Properties

Label 570.2.c.e.569.2
Level $570$
Weight $2$
Character 570.569
Analytic conductor $4.551$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $8$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \(x^{8} - x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 569.2
Root \(-0.258819 + 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 570.569
Dual form 570.2.c.e.569.6

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} +(-1.41421 + 1.00000i) q^{3} -1.00000 q^{4} +(1.73205 + 1.41421i) q^{5} +(1.00000 + 1.41421i) q^{6} +2.44949i q^{7} +1.00000i q^{8} +(1.00000 - 2.82843i) q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +(-1.41421 + 1.00000i) q^{3} -1.00000 q^{4} +(1.73205 + 1.41421i) q^{5} +(1.00000 + 1.41421i) q^{6} +2.44949i q^{7} +1.00000i q^{8} +(1.00000 - 2.82843i) q^{9} +(1.41421 - 1.73205i) q^{10} +1.41421i q^{11} +(1.41421 - 1.00000i) q^{12} -4.24264 q^{13} +2.44949 q^{14} +(-3.86370 - 0.267949i) q^{15} +1.00000 q^{16} -6.92820 q^{17} +(-2.82843 - 1.00000i) q^{18} +(4.00000 - 1.73205i) q^{19} +(-1.73205 - 1.41421i) q^{20} +(-2.44949 - 3.46410i) q^{21} +1.41421 q^{22} -3.46410 q^{23} +(-1.00000 - 1.41421i) q^{24} +(1.00000 + 4.89898i) q^{25} +4.24264i q^{26} +(1.41421 + 5.00000i) q^{27} -2.44949i q^{28} -2.44949 q^{29} +(-0.267949 + 3.86370i) q^{30} +6.92820i q^{31} -1.00000i q^{32} +(-1.41421 - 2.00000i) q^{33} +6.92820i q^{34} +(-3.46410 + 4.24264i) q^{35} +(-1.00000 + 2.82843i) q^{36} +4.24264 q^{37} +(-1.73205 - 4.00000i) q^{38} +(6.00000 - 4.24264i) q^{39} +(-1.41421 + 1.73205i) q^{40} -12.2474 q^{41} +(-3.46410 + 2.44949i) q^{42} +7.34847i q^{43} -1.41421i q^{44} +(5.73205 - 3.48477i) q^{45} +3.46410i q^{46} +3.46410 q^{47} +(-1.41421 + 1.00000i) q^{48} +1.00000 q^{49} +(4.89898 - 1.00000i) q^{50} +(9.79796 - 6.92820i) q^{51} +4.24264 q^{52} +6.00000i q^{53} +(5.00000 - 1.41421i) q^{54} +(-2.00000 + 2.44949i) q^{55} -2.44949 q^{56} +(-3.92480 + 6.44949i) q^{57} +2.44949i q^{58} +4.89898 q^{59} +(3.86370 + 0.267949i) q^{60} -8.00000 q^{61} +6.92820 q^{62} +(6.92820 + 2.44949i) q^{63} -1.00000 q^{64} +(-7.34847 - 6.00000i) q^{65} +(-2.00000 + 1.41421i) q^{66} +6.92820 q^{68} +(4.89898 - 3.46410i) q^{69} +(4.24264 + 3.46410i) q^{70} +4.89898 q^{71} +(2.82843 + 1.00000i) q^{72} -14.6969i q^{73} -4.24264i q^{74} +(-6.31319 - 5.92820i) q^{75} +(-4.00000 + 1.73205i) q^{76} -3.46410 q^{77} +(-4.24264 - 6.00000i) q^{78} +10.3923i q^{79} +(1.73205 + 1.41421i) q^{80} +(-7.00000 - 5.65685i) q^{81} +12.2474i q^{82} -10.3923 q^{83} +(2.44949 + 3.46410i) q^{84} +(-12.0000 - 9.79796i) q^{85} +7.34847 q^{86} +(3.46410 - 2.44949i) q^{87} -1.41421 q^{88} +2.44949 q^{89} +(-3.48477 - 5.73205i) q^{90} -10.3923i q^{91} +3.46410 q^{92} +(-6.92820 - 9.79796i) q^{93} -3.46410i q^{94} +(9.37769 + 2.65685i) q^{95} +(1.00000 + 1.41421i) q^{96} +12.7279 q^{97} -1.00000i q^{98} +(4.00000 + 1.41421i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 8q^{4} + 8q^{6} + 8q^{9} + O(q^{10}) \) \( 8q - 8q^{4} + 8q^{6} + 8q^{9} + 8q^{16} + 32q^{19} - 8q^{24} + 8q^{25} - 16q^{30} - 8q^{36} + 48q^{39} + 32q^{45} + 8q^{49} + 40q^{54} - 16q^{55} - 64q^{61} - 8q^{64} - 16q^{66} - 32q^{76} - 56q^{81} - 96q^{85} + 8q^{96} + 32q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −1.41421 + 1.00000i −0.816497 + 0.577350i
