 q^{81} + 8 q^{82} + 8 q^{84} + 36 q^{85} + 16 q^{87} - 4 q^{90} - 16 q^{94} + 32 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/420\mathbb{Z}\right)^\times\).

\(n\) \(211\) \(241\) \(281\) \(337\)
\(\chi(n)\) \(-1\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421i 1.00000i
\(3\) −1.00000 + 1.41421i −0.577350 + 0.816497i
\(4\) −2.00000 −1.00000
\(5\) 2.12132 + 0.707107i 0.948683 + 0.316228i
\(6\) 2.00000 + 1.41421i 0.816497 + 0.577350i
\(7\) 1.00000 0.377964
\(8\) 2.82843i 1.00000i
\(9\) −1.00000 2.82843i −0.333333 0.942809i
\(10\) 1.00000 3.00000i 0.316228 0.948683i
\(11\) −4.24264 −1.27920 −0.639602 0.768706i \(-0.720901\pi\)
−0.639602 + 0.768706i \(0.720901\pi\)
\(12\) 2.00000 2.82843i 0.577350 0.816497i
\(13\) 6.00000i 1.66410i 0.554700 + 0.832050i \(0.312833\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) 1.41421i 0.377964i
\(15\) −3.12132 + 2.29289i −0.805921 + 0.592022i
\(16\) 4.00000 1.00000
\(17\) 4.24264 1.02899 0.514496 0.857493i \(-0.327979\pi\)
0.514496 + 0.857493i \(0.327979\pi\)
\(18\) −4.00000 + 1.41421i −0.942809 + 0.333333i
\(19\) 6.00000i 1.37649i 0.725476 + 0.688247i \(0.241620\pi\)
−0.725476 + 0.688247i \(0.758380\pi\)
\(20\) −4.24264 1.41421i −0.948683 0.316228i
\(21\) −1.00000 + 1.41421i −0.218218 + 0.308607i
\(22\) 6.00000i 1.27920i
\(23\) 1.41421i 0.294884i 0.989071 + 0.147442i \(0.0471040\pi\)
−0.989071 + 0.147442i \(0.952896\pi\)
\(24\) −4.00000 2.82843i −0.816497 0.577350i
\(25\) 4.00000 + 3.00000i 0.800000 + 0.600000i
\(26\) 8.48528 1.66410
\(27\) 5.00000 + 1.41421i 0.962250 + 0.272166i
\(28\) −2.00000 −0.377964
\(29\) 2.82843i 0.525226i −0.964901 0.262613i \(-0.915416\pi\)
0.964901 0.262613i \(-0.0845842\pi\)
\(30\) 3.24264 + 4.41421i 0.592022 + 0.805921i
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 5.65685i 1.00000i
\(33\) 4.24264 6.00000i 0.738549 1.04447i
\(34\) 6.00000i 1.02899i
\(35\) 2.12132 + 0.707107i 0.358569 + 0.119523i
\(36\) 2.00000 + 5.65685i 0.333333 + 0.942809i
\(37\) 6.00000i 0.986394i 0.869918 + 0.493197i \(0.164172\pi\)
−0.869918 + 0.493197i \(0.835828\pi\)
\(38\) 8.48528 1.37649
\(39\) −8.48528 6.00000i −1.35873 0.960769i
\(40\) −2.00000 + 6.00000i −0.316228 + 0.948683i
\(41\) 1.41421i 0.220863i 0.993884 + 0.110432i \(0.0352233\pi\)
−0.993884 + 0.110432i \(0.964777\pi\)
\(42\) 2.00000 + 1.41421i 0.308607 + 0.218218i
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) 8.48528 1.27920
\(45\) −0.121320 6.70711i −0.0180854 0.999836i
\(46\) 2.00000 0.294884
\(47\) 2.82843i 0.412568i −0.978492 0.206284i \(-0.933863\pi\)
0.978492 0.206284i \(-0.0661372\pi\)
\(48\) −4.00000 + 5.65685i −0.577350 + 0.816497i
\(49\) 1.00000 0.142857
\(50\) 4.24264 5.65685i 0.600000 0.800000i
\(51\) −4.24264 + 6.00000i −0.594089 + 0.840168i
\(52\) 12.0000i 1.66410i
\(53\) −8.48528 −1.16554 −0.582772 0.812636i \(-0.698032\pi\)
−0.582772 + 0.812636i \(0.698032\pi\)
\(54\) 2.00000 7.07107i 0.272166 0.962250i
\(55\) −9.00000 3.00000i −1.21356 0.404520i
\(56\) 2.82843i 0.377964i
\(57\) −8.48528 6.00000i −1.12390 0.794719i
\(58\) −4.00000 −0.525226
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 6.24264 4.58579i 0.805921 0.592022i
\(61\) −10.0000 −1.28037 −0.640184 0.768221i \(-0.721142\pi\)
−0.640184 + 0.768221i \(0.721142\pi\)
\(62\) 0 0
\(63\) −1.00000 2.82843i −0.125988 0.356348i
\(64\) −8.00000 −1.00000
\(65\) −4.24264 + 12.7279i −0.526235 + 1.57870i
\(66\) −8.48528 6.00000i −1.04447 0.738549i
\(67\) −4.00000 −0.488678 −0.244339 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) −8.48528 −1.02899
\(69\) −2.00000 1.41421i −0.240772 0.170251i
\(70\) 1.00000 3.00000i 0.119523 0.358569i
\(71\) 12.7279 1.51053 0.755263 0.655422i \(-0.227509\pi\)
0.755263 + 0.655422i \(0.227509\pi\)
\(72\) 8.00000 2.82843i 0.942809 0.333333i
\(73\) 6.00000i 0.702247i −0.936329 0.351123i \(-0.885800\pi\)
0.936329 0.351123i \(-0.114200\pi\)
\(74\) 8.48528 0.986394
\(75\) −8.24264 + 2.65685i −0.951778 + 0.306787i
\(76\) 12.0000i 1.37649i
\(77\) −4.24264 −0.483494
\(78\) −8.48528 + 12.0000i −0.960769 + 1.35873i
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) 8.48528 + 2.82843i 0.948683 + 0.316228i
\(81\) −7.00000 + 5.65685i −0.777778 + 0.628539i
\(82\) 2.00000 0.220863
\(83\) 2.82843i 0.310460i −0.987878 0.155230i \(-0.950388\pi\)
0.987878 0.155230i \(-0.0496119\pi\)
\(84\) 2.00000 2.82843i 0.218218 0.308607i
\(85\) 9.00000 + 3.00000i 0.976187 + 0.325396i
\(86\) 11.3137i 1.21999i
\(87\) 4.00000 + 2.82843i 0.428845 + 0.303239i
\(88\) 12.0000i 1.27920i
\(89\) 7.07107i 0.749532i −0.927119 0.374766i \(-0.877723\pi\)