\(4\) −1.00000 −0.500000
\(5\) 1.73205 + 1.41421i 0.774597 + 0.632456i
\(6\) 1.00000 + 1.41421i 0.408248 + 0.577350i
\(7\) 2.44949i 0.925820i 0.886405 + 0.462910i \(0.153195\pi\)
−0.886405 + 0.462910i \(0.846805\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 1.00000 2.82843i 0.333333 0.942809i
\(10\) 1.41421 1.73205i 0.447214 0.547723i
\(11\) 1.41421i 0.426401i 0.977008 + 0.213201i \(0.0683888\pi\)
−0.977008 + 0.213201i \(0.931611\pi\)
\(12\) 1.41421 1.00000i 0.408248 0.288675i
\(13\) −4.24264 −1.17670 −0.588348 0.808608i \(-0.700222\pi\)
−0.588348 + 0.808608i \(0.700222\pi\)
\(14\) 2.44949 0.654654
\(15\) −3.86370 0.267949i −0.997604 0.0691842i
\(16\) 1.00000 0.250000
\(17\) −6.92820 −1.68034 −0.840168 0.542326i \(-0.817544\pi\)
−0.840168 + 0.542326i \(0.817544\pi\)
\(18\) −2.82843 1.00000i −0.666667 0.235702i
\(19\) 4.00000 1.73205i 0.917663 0.397360i
\(20\) −1.73205 1.41421i −0.387298 0.316228i
\(21\) −2.44949 3.46410i −0.534522 0.755929i
\(22\) 1.41421 0.301511
\(23\) −3.46410 −0.722315 −0.361158 0.932505i \(-0.617618\pi\)
−0.361158 + 0.932505i \(0.617618\pi\)
\(24\) −1.00000 1.41421i −0.204124 0.288675i
\(25\) 1.00000 + 4.89898i 0.200000 + 0.979796i
\(26\) 4.24264i 0.832050i
\(27\) 1.41421 + 5.00000i 0.272166 + 0.962250i
\(28\) 2.44949i 0.462910i
\(29\) −2.44949 −0.454859 −0.227429 0.973795i \(-0.573032\pi\)
−0.227429 + 0.973795i \(0.573032\pi\)
\(30\) −0.267949 + 3.86370i −0.0489206 + 0.705412i
\(31\) 6.92820i 1.24434i 0.782881 + 0.622171i \(0.213749\pi\)
−0.782881 + 0.622171i \(0.786251\pi\)
\(32\) 1.00000i 0.176777i
\(33\) −1.41421 2.00000i −0.246183 0.348155i
\(34\) 6.92820i 1.18818i
\(35\) −3.46410 + 4.24264i −0.585540 + 0.717137i
\(36\) −1.00000 + 2.82843i −0.166667 + 0.471405i
\(37\) 4.24264 0.697486 0.348743 0.937218i \(-0.386609\pi\)
0.348743 + 0.937218i \(0.386609\pi\)
\(38\) −1.73205 4.00000i −0.280976 0.648886i
\(39\) 6.00000 4.24264i 0.960769 0.679366i
\(40\) −1.41421 + 1.73205i −0.223607 + 0.273861i
\(41\) −12.2474 −1.91273 −0.956365 0.292174i \(-0.905621\pi\)
−0.956365 + 0.292174i \(0.905621\pi\)
\(42\) −3.46410 + 2.44949i −0.534522 + 0.377964i
\(43\) 7.34847i 1.12063i 0.828279 + 0.560316i \(0.189320\pi\)
−0.828279 + 0.560316i \(0.810680\pi\)
\(44\) 1.41421i 0.213201i
\(45\) 5.73205 3.48477i 0.854484 0.519478i
\(46\) 3.46410i 0.510754i
\(47\) 3.46410 0.505291 0.252646 0.967559i \(-0.418699\pi\)
0.252646 + 0.967559i \(0.418699\pi\)
\(48\) −1.41421 + 1.00000i −0.204124 + 0.144338i
\(49\) 1.00000 0.142857
\(50\) 4.89898 1.00000i 0.692820 0.141421i
\(51\) 9.79796 6.92820i 1.37199 0.970143i
\(52\) 4.24264 0.588348
\(53\) 6.00000i 0.824163i 0.911147 + 0.412082i \(0.135198\pi\)
−0.911147 + 0.412082i \(0.864802\pi\)
\(54\) 5.00000 1.41421i 0.680414 0.192450i
\(55\) −2.00000 + 2.44949i −0.269680 + 0.330289i
\(56\) −2.44949 −0.327327
\(57\) −3.92480 + 6.44949i −0.519853 + 0.854256i
\(58\) 2.44949i 0.321634i
\(59\) 4.89898 0.637793 0.318896 0.947790i \(-0.396688\pi\)
0.318896 + 0.947790i \(0.396688\pi\)
\(60\) 3.86370 + 0.267949i 0.498802 + 0.0345921i
\(61\) −8.00000 −1.02430 −0.512148 0.858898i \(-0.671150\pi\)
−0.512148 + 0.858898i \(0.671150\pi\)
\(62\) 6.92820 0.879883