0.927119 0.374766i \(-0.122277\pi\)
\(90\) −9.48528 + 0.171573i −0.999836 + 0.0180854i
\(91\) 6.00000i 0.628971i
\(92\) 2.82843i 0.294884i
\(93\) 0 0
\(94\) −4.00000 −0.412568
\(95\) −4.24264 + 12.7279i −0.435286 + 1.30586i
\(96\) 8.00000 + 5.65685i 0.816497 + 0.577350i
\(97\) 6.00000i 0.609208i −0.952479 0.304604i \(-0.901476\pi\)
0.952479 0.304604i \(-0.0985241\pi\)
\(98\) 1.41421i 0.142857i
\(99\) 4.24264 + 12.0000i 0.426401 + 1.20605i
\(100\) −8.00000 6.00000i −0.800000 0.600000i
\(101\) 15.5563i 1.54791i −0.633238 0.773957i \(-0.718274\pi\)
0.633238 0.773957i \(-0.281726\pi\)
\(102\) 8.48528 + 6.00000i 0.840168 + 0.594089i
\(103\) 14.0000 1.37946 0.689730 0.724066i \(-0.257729\pi\)
0.689730 + 0.724066i \(0.257729\pi\)
\(104\) −16.9706 −1.66410
\(105\) −3.12132 + 2.29289i −0.304610 + 0.223763i
\(106\) 12.0000i 1.16554i
\(107\) 7.07107i 0.683586i −0.939775 0.341793i \(-0.888966\pi\)
0.939775 0.341793i \(-0.111034\pi\)
\(108\) −10.0000 2.82843i −0.962250 0.272166i
\(109\) 2.00000 0.191565 0.0957826 0.995402i \(-0.469465\pi\)
0.0957826 + 0.995402i \(0.469465\pi\)
\(110\) −4.24264 + 12.7279i −0.404520 + 1.21356i
\(111\) −8.48528 6.00000i −0.805387 0.569495i
\(112\) 4.00000 0.377964
\(113\) 8.48528 0.798228 0.399114 0.916901i \(-0.369318\pi\)
0.399114 + 0.916901i \(0.369318\pi\)
\(114\) −8.48528 + 12.0000i −0.794719 + 1.12390i
\(115\) −1.00000 + 3.00000i −0.0932505 + 0.279751i
\(116\) 5.65685i 0.525226i
\(117\) 16.9706 6.00000i 1.56893 0.554700i
\(118\) 0 0
\(119\) 4.24264 0.388922
\(120\) −6.48528 8.82843i −0.592022 0.805921i
\(121\) 7.00000 0.636364
\(122\) 14.1421i 1.28037i
\(123\) −2.00000 1.41421i −0.180334 0.127515i
\(124\) 0 0
\(125\) 6.36396 + 9.19239i 0.569210 + 0.822192i
\(126\) −4.00000 + 1.41421i −0.356348 + 0.125988i
\(127\) −16.0000 −1.41977 −0.709885 0.704317i \(-0.751253\pi\)
−0.709885 + 0.704317i \(0.751253\pi\)
\(128\) 11.3137i 1.00000i
\(129\) −8.00000 + 11.3137i −0.704361 + 0.996116i
\(130\) 18.0000 + 6.00000i 1.57870 + 0.526235i
\(131\) −8.48528 −0.741362 −0.370681 0.928760i \(-0.620876\pi\)
−0.370681 + 0.928760i \(0.620876\pi\)
\(132\) −8.48528 + 12.0000i −0.738549 + 1.04447i
\(133\) 6.00000i 0.520266i
\(134\) 5.65685i 0.488678i
\(135\) 9.60660 + 6.53553i 0.826805 + 0.562489i
\(136\) 12.0000i 1.02899i
\(137\) −16.9706 −1.44989 −0.724947 0.688805i \(-0.758136\pi\)
−0.724947 + 0.688805i \(0.758136\pi\)
\(138\) −2.00000 + 2.82843i −0.170251 + 0.240772i
\(139\) 12.0000i 1.01783i −0.860818 0.508913i \(-0.830047\pi\)
0.860818 0.508913i \(-0.169953\pi\)
\(140\) −4.24264 1.41421i −0.358569 0.119523i
\(141\) 4.00000 + 2.82843i 0.336861 + 0.238197i
\(142\) 18.0000i 1.51053i
\(143\) 25.4558i 2.12872i
\(144\) −4.00000 11.3137i −0.333333 0.942809i
\(145\) 2.00000 6.00000i 0.166091 0.498273i
\(146\) −8.48528 −0.702247
\(147\) −1.00000 + 1.41421i −0.0824786 + 0.116642i
\(148\) 12.0000i 0.986394i
\(149\) 11.3137i 0.926855i −0.886135 0.463428i \(-0.846619\pi\)
0.886135 0.463428i \(-0.153381\pi\)
\(150\) 3.75736 + 11.6569i 0.306787 + 0.951778i
\(151\) 12.0000i 0.976546i −0.872691 0.488273i \(-0.837627\pi\)
0.872691 0.488273i \(-0.162373\pi\)
\(152\) −16.9706 −1.37649
\(153\) −4.24264 12.0000i −0.342997 0.970143i
\(154\) 6.00000i 0.483494i
\(155\) 0 0
\(156\) 16.9706 + 12.0000i 1.35873 + 0.960769i
\(157\) 18.0000i 1.43656i 0.695756 + 0.718278i \(0.255069\pi\)
−0.695756 + 0.718278i \(0.744931\pi\)
\(158\) 0 0
\(159\) 8.48528 12.0000i 0.672927 0.951662i
\(160\) 4.00000 12.0000i 0.316228 0.948683i
\(161\) 1.41421i 0.111456i
\(162\) 8.00000 + 9.89949i 0.628539 + 0.777778i
\(163\) 20.0000 1.56652 0.783260 0.621694i \(-0.213555\pi\)
0.783260 + 0.621694i \(0.213555\pi\)
\(164\) 2.82843i 0.220863i
\(165\) 13.2426 9.72792i 1.03094 0.757318i
\(166\) −4.00000 −0.310460
\(167\) 14.1421i 1.09435i 0.837018 + 0.547176i \(0.184297\pi\)
−0.837018 + 0.547176i \(0.815703\pi\)
\(168\) −4.00000 2.82843i −0.308607 0.218218i
\(169\) −23.0000 −1.76923
\(170\) 4.24264 12.7279i 0.325396 0.976187i
\(171\) 16.9706 6.00000i 1.29777 0.458831i
\(172\) −16.0000 −1.21999
\(173\) 12.7279 0.967686 0.483843 0.875155i \(-0.339241\pi\)
0.483843 + 0.875155i \(0.339241\pi\)
\(174\) 4.00000 5.65685i 0.303239 0.428845i
\(175\) 4.00000 + 3.00000i 0.302372 + 0.226779i
\(176\) −16.9706 −1.27920
\(177\) 0 0
\(178\) −10.0000 −0.749532
\(179\) 4.24264 0.317110 0.158555 0.987350i \(-0.449317\pi\)
0.158555 + 0.987350i \(0.449317\pi\)
\(180\) 0.242641 + 13.4142i 0.0180854 + 0.999836i
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 8.48528 0.628971
\(183\) 10.0000 14.1421i 0.739221 1.04542i
\(184\) −4.00000 −0.294884
\(185\) −4.24264 + 12.7279i −0.311925 + 0.935775i
\(186\) 0 0
\(187\) −18.0000 −1.31629
\(188\) 5.65685i 0.412568i
\(189\) 5.00000 + 1.41421i 0.363696 + 0.102869i
\(190\) 18.0000 + 6.00000i 1.30586 + 0.435286i
\(191\) 12.7279 0.920960 0.460480 0.887670i \(-0.347677\pi\)
0.460480 + 0.887670i \(0.347677\pi\)
\(192\) 8.00000 11.3137i 0.577350 0.816497i
\(193\) 18.0000i 1.29567i 0.761781 + 0.647834i \(0.224325\pi\)
−0.761781 + 0.647834i \(0.775675\pi\)
\(194\) −8.48528 −0.609208
\(195\) −13.7574 18.7279i −0.985185 1.34113i
\(196\) −2.00000 −0.142857
\(197\) 25.4558 1.81365 0.906827 0.421503i \(-0.138497\pi\)
0.906827 + 0.421503i \(0.138497\pi\)
\(198\) 16.9706 6.00000i 1.20605 0.426401i
\(199\) 6.00000i 0.425329i −0.977125 0.212664i \(-0.931786\pi\)
0.977125 0.212664i \(-0.0682141\pi\)
\(200\) −8.48528 + 11.3137i −0.600000 + 0.800000i
\(201\) 4.00000 5.65685i 0.282138 0.399004i
\(202\) −22.0000 −1.54791
\(203\) 2.82843i 0.198517i
\(204\) 8.48528 12.0000i 0.594089 0.840168i
\(205\) −1.00000 + 3.00000i −0.0698430 + 0.209529i
\(206\) 19.7990i 1.37946i
\(207\) 4.00000 1.41421i 0.278019 0.0982946i
\(208\) 24.0000i 1.66410i
\(209\) 25.4558i 1.76082i
\(210\) 3.24264 + 4.41421i 0.223763 + 0.304610i
\(211\) 12.0000i 0.826114i −0.910705 0.413057i \(-0.864461\pi\)
0.910705 0.413057i \(-0.135539\pi\)
\(212\) 16.9706 1.16554
\(213\) −12.7279 + 18.0000i −0.872103 + 1.23334i
\(214\) −10.0000 −0.683586
\(215\) 16.9706 + 5.65685i 1.15738 + 0.385794i
\(216\) −4.00000 + 14.1421i −0.272166 + 0.962250i
\(217\) 0 0
\(218\) 2.82843i 0.191565i
\(219\) 8.48528 + 6.00000i 0.573382 + 0.405442i
\(220\) 18.0000 + 6.00000i 1.21356 + 0.404520i
\(221\) 25.4558i 1.71235i
\(222\) −8.48528 + 12.0000i −0.569495 + 0.805387i
\(223\) 8.00000 0.535720 0.267860 0.963458i \(-0.413684\pi\)
0.267860 + 0.963458i \(0.413684\pi\)
\(224\) 5.65685i 0.377964i
\(225\) 4.48528 14.3137i 0.299019 0.954247i
\(226\) 12.0000i 0.798228i
\(227\) 22.6274i 1.50183i 0.660396 + 0.750917i \(0.270388\pi\)
−0.660396 + 0.750917i \(0.729612\pi\)
\(228\) 16.9706 + 12.0000i 1.12390 + 0.794719i
\(229\) 14.0000 0.925146 0.462573 0.886581i \(-0.346926\pi\)
0.462573 + 0.886581i \(0.346926\pi\)
\(230\) 4.24264 + 1.41421i 0.279751 + 0.0932505i
\(231\) 4.24264 6.00000i 0.279145 0.394771i
\(232\) 8.00000 0.525226
\(233\) −16.9706 −1.11178 −0.555889 0.831256i \(-0.687622\pi\)
−0.555889 + 0.831256i \(0.687622\pi\)
\(234\) −8.48528 24.0000i −0.554700 1.56893i
\(235\) 2.00000 6.00000i 0.130466 0.391397i
\(236\) 0 0
\(237\) 0 0
\(238\) 6.00000i 0.388922i
\(239\) −4.24264 −0.274434 −0.137217 0.990541i \(-0.543816\pi\)
−0.137217 + 0.990541i \(0.543816\pi\)
\(240\) −12.4853 + 9.17157i −0.805921 + 0.592022i
\(241\) 26.0000 1.67481 0.837404 0.546585i \(-0.184072\pi\)
0.837404 + 0.546585i \(0.184072\pi\)
\(242\) 9.89949i 0.636364i
\(243\) −1.00000 15.5563i −0.0641500 0.997940i
\(244\) 20.0000 1.28037
\(245\) 2.12132 + 0.707107i 0.135526 + 0.0451754i
\(246\) −2.00000 + 2.82843i −0.127515 + 0.180334i
\(247\) −36.0000 −2.29063
\(248\) 0 0
\(249\) 4.00000 + 2.82843i 0.253490 + 0.179244i
\(250\) 13.0000 9.00000i 0.822192 0.569210i
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 2.00000 + 5.65685i 0.125988 + 0.356348i
\(253\) 6.00000i 0.377217i
\(254\) 22.6274i 1.41977i
\(255\) −13.2426 + 9.72792i −0.829286 + 0.609186i
\(256\) 16.0000 1.00000
\(257\) 4.24264 0.264649 0.132324 0.991206i \(-0.457756\pi\)
0.132324 + 0.991206i \(0.457756\pi\)
\(258\) 16.0000 + 11.3137i 0.996116 + 0.704361i
\(259\) 6.00000i 0.372822i
\(260\) 8.48528 25.4558i 0.526235 1.57870i
\(261\) −8.00000 + 2.82843i −0.495188 + 0.175075i
\(262\) 12.0000i 0.741362i
\(263\) 15.5563i 0.959246i −0.877475 0.479623i \(-0.840774\pi\)
0.877475 0.479623i \(-0.159226\pi\)
\(264\) 16.9706 + 12.0000i 1.04447 + 0.738549i
\(265\) −18.0000 6.00000i −1.10573 0.368577i
\(266\) 8.48528 0.520266
\(267\) 10.0000 + 7.07107i 0.611990 + 0.432742i
\(268\) 8.00000 0.488678
\(269\) 18.3848i 1.12094i 0.828175 + 0.560470i \(0.189379\pi\)
−0.828175 + 0.560470i \(0.810621\pi\)
\(270\) 9.24264 13.5858i 0.562489 0.826805i
\(271\) 24.0000i 1.45790i 0.684569 + 0.728948i \(0.259990\pi\)
−0.684569 + 0.728948i \(0.740010\pi\)
\(272\) 16.9706 1.02899
\(273\) −8.48528 6.00000i −0.513553 0.363137i
\(274\) 24.0000i 1.44989i
\(275\) −16.9706 12.7279i −1.02336 0.767523i
\(276\) 4.00000 + 2.82843i 0.240772 + 0.170251i
\(277\) 6.00000i 0.360505i 0.983620 + 0.180253i \(0.0576915\pi\)
−0.983620 + 0.180253i \(0.942309\pi\)
\(278\) −16.9706 −1.01783
\(279\) 0 0
\(280\) −2.00000 + 6.00000i −0.119523 + 0.358569i