\(63\) 6.92820 + 2.44949i 0.872872 + 0.308607i
\(64\) −1.00000 −0.125000
\(65\) −7.34847 6.00000i −0.911465 0.744208i
\(66\) −2.00000 + 1.41421i −0.246183 + 0.174078i
\(67\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(68\) 6.92820 0.840168
\(69\) 4.89898 3.46410i 0.589768 0.417029i
\(70\) 4.24264 + 3.46410i 0.507093 + 0.414039i
\(71\) 4.89898 0.581402 0.290701 0.956814i \(-0.406112\pi\)
0.290701 + 0.956814i \(0.406112\pi\)
\(72\) 2.82843 + 1.00000i 0.333333 + 0.117851i
\(73\) 14.6969i 1.72015i −0.510171 0.860073i \(-0.670418\pi\)
0.510171 0.860073i \(-0.329582\pi\)
\(74\) 4.24264i 0.493197i
\(75\) −6.31319 5.92820i −0.728985 0.684530i
\(76\) −4.00000 + 1.73205i −0.458831 + 0.198680i
\(77\) −3.46410 −0.394771
\(78\) −4.24264 6.00000i −0.480384 0.679366i
\(79\) 10.3923i 1.16923i 0.811312 + 0.584613i \(0.198754\pi\)
−0.811312 + 0.584613i \(0.801246\pi\)
\(80\) 1.73205 + 1.41421i 0.193649 + 0.158114i
\(81\) −7.00000 5.65685i −0.777778 0.628539i
\(82\) 12.2474i 1.35250i
\(83\) −10.3923 −1.14070 −0.570352 0.821401i \(-0.693193\pi\)
−0.570352 + 0.821401i \(0.693193\pi\)
\(84\) 2.44949 + 3.46410i 0.267261 + 0.377964i
\(85\) −12.0000 9.79796i −1.30158 1.06274i
\(86\) 7.34847 0.792406
\(87\) 3.46410 2.44949i 0.371391 0.262613i
\(88\) −1.41421 −0.150756
\(89\) 2.44949 0.259645 0.129823 0.991537i \(-0.458559\pi\)
0.129823 + 0.991537i \(0.458559\pi\)
\(90\) −3.48477 5.73205i −0.367327 0.604211i
\(91\) 10.3923i 1.08941i
\(92\) 3.46410 0.361158
\(93\) −6.92820 9.79796i −0.718421 1.01600i
\(94\) 3.46410i 0.357295i
\(95\) 9.37769 + 2.65685i 0.962131 + 0.272587i
\(96\) 1.00000 + 1.41421i 0.102062 + 0.144338i
\(97\) 12.7279 1.29232 0.646162 0.763200i \(-0.276373\pi\)
0.646162 + 0.763200i \(0.276373\pi\)
\(98\) 1.00000i 0.101015i
\(99\) 4.00000 + 1.41421i 0.402015 + 0.142134i
\(100\) −1.00000 4.89898i −0.100000 0.489898i
\(101\) 2.82843i 0.281439i −0.990050 0.140720i \(-0.955058\pi\)
0.990050 0.140720i \(-0.0449416\pi\)
\(102\) −6.92820 9.79796i −0.685994 0.970143i
\(103\) 8.48528 0.836080 0.418040 0.908429i \(-0.362717\pi\)
0.418040 + 0.908429i \(0.362717\pi\)
\(104\) 4.24264i 0.416025i
\(105\) 0.656339 9.46410i 0.0640521 0.923602i
\(106\) 6.00000 0.582772
\(107\) 18.0000i 1.74013i −0.492941 0.870063i \(-0.664078\pi\)
0.492941 0.870063i \(-0.335922\pi\)
\(108\) −1.41421 5.00000i −0.136083 0.481125i
\(109\) 6.92820i 0.663602i 0.943349 + 0.331801i \(0.107656\pi\)
−0.943349 + 0.331801i \(0.892344\pi\)
\(110\) 2.44949 + 2.00000i 0.233550 + 0.190693i
\(111\) −6.00000 + 4.24264i −0.569495 + 0.402694i
\(112\) 2.44949i 0.231455i
\(113\) 18.0000i 1.69330i 0.532152 + 0.846649i \(0.321383\pi\)
−0.532152 + 0.846649i \(0.678617\pi\)
\(114\) 6.44949 + 3.92480i 0.604050 + 0.367592i
\(115\) −6.00000 4.89898i −0.559503 0.456832i
\(116\) 2.44949 0.227429
\(117\) −4.24264 + 12.0000i −0.392232 + 1.10940i
\(118\) 4.89898i 0.450988i
\(119\) 16.9706i 1.55569i
\(120\) 0.267949 3.86370i 0.0244603 0.352706i
\(121\) 9.00000 0.818182
\(122\) 8.00000i 0.724286i
\(123\) 17.3205 12.2474i 1.56174 1.10432i
\(124\) 6.92820i 0.622171i
\(125\) −5.19615 + 9.89949i −0.464758 + 0.885438i
\(126\) 2.44949 6.92820i 0.218218 0.617213i
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −7.34847 10.3923i −0.646997 0.914991i