\(281\) 2.82843i 0.168730i −0.996435 0.0843649i \(-0.973114\pi\)
0.996435 0.0843649i \(-0.0268861\pi\)
\(282\) 4.00000 5.65685i 0.238197 0.336861i
\(283\) −4.00000 −0.237775 −0.118888 0.992908i \(-0.537933\pi\)
−0.118888 + 0.992908i \(0.537933\pi\)
\(284\) −25.4558 −1.51053
\(285\) −13.7574 18.7279i −0.814916 1.10935i
\(286\) −36.0000 −2.12872
\(287\) 1.41421i 0.0834784i
\(288\) −16.0000 + 5.65685i −0.942809 + 0.333333i
\(289\) 1.00000 0.0588235
\(290\) −8.48528 2.82843i −0.498273 0.166091i
\(291\) 8.48528 + 6.00000i 0.497416 + 0.351726i
\(292\) 12.0000i 0.702247i
\(293\) 21.2132 1.23929 0.619644 0.784883i \(-0.287277\pi\)
0.619644 + 0.784883i \(0.287277\pi\)
\(294\) 2.00000 + 1.41421i 0.116642 + 0.0824786i
\(295\) 0 0
\(296\) −16.9706 −0.986394
\(297\) −21.2132 6.00000i −1.23091 0.348155i
\(298\) −16.0000 −0.926855
\(299\) −8.48528 −0.490716
\(300\) 16.4853 5.31371i 0.951778 0.306787i
\(301\) 8.00000 0.461112
\(302\) −16.9706 −0.976546
\(303\) 22.0000 + 15.5563i 1.26387 + 0.893689i
\(304\) 24.0000i 1.37649i
\(305\) −21.2132 7.07107i −1.21466 0.404888i
\(306\) −16.9706 + 6.00000i −0.970143 + 0.342997i
\(307\) 20.0000 1.14146 0.570730 0.821138i \(-0.306660\pi\)
0.570730 + 0.821138i \(0.306660\pi\)
\(308\) 8.48528 0.483494
\(309\) −14.0000 + 19.7990i −0.796432 + 1.12633i
\(310\) 0 0
\(311\) −25.4558 −1.44347 −0.721734 0.692170i \(-0.756655\pi\)
−0.721734 + 0.692170i \(0.756655\pi\)
\(312\) 16.9706 24.0000i 0.960769 1.35873i
\(313\) 18.0000i 1.01742i −0.860938 0.508710i \(-0.830123\pi\)
0.860938 0.508710i \(-0.169877\pi\)
\(314\) 25.4558 1.43656
\(315\) −0.121320 6.70711i −0.00683563 0.377903i
\(316\) 0 0
\(317\) −25.4558 −1.42974 −0.714871 0.699256i \(-0.753515\pi\)
−0.714871 + 0.699256i \(0.753515\pi\)
\(318\) −16.9706 12.0000i −0.951662 0.672927i
\(319\) 12.0000i 0.671871i
\(320\) −16.9706 5.65685i −0.948683 0.316228i
\(321\) 10.0000 + 7.07107i 0.558146 + 0.394669i
\(322\) 2.00000 0.111456
\(323\) 25.4558i 1.41640i
\(324\) 14.0000 11.3137i 0.777778 0.628539i
\(325\) −18.0000 + 24.0000i −0.998460 + 1.33128i
\(326\) 28.2843i 1.56652i
\(327\) −2.00000 + 2.82843i −0.110600 + 0.156412i
\(328\) −4.00000 −0.220863
\(329\) 2.82843i 0.155936i
\(330\) −13.7574 18.7279i −0.757318 1.03094i
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 5.65685i 0.310460i
\(333\) 16.9706 6.00000i 0.929981 0.328798i
\(334\) 20.0000 1.09435
\(335\) −8.48528 2.82843i −0.463600 0.154533i
\(336\) −4.00000 + 5.65685i −0.218218 + 0.308607i
\(337\) 12.0000i 0.653682i −0.945079 0.326841i \(-0.894016\pi\)
0.945079 0.326841i \(-0.105984\pi\)
\(338\) 32.5269i 1.76923i
\(339\) −8.48528 + 12.0000i −0.460857 + 0.651751i
\(340\) −18.0000 6.00000i −0.976187 0.325396i
\(341\) 0 0
\(342\) −8.48528 24.0000i −0.458831 1.29777i
\(343\) 1.00000 0.0539949
\(344\) 22.6274i 1.21999i
\(345\) −3.24264 4.41421i −0.174578 0.237653i
\(346\) 18.0000i 0.967686i
\(347\) 1.41421i 0.0759190i 0.999279 + 0.0379595i \(0.0120858\pi\)
−0.999279 + 0.0379595i \(0.987914\pi\)
\(348\) −8.00000 5.65685i −0.428845 0.303239i
\(349\) 26.0000 1.39175 0.695874 0.718164i \(-0.255017\pi\)
0.695874 + 0.718164i \(0.255017\pi\)
\(350\) 4.24264 5.65685i 0.226779 0.302372i
\(351\) −8.48528 + 30.0000i −0.452911 + 1.60128i
\(352\) 24.0000i 1.27920i
\(353\) −4.24264 −0.225813 −0.112906 0.993606i \(-0.536016\pi\)
−0.112906 + 0.993606i \(0.536016\pi\)
\(354\) 0 0
\(355\) 27.0000 + 9.00000i 1.43301 + 0.477670i
\(356\) 14.1421i 0.749532i
\(357\) −4.24264 + 6.00000i −0.224544 + 0.317554i
\(358\) 6.00000i 0.317110i
\(359\) −4.24264 −0.223918 −0.111959 0.993713i \(-0.535713\pi\)
−0.111959 + 0.993713i \(0.535713\pi\)
\(360\) 18.9706 0.343146i 0.999836 0.0180854i
\(361\) −17.0000 −0.894737
\(362\) 2.82843i 0.148659i
\(363\) −7.00000 + 9.89949i −0.367405 + 0.519589i
\(364\) 12.0000i 0.628971i
\(365\) 4.24264 12.7279i 0.222070 0.666210i
\(366\) −20.0000 14.1421i −1.04542 0.739221i
\(367\) 8.00000 0.417597 0.208798 0.977959i \(-0.433045\pi\)
0.208798 + 0.977959i \(0.433045\pi\)
\(368\) 5.65685i 0.294884i
\(369\) 4.00000 1.41421i 0.208232 0.0736210i
\(370\) 18.0000 + 6.00000i 0.935775 + 0.311925i
\(371\) −8.48528 −0.440534
\(372\) 0 0
\(373\) 12.0000i 0.621336i 0.950518 + 0.310668i \(0.100553\pi\)
−0.950518 + 0.310668i \(0.899447\pi\)
\(374\) 25.4558i 1.31629i
\(375\) −19.3640 0.192388i −0.999951 0.00993488i
\(376\) 8.00000 0.412568
\(377\) 16.9706 0.874028
\(378\) 2.00000 7.07107i 0.102869 0.363696i
\(379\) 36.0000i 1.84920i −0.380945 0.924598i \(-0.624401\pi\)
0.380945 0.924598i \(-0.375599\pi\)
\(380\) 8.48528 25.4558i 0.435286 1.30586i
\(381\) 16.0000 22.6274i 0.819705 1.15924i