\(130\) −6.00000 + 7.34847i −0.526235 + 0.644503i
\(131\) 1.41421i 0.123560i −0.998090 0.0617802i \(-0.980322\pi\)
0.998090 0.0617802i \(-0.0196778\pi\)
\(132\) 1.41421 + 2.00000i 0.123091 + 0.174078i
\(133\) 4.24264 + 9.79796i 0.367884 + 0.849591i
\(134\) 0 0
\(135\) −4.62158 + 10.6603i −0.397762 + 0.917489i
\(136\) 6.92820i 0.594089i
\(137\) 17.3205 1.47979 0.739895 0.672722i \(-0.234875\pi\)
0.739895 + 0.672722i \(0.234875\pi\)
\(138\) −3.46410 4.89898i −0.294884 0.417029i
\(139\) 4.00000 0.339276 0.169638 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 3.46410 4.24264i 0.292770 0.358569i
\(141\) −4.89898 + 3.46410i −0.412568 + 0.291730i
\(142\) 4.89898i 0.411113i
\(143\) 6.00000i 0.501745i
\(144\) 1.00000 2.82843i 0.0833333 0.235702i
\(145\) −4.24264 3.46410i −0.352332 0.287678i
\(146\) −14.6969 −1.21633
\(147\) −1.41421 + 1.00000i −0.116642 + 0.0824786i
\(148\) −4.24264 −0.348743
\(149\) 11.3137i 0.926855i −0.886135 0.463428i \(-0.846619\pi\)
0.886135 0.463428i \(-0.153381\pi\)
\(150\) −5.92820 + 6.31319i −0.484036 + 0.515470i
\(151\) 13.8564i 1.12762i 0.825905 + 0.563809i \(0.190665\pi\)
−0.825905 + 0.563809i \(0.809335\pi\)
\(152\) 1.73205 + 4.00000i 0.140488 + 0.324443i
\(153\) −6.92820 + 19.5959i −0.560112 + 1.58424i
\(154\) 3.46410i 0.279145i
\(155\) −9.79796 + 12.0000i −0.786991 + 0.963863i
\(156\) −6.00000 + 4.24264i −0.480384 + 0.339683i
\(157\) 14.6969i 1.17294i −0.809970 0.586472i \(-0.800517\pi\)
0.809970 0.586472i \(-0.199483\pi\)
\(158\) 10.3923 0.826767
\(159\) −6.00000 8.48528i −0.475831 0.672927i
\(160\) 1.41421 1.73205i 0.111803 0.136931i
\(161\) 8.48528i 0.668734i
\(162\) −5.65685 + 7.00000i −0.444444 + 0.549972i
\(163\) 12.2474i 0.959294i 0.877461 + 0.479647i \(0.159235\pi\)
−0.877461 + 0.479647i \(0.840765\pi\)
\(164\) 12.2474 0.956365
\(165\) 0.378937 5.46410i 0.0295002 0.425380i
\(166\) 10.3923i 0.806599i
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 3.46410 2.44949i 0.267261 0.188982i
\(169\) 5.00000 0.384615
\(170\) −9.79796 + 12.0000i −0.751469 + 0.920358i
\(171\) −0.898979 13.0458i −0.0687467 0.997634i
\(172\) 7.34847i 0.560316i
\(173\) 6.00000i 0.456172i 0.973641 + 0.228086i \(0.0732467\pi\)
−0.973641 + 0.228086i \(0.926753\pi\)
\(174\) −2.44949 3.46410i −0.185695 0.262613i
\(175\) −12.0000 + 2.44949i −0.907115 + 0.185164i
\(176\) 1.41421i 0.106600i
\(177\) −6.92820 + 4.89898i −0.520756 + 0.368230i
\(178\) 2.44949i 0.183597i
\(179\) 4.89898 0.366167 0.183083 0.983097i \(-0.441392\pi\)
0.183083 + 0.983097i \(0.441392\pi\)
\(180\) −5.73205 + 3.48477i −0.427242 + 0.259739i
\(181\) 13.8564i 1.02994i −0.857209 0.514969i \(-0.827803\pi\)
0.857209 0.514969i \(-0.172197\pi\)
\(182\) −10.3923 −0.770329
\(183\) 11.3137 8.00000i 0.836333 0.591377i
\(184\) 3.46410i 0.255377i
\(185\) 7.34847 + 6.00000i 0.540270 + 0.441129i
\(186\) −9.79796 + 6.92820i −0.718421 + 0.508001i
\(187\) 9.79796i 0.716498i
\(188\) −3.46410 −0.252646
\(189\) −12.2474 + 3.46410i −0.890871 + 0.251976i
\(190\) 2.65685 9.37769i 0.192748 0.680329i
\(191\) 24.0416i 1.73959i 0.493412 + 0.869796i \(0.335749\pi\)
−0.493412 + 0.869796i \(0.664251\pi\)
\(192\) 1.41421 1.00000i 0.102062 0.0721688i
\(193\) 12.7279 0.916176 0.458088 0.888907i \(-0.348534\pi\)
0.458088 + 0.888907i \(0.348534\pi\)
\(194\) 12.7279i 0.913812i
\(195\) 16.3923 + 1.13681i 1.17388 + 0.0814088i
\(196\) −1.00000 −0.0714286
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 1.41421 4.00000i 0.100504 0.284268i
\(199\) −16.0000 −1.13421 −0.567105 0.823646i \(-0.691937\pi\)
−0.567105 + 0.823646i \(0.691937\pi\)
\(200\) −4.89898 + 1.00000i −0.346410 + 0.0707107i
\(201\) 0 0
\(202\) −2.82843 −0.199007
\(203\) 6.00000i 0.421117i
\(204\) −9.79796 + 6.92820i −0.685994 + 0.485071i
\(205\) −21.2132 17.3205i −1.48159 1.20972i
\(206\) 8.48528i 0.591198i
\(207\) −3.46410 + 9.79796i −0.240772 + 0.681005i
\(208\) −4.24264 −0.294174
\(209\) 2.44949 + 5.65685i 0.169435 + 0.391293i
\(210\) −9.46410 0.656339i −0.653085 0.0452917i
\(211\) 3.46410i 0.238479i 0.992866 + 0.119239i \(0.0380456\pi\)
−0.992866 + 0.119239i \(0.961954\pi\)
\(212\) 6.00000i 0.412082i
\(213\) −6.92820 + 4.89898i −0.474713 + 0.335673i
\(214\) −18.0000 −1.23045
\(215\) −10.3923 + 12.7279i −0.708749 + 0.868037i
\(216\) −5.00000 + 1.41421i −0.340207 + 0.0962250i
\(217\) −16.9706 −1.15204
\(218\) 6.92820 0.469237
\(219\) 14.6969 + 20.7846i 0.993127 + 1.40449i
\(220\) 2.00000 2.44949i 0.134840 0.165145i
\(221\) 29.3939 1.97725
\(222\) 4.24264 + 6.00000i 0.284747 + 0.402694i
\(223\) 25.4558 1.70465 0.852325 0.523013i \(-0.175192\pi\)
0.852325 + 0.523013i \(0.175192\pi\)
\(224\) 2.44949 0.163663
\(225\) 14.8564 + 2.07055i 0.990427 + 0.138037i
\(226\) 18.0000 1.19734
\(227\) 12.0000i 0.796468i −0.917284 0.398234i \(-0.869623\pi\)
0.917284 0.398234i \(-0.130377\pi\)
\(228\) 3.92480 6.44949i 0.259926 0.427128i
\(229\) 28.0000 1.85029 0.925146 0.379611i \(-0.123942\pi\)
0.925146 + 0.379611i \(0.123942\pi\)
\(230\) −4.89898 + 6.00000i −0.323029 + 0.395628i
\(231\) 4.89898 3.46410i 0.322329 0.227921i
\(232\) 2.44949i 0.160817i
\(233\) 10.3923 0.680823 0.340411 0.940277i \(-0.389434\pi\)
0.340411 + 0.940277i \(0.389434\pi\)
\(234\) 12.0000 + 4.24264i 0.784465 + 0.277350i
\(235\) 6.00000 + 4.89898i 0.391397 + 0.319574i
\(236\) −4.89898 −0.318896
\(237\) −10.3923 14.6969i −0.675053 0.954669i
\(238\) −16.9706 −1.10004
\(239\) 1.41421i 0.0914779i −0.998953 0.0457389i \(-0.985436\pi\)
0.998953 0.0457389i \(-0.0145642\pi\)
\(240\) −3.86370 0.267949i −0.249401 0.0172960i
\(241\) 13.8564i 0.892570i 0.894891 + 0.446285i \(0.147253\pi\)
−0.894891 + 0.446285i \(0.852747\pi\)
\(242\) 9.00000i 0.578542i
\(243\) 15.5563 + 1.00000i 0.997940 + 0.0641500i
\(244\) 8.00000 0.512148
\(245\) 1.73205 + 1.41421i 0.110657 + 0.0903508i
\(246\) −12.2474 17.3205i −0.780869 1.10432i
\(247\) −16.9706 + 7.34847i −1.07981 + 0.467572i
\(248\) −6.92820 −0.439941
\(249\) 14.6969 10.3923i 0.931381 0.658586i
\(250\) 9.89949 + 5.19615i 0.626099 + 0.328634i
\(251\) 1.41421i 0.0892644i −0.999003 0.0446322i \(-0.985788\pi\)
0.999003 0.0446322i \(-0.0142116\pi\)
\(252\) −6.92820 2.44949i −0.436436 0.154303i
\(253\) 4.89898i 0.307996i
\(254\) 0 0
\(255\) 26.7685 + 1.85641i 1.67631 + 0.116253i
\(256\) 1.00000 0.0625000
\(257\) 6.00000i 0.374270i −0.982334 0.187135i \(-0.940080\pi\)
0.982334 0.187135i \(-0.0599201\pi\)
\(258\) −10.3923 + 7.34847i −0.646997 + 0.457496i
\(259\) 10.3923i 0.645746i
\(260\) 7.34847 + 6.00000i 0.455733 + 0.372104i