\(382\) 18.0000i 0.920960i
\(383\) 11.3137i 0.578103i −0.957313 0.289052i \(-0.906660\pi\)
0.957313 0.289052i \(-0.0933400\pi\)
\(384\) −16.0000 11.3137i −0.816497 0.577350i
\(385\) −9.00000 3.00000i −0.458682 0.152894i
\(386\) 25.4558 1.29567
\(387\) −8.00000 22.6274i −0.406663 1.15022i
\(388\) 12.0000i 0.609208i
\(389\) 2.82843i 0.143407i −0.997426 0.0717035i \(-0.977156\pi\)
0.997426 0.0717035i \(-0.0228435\pi\)
\(390\) −26.4853 + 19.4558i −1.34113 + 0.985185i
\(391\) 6.00000i 0.303433i
\(392\) 2.82843i 0.142857i
\(393\) 8.48528 12.0000i 0.428026 0.605320i
\(394\) 36.0000i 1.81365i
\(395\) 0 0
\(396\) −8.48528 24.0000i −0.426401 1.20605i
\(397\) 30.0000i 1.50566i −0.658217 0.752828i \(-0.728689\pi\)
0.658217 0.752828i \(-0.271311\pi\)
\(398\) −8.48528 −0.425329
\(399\) −8.48528 6.00000i −0.424795 0.300376i
\(400\) 16.0000 + 12.0000i 0.800000 + 0.600000i
\(401\) 14.1421i 0.706225i 0.935581 + 0.353112i \(0.114877\pi\)
−0.935581 + 0.353112i \(0.885123\pi\)
\(402\) −8.00000 5.65685i −0.399004 0.282138i
\(403\) 0 0
\(404\) 31.1127i 1.54791i
\(405\) −18.8492 + 7.05025i −0.936626 + 0.350330i
\(406\) −4.00000 −0.198517
\(407\) 25.4558i 1.26180i
\(408\) −16.9706 12.0000i −0.840168 0.594089i
\(409\) −22.0000 −1.08783 −0.543915 0.839140i \(-0.683059\pi\)
−0.543915 + 0.839140i \(0.683059\pi\)
\(410\) 4.24264 + 1.41421i 0.209529 + 0.0698430i
\(411\) 16.9706 24.0000i 0.837096 1.18383i
\(412\) −28.0000 −1.37946
\(413\) 0 0
\(414\) −2.00000 5.65685i −0.0982946 0.278019i
\(415\) 2.00000 6.00000i 0.0981761 0.294528i
\(416\) 33.9411 1.66410
\(417\) 16.9706 + 12.0000i 0.831052 + 0.587643i
\(418\) −36.0000 −1.76082
\(419\) −16.9706 −0.829066 −0.414533 0.910034i \(-0.636055\pi\)
−0.414533 + 0.910034i \(0.636055\pi\)
\(420\) 6.24264 4.58579i 0.304610 0.223763i
\(421\) 8.00000 0.389896 0.194948 0.980814i \(-0.437546\pi\)
0.194948 + 0.980814i \(0.437546\pi\)
\(422\) −16.9706 −0.826114
\(423\) −8.00000 + 2.82843i −0.388973 + 0.137523i
\(424\) 24.0000i 1.16554i
\(425\) 16.9706 + 12.7279i 0.823193 + 0.617395i
\(426\) 25.4558 + 18.0000i 1.23334 + 0.872103i
\(427\) −10.0000 −0.483934
\(428\) 14.1421i 0.683586i
\(429\) 36.0000 + 25.4558i 1.73810 + 1.22902i
\(430\) 8.00000 24.0000i 0.385794 1.15738i
\(431\) 4.24264 0.204361 0.102180 0.994766i \(-0.467418\pi\)
0.102180 + 0.994766i \(0.467418\pi\)
\(432\) 20.0000 + 5.65685i 0.962250 + 0.272166i
\(433\) 18.0000i 0.865025i −0.901628 0.432512i \(-0.857627\pi\)
0.901628 0.432512i \(-0.142373\pi\)
\(434\) 0 0
\(435\) 6.48528 + 8.82843i 0.310945 + 0.423291i
\(436\) −4.00000 −0.191565
\(437\) −8.48528 −0.405906
\(438\) 8.48528 12.0000i 0.405442 0.573382i
\(439\) 18.0000i 0.859093i 0.903045 + 0.429547i \(0.141327\pi\)
−0.903045 + 0.429547i \(0.858673\pi\)
\(440\) 8.48528 25.4558i 0.404520 1.21356i
\(441\) −1.00000 2.82843i −0.0476190 0.134687i
\(442\) 36.0000 1.71235
\(443\) 35.3553i 1.67978i 0.542754 + 0.839891i \(0.317381\pi\)
−0.542754 + 0.839891i \(0.682619\pi\)
\(444\) 16.9706 + 12.0000i 0.805387 + 0.569495i
\(445\) 5.00000 15.0000i 0.237023 0.711068i
\(446\) 11.3137i 0.535720i
\(447\) 16.0000 + 11.3137i 0.756774 + 0.535120i
\(448\) −8.00000 −0.377964
\(449\) 5.65685i 0.266963i 0.991051 + 0.133482i \(0.0426157\pi\)
−0.991051 + 0.133482i \(0.957384\pi\)
\(450\) −20.2426 6.34315i −0.954247 0.299019i
\(451\) 6.00000i 0.282529i
\(452\) −16.9706 −0.798228
\(453\) 16.9706 + 12.0000i 0.797347 + 0.563809i
\(454\) 32.0000 1.50183
\(455\) −4.24264 + 12.7279i −0.198898 + 0.596694i
\(456\) 16.9706 24.0000i 0.794719 1.12390i
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) 19.7990i 0.925146i
\(459\) 21.2132 + 6.00000i 0.990148 + 0.280056i
\(460\) 2.00000 6.00000i 0.0932505 0.279751i
\(461\) 15.5563i 0.724531i −0.932075 0.362266i \(-0.882003\pi\)
0.932075 0.362266i \(-0.117997\pi\)
\(462\) −8.48528 6.00000i −0.394771 0.279145i
\(463\) −4.00000 −0.185896 −0.0929479 0.995671i \(-0.529629\pi\)
−0.0929479 + 0.995671i \(0.529629\pi\)
\(464\) 11.3137i 0.525226i
\(465\) 0 0
\(466\) 24.0000i 1.11178i
\(467\) 5.65685i 0.261768i 0.991398 + 0.130884i \(0.0417815\pi\)
−0.991398 + 0.130884i \(0.958218\pi\)
\(468\) −33.9411 + 12.0000i −1.56893 + 0.554700i
\(469\) −4.00000 −0.184703
\(470\) −8.48528 2.82843i −0.391397 0.130466i
\(471\) −25.4558 18.0000i −1.17294 0.829396i
\(472\) 0 0
\(473\) −33.9411 −1.56061
\(474\) 0 0
\(475\) −18.0000 + 24.0000i −0.825897 + 1.10120i
\(476\) −8.48528 −0.388922
\(477\) 8.48528 + 24.0000i 0.388514 + 1.09888i
\(478\) 6.00000i 0.274434i
\(479\) 8.48528 0.387702 0.193851 0.981031i \(-0.437902\pi\)
0.193851 + 0.981031i \(0.437902\pi\)