\(261\) −2.44949 + 6.92820i −0.151620 + 0.428845i
\(262\) −1.41421 −0.0873704
\(263\) 3.46410 0.213606 0.106803 0.994280i \(-0.465939\pi\)
0.106803 + 0.994280i \(0.465939\pi\)
\(264\) 2.00000 1.41421i 0.123091 0.0870388i
\(265\) −8.48528 + 10.3923i −0.521247 + 0.638394i
\(266\) 9.79796 4.24264i 0.600751 0.260133i
\(267\) −3.46410 + 2.44949i −0.212000 + 0.149906i
\(268\) 0 0
\(269\) −17.1464 −1.04544 −0.522718 0.852506i \(-0.675082\pi\)
−0.522718 + 0.852506i \(0.675082\pi\)
\(270\) 10.6603 + 4.62158i 0.648762 + 0.281260i
\(271\) 4.00000 0.242983 0.121491 0.992592i \(-0.461232\pi\)
0.121491 + 0.992592i \(0.461232\pi\)
\(272\) −6.92820 −0.420084
\(273\) 10.3923 + 14.6969i 0.628971 + 0.889499i
\(274\) 17.3205i 1.04637i
\(275\) −6.92820 + 1.41421i −0.417786 + 0.0852803i
\(276\) −4.89898 + 3.46410i −0.294884 + 0.208514i
\(277\) 19.5959i 1.17740i 0.808350 + 0.588702i \(0.200361\pi\)
−0.808350 + 0.588702i \(0.799639\pi\)
\(278\) 4.00000i 0.239904i
\(279\) 19.5959 + 6.92820i 1.17318 + 0.414781i
\(280\) −4.24264 3.46410i −0.253546 0.207020i
\(281\) −7.34847 −0.438373 −0.219186 0.975683i \(-0.570340\pi\)
−0.219186 + 0.975683i \(0.570340\pi\)
\(282\) 3.46410 + 4.89898i 0.206284 + 0.291730i
\(283\) 12.2474i 0.728035i 0.931392 + 0.364018i \(0.118595\pi\)
−0.931392 + 0.364018i \(0.881405\pi\)
\(284\) −4.89898 −0.290701
\(285\) −15.9189 + 5.62033i −0.942955 + 0.332920i
\(286\) −6.00000 −0.354787
\(287\) 30.0000i 1.77084i
\(288\) −2.82843 1.00000i −0.166667 0.0589256i
\(289\) 31.0000 1.82353
\(290\) −3.46410 + 4.24264i −0.203419 + 0.249136i
\(291\) −18.0000 + 12.7279i −1.05518 + 0.746124i
\(292\) 14.6969i 0.860073i
\(293\) 6.00000i 0.350524i −0.984522 0.175262i \(-0.943923\pi\)
0.984522 0.175262i \(-0.0560772\pi\)
\(294\) 1.00000 + 1.41421i 0.0583212 + 0.0824786i
\(295\) 8.48528 + 6.92820i 0.494032 + 0.403376i
\(296\) 4.24264i 0.246598i
\(297\) −7.07107 + 2.00000i −0.410305 + 0.116052i
\(298\) −11.3137 −0.655386
\(299\) 14.6969 0.849946
\(300\) 6.31319 + 5.92820i 0.364492 + 0.342265i
\(301\) −18.0000 −1.03750
\(302\) 13.8564 0.797347
\(303\) 2.82843 + 4.00000i 0.162489 + 0.229794i
\(304\) 4.00000 1.73205i 0.229416 0.0993399i
\(305\) −13.8564 11.3137i −0.793416 0.647821i
\(306\) 19.5959 + 6.92820i 1.12022 + 0.396059i
\(307\) −25.4558 −1.45284 −0.726421 0.687250i \(-0.758818\pi\)
−0.726421 + 0.687250i \(0.758818\pi\)
\(308\) 3.46410 0.197386
\(309\) −12.0000 + 8.48528i −0.682656 + 0.482711i
\(310\) 12.0000 + 9.79796i 0.681554 + 0.556487i
\(311\) 26.8701i 1.52366i 0.647776 + 0.761831i \(0.275699\pi\)
−0.647776 + 0.761831i \(0.724301\pi\)
\(312\) 4.24264 + 6.00000i 0.240192 + 0.339683i
\(313\) 4.89898i 0.276907i 0.990369 + 0.138453i \(0.0442131\pi\)
−0.990369 + 0.138453i \(0.955787\pi\)
\(314\) −14.6969 −0.829396
\(315\) 8.53590 + 14.0406i 0.480943 + 0.791098i
\(316\) 10.3923i 0.584613i
\(317\) 18.0000i 1.01098i −0.862832 0.505490i \(-0.831312\pi\)
0.862832 0.505490i \(-0.168688\pi\)
\(318\) −8.48528 + 6.00000i −0.475831 + 0.336463i
\(319\) 3.46410i 0.193952i
\(320\) −1.73205 1.41421i −0.0968246 0.0790569i
\(321\) 18.0000 + 25.4558i 1.00466 + 1.42081i
\(322\) −8.48528 −0.472866
\(323\) −27.7128 + 12.0000i −1.54198 + 0.667698i
\(324\) 7.00000 + 5.65685i 0.388889 + 0.314270i