\(480\) 12.9706 + 17.6569i 0.592022 + 0.805921i
\(481\) −36.0000 −1.64146
\(482\) 36.7696i 1.67481i
\(483\) −2.00000 1.41421i −0.0910032 0.0643489i
\(484\) −14.0000 −0.636364
\(485\) 4.24264 12.7279i 0.192648 0.577945i
\(486\) −22.0000 + 1.41421i −0.997940 + 0.0641500i
\(487\) 20.0000 0.906287 0.453143 0.891438i \(-0.350303\pi\)
0.453143 + 0.891438i \(0.350303\pi\)
\(488\) 28.2843i 1.28037i
\(489\) −20.0000 + 28.2843i −0.904431 + 1.27906i
\(490\) 1.00000 3.00000i 0.0451754 0.135526i
\(491\) −29.6985 −1.34027 −0.670137 0.742237i \(-0.733765\pi\)
−0.670137 + 0.742237i \(0.733765\pi\)
\(492\) 4.00000 + 2.82843i 0.180334 + 0.127515i
\(493\) 12.0000i 0.540453i
\(494\) 50.9117i 2.29063i
\(495\) 0.514719 + 28.4558i 0.0231349 + 1.27900i
\(496\) 0 0
\(497\) 12.7279 0.570925
\(498\) 4.00000 5.65685i 0.179244 0.253490i
\(499\) 12.0000i 0.537194i 0.963253 + 0.268597i \(0.0865599\pi\)
−0.963253 + 0.268597i \(0.913440\pi\)
\(500\) −12.7279 18.3848i −0.569210 0.822192i
\(501\) −20.0000 14.1421i −0.893534 0.631824i
\(502\) 0 0
\(503\) 5.65685i 0.252227i 0.992016 + 0.126113i \(0.0402503\pi\)
−0.992016 + 0.126113i \(0.959750\pi\)
\(504\) 8.00000 2.82843i 0.356348 0.125988i
\(505\) 11.0000 33.0000i 0.489494 1.46848i
\(506\) −8.48528 −0.377217
\(507\) 23.0000 32.5269i 1.02147 1.44457i
\(508\) 32.0000 1.41977
\(509\) 24.0416i 1.06563i −0.846233 0.532813i \(-0.821135\pi\)
0.846233 0.532813i \(-0.178865\pi\)
\(510\) 13.7574 + 18.7279i 0.609186 + 0.829286i
\(511\) 6.00000i 0.265424i
\(512\) 22.6274i 1.00000i
\(513\) −8.48528 + 30.0000i −0.374634 + 1.32453i
\(514\) 6.00000i 0.264649i
\(515\) 29.6985 + 9.89949i 1.30867 + 0.436224i
\(516\) 16.0000 22.6274i 0.704361 0.996116i
\(517\) 12.0000i 0.527759i
\(518\) 8.48528 0.372822
\(519\) −12.7279 + 18.0000i −0.558694 + 0.790112i
\(520\) −36.0000 12.0000i −1.57870 0.526235i
\(521\) 7.07107i 0.309789i −0.987931 0.154895i \(-0.950496\pi\)
0.987931 0.154895i \(-0.0495038\pi\)
\(522\) 4.00000 + 11.3137i 0.175075 + 0.495188i
\(523\) −34.0000 −1.48672 −0.743358 0.668894i \(-0.766768\pi\)
−0.743358 + 0.668894i \(0.766768\pi\)
\(524\) 16.9706 0.741362
\(525\) −8.24264 + 2.65685i −0.359738 + 0.115955i
\(526\) −22.0000 −0.959246
\(527\) 0 0
\(528\) 16.9706 24.0000i 0.738549 1.04447i
\(529\) 21.0000 0.913043
\(530\) −8.48528 + 25.4558i −0.368577 + 1.10573i
\(531\) 0 0
\(532\) 12.0000i 0.520266i
\(533\) −8.48528 −0.367538
\(534\) 10.0000 14.1421i 0.432742 0.611990i
\(535\) 5.00000 15.0000i 0.216169 0.648507i
\(536\) 11.3137i 0.488678i
\(537\) −4.24264 + 6.00000i −0.183083 + 0.258919i
\(538\) 26.0000 1.12094
\(539\) −4.24264 −0.182743
\(540\) −19.2132 13.0711i −0.826805 0.562489i
\(541\) −16.0000 −0.687894 −0.343947 0.938989i \(-0.611764\pi\)
−0.343947 + 0.938989i \(0.611764\pi\)
\(542\) 33.9411 1.45790
\(543\) −2.00000 + 2.82843i −0.0858282 + 0.121379i
\(544\) 24.0000i 1.02899i
\(545\) 4.24264 + 1.41421i 0.181735 + 0.0605783i
\(546\) −8.48528 + 12.0000i −0.363137 + 0.513553i
\(547\) −28.0000 −1.19719 −0.598597 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) 33.9411 1.44989
\(549\) 10.0000 + 28.2843i 0.426790 + 1.20714i
\(550\) −18.0000 + 24.0000i −0.767523 + 1.02336i
\(551\) 16.9706 0.722970
\(552\) 4.00000 5.65685i 0.170251 0.240772i
\(553\) 0 0
\(554\) 8.48528 0.360505
\(555\) −13.7574 18.7279i −0.583967 0.794956i
\(556\) 24.0000i 1.01783i
\(557\) −8.48528 −0.359533 −0.179766 0.983709i \(-0.557534\pi\)
−0.179766 + 0.983709i \(0.557534\pi\)
\(558\) 0 0
\(559\) 48.0000i 2.03018i
\(560\) 8.48528 + 2.82843i 0.358569 + 0.119523i
\(561\) 18.0000 25.4558i 0.759961 1.07475i
\(562\) −4.00000 −0.168730
\(563\) 11.3137i 0.476816i −0.971165 0.238408i \(-0.923374\pi\)
0.971165 0.238408i \(-0.0766255\pi\)
\(564\) −8.00000 5.65685i −0.336861 0.238197i
\(565\) 18.0000 + 6.00000i 0.757266 + 0.252422i
\(566\) 5.65685i 0.237775i
\(567\) −7.00000 + 5.65685i −0.293972 + 0.237566i
\(568\) 36.0000i 1.51053i
\(569\) 2.82843i 0.118574i −0.998241 0.0592869i \(-0.981117\pi\)
0.998241 0.0592869i \(-0.0188827\pi\)
\(570\) −26.4853 + 19.4558i −1.10935 + 0.814916i
\(571\) 36.0000i 1.50655i 0.657704 + 0.753277i \(0.271528\pi\)
−0.657704 + 0.753277i \(0.728472\pi\)
\(572\) 50.9117i 2.12872i
\(573\) −12.7279 + 18.0000i −0.531717 + 0.751961i
\(574\) 2.00000 0.0834784
\(575\) −4.24264 + 5.65685i −0.176930 + 0.235907i
\(576\) 8.00000 + 22.6274i 0.333333 + 0.942809i
\(577\) 42.0000i 1.74848i −0.485491 0.874241i \(-0.661359\pi\)
0.485491 0.874241i \(-0.338641\pi\)
\(578\) 1.41421i 0.0588235i
\(579\) −25.4558 18.0000i −1.05791 0.748054i
\(580\) −4.00000 + 12.0000i −0.166091 + 0.498273i
\(581\) 2.82843i 0.117343i
\(582\) 8.48528 12.0000i 0.351726 0.497416i
\(583\) 36.0000 1.49097
\(584\) 16.9706 0.702247
\(585\) 40.2426 0.727922i 1.66383 0.0300959i
\(586\) 30.0000i 1.23929i
\(587\) 28.2843i 1.16742i −0.811963 0.583708i \(-0.801601\pi\)
0.811963 0.583708i \(-0.198399\pi\)
\(588\) 2.00000 2.82843i 0.0824786 0.116642i
\(589\) 0 0
\(590\) 0 0
\(591\) −25.4558 + 36.0000i −1.04711 + 1.48084i
\(592\) 24.0000i 0.986394i
\(593\) −4.24264 −0.174224 −0.0871122 0.996199i \(-0.527764\pi\)
−0.0871122 + 0.996199i \(0.527764\pi\)
\(594\) −8.48528 + 30.0000i −0.348155 + 1.23091i
\(595\) 9.00000 + 3.00000i 0.368964 + 0.122988i
\(596\) 22.6274i 0.926855i
\(597\) 8.48528 + 6.00000i 0.347279 + 0.245564i
\(598\) 12.0000i 0.490716i
\(599\) 12.7279 0.520049 0.260024 0.965602i \(-0.416269\pi\)
0.260024 + 0.965602i \(0.416269\pi\)
\(600\) −7.51472 23.3137i −0.306787 0.951778i
\(601\) −10.0000 −0.407909 −0.203954 0.978980i \(-0.565379\pi\)
−0.203954 + 0.978980i \(0.565379\pi\)
\(602\) 11.3137i 0.461112i
\(603\) 4.00000 + 11.3137i 0.162893 + 0.460730i
\(604\) 24.0000i 0.976546i
\(605\) 14.8492 + 4.94975i 0.603708 + 0.201236i
\(606\) 22.0000 31.1127i 0.893689 1.26387i
\(607\) 32.0000 1.29884 0.649420 0.760430i \(-0.275012\pi\)
0.649420 + 0.760430i \(0.275012\pi\)
\(608\) 33.9411 1.37649
\(609\) 4.00000 + 2.82843i 0.162088 + 0.114614i
\(610\) −10.0000 + 30.0000i −0.404888 + 1.21466i
\(611\) 16.9706 0.686555
\(612\) 8.48528 + 24.0000i 0.342997 + 0.970143i
\(613\) 24.0000i 0.969351i −0.874694 0.484675i \(-0.838938\pi\)
0.874694 0.484675i \(-0.161062\pi\)
\(614\) 28.2843i 1.14146i
\(615\) −3.24264 4.41421i −0.130756 0.177998i
\(616\) 12.0000i 0.483494i
\(617\) −16.9706 −0.683209 −0.341605 0.939844i \(-0.610970\pi\)
−0.341605 + 0.939844i \(0.610970\pi\)
\(618\) 28.0000 + 19.7990i 1.12633 + 0.796432i
\(619\) 12.0000i 0.482321i −0.970485 0.241160i \(-0.922472\pi\)
0.970485 0.241160i \(-0.0775280\pi\)
\(620\) 0 0
\(621\) −2.00000 + 7.07107i −0.0802572 + 0.283752i
\(622\) 36.0000i 1.44347i
\(623\) 7.07107i 0.283296i
\(624\) −33.9411 24.0000i −1.35873 0.960769i
\(625\) 7.00000 + 24.0000i 0.280000 + 0.960000i
\(626\) −25.4558 −1.01742
\(627\) 36.0000 + 25.4558i 1.43770 + 1.01661i
\(628\) 36.0000i 1.43656i
\(629\) 25.4558i 1.01499i
\(630\) −9.48528 + 0.171573i −0.377903 + 0.00683563i
\(631\) 36.0000i 1.43314i −0.697517 0.716569i \(-0.745712\pi\)
0.697517 0.716569i \(-0.254288\pi\)
\(632\) 0 0
\(633\) 16.9706 + 12.0000i 0.674519 + 0.476957i
\(634\) 36.0000i 1.42974i
\(635\) −33.9411 11.3137i −1.34691 0.448971i
\(636\) −16.9706 + 24.0000i −0.672927 + 0.951662i
\(637\) 6.00000i 0.237729i
\(638\) 16.9706 0.671871
\(639\) −12.7279 36.0000i −0.503509 1.42414i
\(640\) −8.00000 + 24.0000i −0.316228 + 0.948683i
\(641\) 48.0833i 1.89917i 0.313503 + 0.949587i \(0.398498\pi\)
−0.313503 + 0.949587i \(0.601502\pi\)
\(642\) 10.0000 14.1421i 0.394669 0.558146i
\(643\) −4.00000 −0.157745 −0.0788723 0.996885i \(-0.525132\pi\)
−0.0788723 + 0.996885i \(0.525132\pi\)
\(644\) 2.82843i 0.111456i
\(645\) −24.9706 + 18.3431i −0.983215 + 0.722261i
\(646\) 36.0000 1.41640
\(647\) 31.1127i 1.22317i 0.791180 + 0.611583i \(0.209467\pi\)
−0.791180 + 0.611583i \(0.790533\pi\)
\(648\) −16.0000 19.7990i −0.628539 0.777778i
\(649\) 0 0
\(650\) 33.9411 + 25.4558i 1.33128 + 0.998460i
\(651\) 0 0
\(652\) −40.0000 −1.56652
\(653\) 16.9706 0.664109 0.332055 0.943260i \(-0.392258\pi\)
0.332055 + 0.943260i \(0.392258\pi\)
\(654\) 4.00000 + 2.82843i 0.156412 + 0.110600i
\(655\) −18.0000 6.00000i −0.703318 0.234439i
\(656\) 5.65685i 0.220863i
\(657\) −16.9706 + 6.00000i −0.662085 + 0.234082i
\(658\) −4.00000 −0.155936
\(659\) 4.24264 0.165270 0.0826349 0.996580i \(-0.473666\pi\)
0.0826349 + 0.996580i \(0.473666\pi\)
\(660\) −26.4853 + 19.4558i −1.03094 + 0.757318i
\(661\) 14.0000 0.544537 0.272268 0.962221i \(-0.412226\pi\)
0.272268 + 0.962221i \(0.412226\pi\)
\(662\) 0 0
\(663\) −36.0000 25.4558i −1.39812 0.988623i
\(664\) 8.00000 0.310460
\(665\) −4.24264 + 12.7279i −0.164523 + 0.493568i
\(666\) −8.48528 24.0000i −0.328798 0.929981i
\(667\) 4.00000 0.154881
\(668\) 28.2843i 1.09435i
\(669\) −8.00000 + 11.3137i −0.309298 + 0.437413i
\(670\) −4.00000 + 12.0000i −0.154533 + 0.463600i
\(671\) 42.4264 1.63785
\(672\) 8.00000 + 5.65685i 0.308607 + 0.218218i
\(673\) 30.0000i 1.15642i 0.815890 + 0.578208i \(0.196248\pi\)
−0.815890 + 0.578208i \(0.803752\pi\)
\(674\) −16.9706 −0.653682
\(675\) 15.7574 + 20.6569i 0.606501 + 0.795083i
\(676\) 46.0000 1.76923
\(677\) 12.7279 0.489174 0.244587 0.969627i \(-0.421348\pi\)