\(325\) −4.24264 20.7846i −0.235339 1.15292i
\(326\) 12.2474 0.678323
\(327\) −6.92820 9.79796i −0.383131 0.541828i
\(328\) 12.2474i 0.676252i
\(329\) 8.48528i 0.467809i
\(330\) −5.46410 0.378937i −0.300789 0.0208598i
\(331\) 6.92820i 0.380808i −0.981706 0.190404i \(-0.939020\pi\)
0.981706 0.190404i \(-0.0609799\pi\)
\(332\) 10.3923 0.570352
\(333\) 4.24264 12.0000i 0.232495 0.657596i
\(334\) 0 0
\(335\) 0 0
\(336\) −2.44949 3.46410i −0.133631 0.188982i
\(337\) 4.24264 0.231111 0.115556 0.993301i \(-0.463135\pi\)
0.115556 + 0.993301i \(0.463135\pi\)
\(338\) 5.00000i 0.271964i
\(339\) −18.0000 25.4558i −0.977626 1.38257i
\(340\) 12.0000 + 9.79796i 0.650791 + 0.531369i
\(341\) −9.79796 −0.530589
\(342\) −13.0458 + 0.898979i −0.705434 + 0.0486112i
\(343\) 19.5959i 1.05808i
\(344\) −7.34847 −0.396203
\(345\) 13.3843 + 0.928203i 0.720584 + 0.0499728i
\(346\) 6.00000 0.322562
\(347\) 24.2487 1.30174 0.650870 0.759190i \(-0.274404\pi\)
0.650870 + 0.759190i \(0.274404\pi\)
\(348\) −3.46410 + 2.44949i −0.185695 + 0.131306i
\(349\) −22.0000 −1.17763 −0.588817 0.808267i \(-0.700406\pi\)
−0.588817 + 0.808267i \(0.700406\pi\)
\(350\) 2.44949 + 12.0000i 0.130931 + 0.641427i
\(351\) −6.00000 21.2132i −0.320256 1.13228i
\(352\) 1.41421 0.0753778
\(353\) −17.3205 −0.921878 −0.460939 0.887432i \(-0.652487\pi\)
−0.460939 + 0.887432i \(0.652487\pi\)
\(354\) 4.89898 + 6.92820i 0.260378 + 0.368230i
\(355\) 8.48528 + 6.92820i 0.450352 + 0.367711i
\(356\) −2.44949 −0.129823
\(357\) 16.9706 + 24.0000i 0.898177 + 1.27021i
\(358\) 4.89898i 0.258919i
\(359\) 18.3848i 0.970311i 0.874428 + 0.485156i \(0.161237\pi\)
−0.874428 + 0.485156i \(0.838763\pi\)
\(360\) 3.48477 + 5.73205i 0.183663 + 0.302106i
\(361\) 13.0000 13.8564i 0.684211 0.729285i
\(362\) −13.8564 −0.728277
\(363\) −12.7279 + 9.00000i −0.668043 + 0.472377i
\(364\) 10.3923i 0.544705i
\(365\) 20.7846 25.4558i 1.08792 1.33242i
\(366\) −8.00000 11.3137i −0.418167 0.591377i
\(367\) 31.8434i 1.66221i −0.556115 0.831105i \(-0.687709\pi\)
0.556115 0.831105i \(-0.312291\pi\)
\(368\) −3.46410 −0.180579
\(369\) −12.2474 + 34.6410i −0.637577 + 1.80334i
\(370\) 6.00000 7.34847i 0.311925 0.382029i
\(371\) −14.6969 −0.763027
\(372\) 6.92820 + 9.79796i 0.359211 + 0.508001i
\(373\) 12.7279 0.659027 0.329513 0.944151i \(-0.393115\pi\)
0.329513 + 0.944151i \(0.393115\pi\)
\(374\) −9.79796 −0.506640
\(375\) −2.55103 19.1962i −0.131734 0.991285i
\(376\) 3.46410i 0.178647i
\(377\) 10.3923 0.535231
\(378\) 3.46410 + 12.2474i 0.178174 + 0.629941i
\(379\) 20.7846i 1.06763i −0.845600 0.533817i \(-0.820757\pi\)
0.845600 0.533817i \(-0.179243\pi\)
\(380\) −9.37769 2.65685i −0.481065 0.136294i
\(381\) 0 0
\(382\) 24.0416 1.23008
\(383\) 6.00000i 0.306586i 0.988181 + 0.153293i \(0.0489878\pi\)
−0.988181 + 0.153293i \(0.951012\pi\)
\(384\) −1.00000 1.41421i −0.0510310 0.0721688i
\(385\) −6.00000 4.89898i −0.305788 0.249675i
\(386\) 12.7279i 0.647834i
\(387\) 20.7846 + 7.34847i 1.05654 + 0.373544i
\(388\) −12.7279 −0.646162
\(389\) 19.7990i 1.00385i 0.864912 + 0.501924i \(0.167374\pi\)
−0.864912 + 0.501924i \(0.832626\pi\)
\(390\) 1.13681 16.3923i 0.0575647 0.830057i
\(391\) 24.0000 1.21373
\(392\) 1.00000i 0.0505076i
\(393\) 1.41421 + 2.00000i 0.0713376 + 0.100887i