0.244587 + 0.969627i \(0.421348\pi\)
\(678\) 16.9706 + 12.0000i 0.651751 + 0.460857i
\(679\) 6.00000i 0.230259i
\(680\) −8.48528 + 25.4558i −0.325396 + 0.976187i
\(681\) −32.0000 22.6274i −1.22624 0.867085i
\(682\) 0 0
\(683\) 32.5269i 1.24461i −0.782776 0.622304i \(-0.786197\pi\)
0.782776 0.622304i \(-0.213803\pi\)
\(684\) −33.9411 + 12.0000i −1.29777 + 0.458831i
\(685\) −36.0000 12.0000i −1.37549 0.458496i
\(686\) 1.41421i 0.0539949i
\(687\) −14.0000 + 19.7990i −0.534133 + 0.755379i
\(688\) 32.0000 1.21999
\(689\) 50.9117i 1.93958i
\(690\) −6.24264 + 4.58579i −0.237653 + 0.174578i
\(691\) 36.0000i 1.36950i −0.728776 0.684752i \(-0.759910\pi\)
0.728776 0.684752i \(-0.240090\pi\)
\(692\) −25.4558 −0.967686
\(693\) 4.24264 + 12.0000i 0.161165 + 0.455842i
\(694\) 2.00000 0.0759190
\(695\) 8.48528 25.4558i 0.321865 0.965595i
\(696\) −8.00000 + 11.3137i −0.303239 + 0.428845i
\(697\) 6.00000i 0.227266i
\(698\) 36.7696i 1.39175i
\(699\) 16.9706 24.0000i 0.641886 0.907763i
\(700\) −8.00000 6.00000i −0.302372 0.226779i
\(701\) 19.7990i 0.747798i −0.927470 0.373899i \(-0.878021\pi\)
0.927470 0.373899i \(-0.121979\pi\)
\(702\) 42.4264 + 12.0000i 1.60128 + 0.452911i
\(703\) −36.0000 −1.35777
\(704\) 33.9411 1.27920
\(705\) 6.48528 + 8.82843i 0.244250 + 0.332498i
\(706\) 6.00000i 0.225813i
\(707\) 15.5563i 0.585057i
\(708\) 0 0
\(709\) −10.0000 −0.375558 −0.187779 0.982211i \(-0.560129\pi\)
−0.187779 + 0.982211i \(0.560129\pi\)
\(710\) 12.7279 38.1838i 0.477670 1.43301i
\(711\) 0 0
\(712\) 20.0000 0.749532
\(713\) 0 0
\(714\) 8.48528 + 6.00000i 0.317554 + 0.224544i
\(715\) 18.0000 54.0000i 0.673162 2.01949i
\(716\) −8.48528 −0.317110
\(717\) 4.24264 6.00000i 0.158444 0.224074i
\(718\) 6.00000i 0.223918i
\(719\) 33.9411 1.26579 0.632895 0.774237i \(-0.281866\pi\)
0.632895 + 0.774237i \(0.281866\pi\)
\(720\) −0.485281 26.8284i −0.0180854 0.999836i
\(721\) 14.0000 0.521387
\(722\) 24.0416i 0.894737i
\(723\) −26.0000 + 36.7696i −0.966950 + 1.36747i
\(724\) −4.00000 −0.148659
\(725\) 8.48528 11.3137i 0.315135 0.420181i
\(726\) 14.0000 + 9.89949i 0.519589 + 0.367405i
\(727\) 26.0000 0.964287 0.482143 0.876092i \(-0.339858\pi\)
0.482143 + 0.876092i \(0.339858\pi\)
\(728\) −16.9706 −0.628971
\(729\) 23.0000 + 14.1421i 0.851852 + 0.523783i
\(730\) −18.0000 6.00000i −0.666210 0.222070i
\(731\) 33.9411 1.25536
\(732\) −20.0000 + 28.2843i −0.739221 + 1.04542i
\(733\) 6.00000i 0.221615i −0.993842 0.110808i \(-0.964656\pi\)
0.993842 0.110808i \(-0.0353437\pi\)
\(734\) 11.3137i 0.417597i
\(735\) −3.12132 + 2.29289i −0.115132 + 0.0845746i
\(736\) 8.00000 0.294884
\(737\) 16.9706 0.625119
\(738\) −2.00000 5.65685i −0.0736210 0.208232i
\(739\) 24.0000i 0.882854i −0.897297 0.441427i \(-0.854472\pi\)
0.897297 0.441427i \(-0.145528\pi\)
\(740\) 8.48528 25.4558i 0.311925 0.935775i
\(741\) 36.0000 50.9117i 1.32249 1.87029i
\(742\) 12.0000i 0.440534i
\(743\) 1.41421i 0.0518825i 0.999663 + 0.0259412i \(0.00825828\pi\)
−0.999663 + 0.0259412i \(0.991742\pi\)
\(744\) 0 0
\(745\) 8.00000 24.0000i 0.293097 0.879292i
\(746\) 16.9706 0.621336
\(747\) −8.00000 + 2.82843i −0.292705 + 0.103487i
\(748\) 36.0000 1.31629
\(749\) 7.07107i 0.258371i
\(750\) −0.272078 + 27.3848i −0.00993488 + 0.999951i
\(751\) 12.0000i 0.437886i 0.975738 + 0.218943i \(0.0702609\pi\)
−0.975738 + 0.218943i \(0.929739\pi\)
\(752\) 11.3137i 0.412568i
\(753\) 0 0
\(754\) 24.0000i 0.874028i
\(755\) 8.48528 25.4558i 0.308811 0.926433i
\(756\) −10.0000 2.82843i −0.363696 0.102869i
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) −50.9117 −1.84920
\(759\) 8.48528 + 6.00000i 0.307996 + 0.217786i
\(760\) −36.0000 12.0000i −1.30586 0.435286i
\(761\) 52.3259i 1.89681i 0.317058 + 0.948406i \(0.397305\pi\)
−0.317058 + 0.948406i \(0.602695\pi\)
\(762\) −32.0000 22.6274i −1.15924 0.819705i
\(763\) 2.00000 0.0724049
\(764\) −25.4558 −0.920960
\(765\) −0.514719 28.4558i −0.0186097 1.02882i
\(766\) −16.0000 −0.578103
\(767\) 0 0
\(768\) −16.0000 + 22.6274i −0.577350 + 0.816497i
\(769\) 14.0000 0.504853 0.252426 0.967616i \(-0.418771\pi\)
0.252426 + 0.967616i \(0.418771\pi\)
\(770\) −4.24264 + 12.7279i −0.152894 + 0.458682i
\(771\) −4.24264 + 6.00000i −0.152795 + 0.216085i
\(772\) 36.0000i 1.29567i
\(773\) 29.6985 1.06818 0.534090 0.845428i \(-0.320654\pi\)
0.534090 + 0.845428i \(0.320654\pi\)
\(774\) −32.0000 + 11.3137i −1.15022 + 0.406663i
\(775\) 0 0
\(776\) 16.9706 0.609208
\(777\) −8.48528 6.00000i −0.304408 0.215249i
\(778\) −4.00000 −0.143407
\(779\) −8.48528 −0.304017
\(780\) 27.5147 + 37.4558i 0.985185 + 1.34113i
\(781\) −54.0000 −1.93227