\(394\) 0 0
\(395\) −14.6969 + 18.0000i −0.739483 + 0.905678i
\(396\) −4.00000 1.41421i −0.201008 0.0710669i
\(397\) 19.5959i 0.983491i 0.870739 + 0.491745i \(0.163641\pi\)
−0.870739 + 0.491745i \(0.836359\pi\)
\(398\) 16.0000i 0.802008i
\(399\) −15.7980 9.61377i −0.790887 0.481290i
\(400\) 1.00000 + 4.89898i 0.0500000 + 0.244949i
\(401\) −22.0454 −1.10090 −0.550448 0.834870i \(-0.685543\pi\)
−0.550448 + 0.834870i \(0.685543\pi\)
\(402\) 0 0
\(403\) 29.3939i 1.46421i
\(404\) 2.82843i 0.140720i
\(405\) −4.12436 19.6975i −0.204941 0.978774i
\(406\) −6.00000 −0.297775
\(407\) 6.00000i 0.297409i
\(408\) 6.92820 + 9.79796i 0.342997 + 0.485071i
\(409\) 20.7846i 1.02773i −0.857870 0.513866i \(-0.828213\pi\)
0.857870 0.513866i \(-0.171787\pi\)
\(410\) −17.3205 + 21.2132i −0.855399 + 1.04765i
\(411\) −24.4949 + 17.3205i −1.20824 + 0.854358i
\(412\) −8.48528 −0.418040
\(413\) 12.0000i 0.590481i
\(414\) 9.79796 + 3.46410i 0.481543 + 0.170251i
\(415\) −18.0000 14.6969i −0.883585 0.721444i
\(416\) 4.24264i 0.208013i
\(417\) −5.65685 + 4.00000i −0.277017 + 0.195881i
\(418\) 5.65685 2.44949i 0.276686 0.119808i
\(419\) 9.89949i 0.483622i −0.970323 0.241811i \(-0.922259\pi\)
0.970323 0.241811i \(-0.0777414\pi\)
\(420\) −0.656339 + 9.46410i −0.0320261 + 0.461801i
\(421\) 13.8564i 0.675320i 0.941268 + 0.337660i \(0.109635\pi\)
−0.941268 + 0.337660i \(0.890365\pi\)
\(422\) 3.46410 0.168630
\(423\) 3.46410 9.79796i 0.168430 0.476393i
\(424\) −6.00000 −0.291386
\(425\) −6.92820 33.9411i −0.336067 1.64639i
\(426\) 4.89898 + 6.92820i 0.237356 + 0.335673i
\(427\) 19.5959i 0.948313i
\(428\) 18.0000i 0.870063i
\(429\) 6.00000 + 8.48528i 0.289683 + 0.409673i
\(430\) 12.7279 + 10.3923i 0.613795 + 0.501161i
\(431\) 19.5959 0.943902 0.471951 0.881625i \(-0.343550\pi\)
0.471951 + 0.881625i \(0.343550\pi\)
\(432\) 1.41421 + 5.00000i 0.0680414 + 0.240563i
\(433\) −38.1838 −1.83499 −0.917497 0.397742i \(-0.869794\pi\)
−0.917497 + 0.397742i \(0.869794\pi\)
\(434\) 16.9706i 0.814613i
\(435\) 9.46410 + 0.656339i 0.453769 + 0.0314690i
\(436\) 6.92820i 0.331801i
\(437\) −13.8564 + 6.00000i −0.662842 + 0.287019i
\(438\) 20.7846 14.6969i 0.993127 0.702247i
\(439\) 3.46410i 0.165333i 0.996577 + 0.0826663i \(0.0263436\pi\)
−0.996577 + 0.0826663i \(0.973656\pi\)
\(440\) −2.44949 2.00000i −0.116775 0.0953463i
\(441\) 1.00000 2.82843i 0.0476190 0.134687i
\(442\) 29.3939i 1.39812i
\(443\) −17.3205 −0.822922 −0.411461 0.911427i \(-0.634981\pi\)
−0.411461 + 0.911427i \(0.634981\pi\)
\(444\) 6.00000 4.24264i 0.284747 0.201347i
\(445\) 4.24264 + 3.46410i 0.201120 + 0.164214i
\(446\) 25.4558i 1.20537i
\(447\) 11.3137 + 16.0000i 0.535120 + 0.756774i
\(448\) 2.44949i 0.115728i
\(449\) −12.2474 −0.577993 −0.288996 0.957330i \(-0.593322\pi\)
−0.288996 + 0.957330i \(0.593322\pi\)
\(450\) 2.07055 14.8564i 0.0976068 0.700338i
\(451\) 17.3205i 0.815591i
\(452\) 18.0000i 0.846649i
\(453\) −13.8564 19.5959i −0.651031 0.920697i
\(454\) −12.0000 −0.563188
\(455\) 14.6969 18.0000i 0.689003 0.843853i
\(456\) −6.44949 3.92480i −0.302025 0.183796i
\(457\) 24.4949i 1.14582i 0.819617 + 0.572911i \(0.194186\pi\)
−0.819617 + 0.572911i \(0.805814\pi\)
\(458\) 28.0000i 1.30835i
\(459\) −9.79796 34.6410i −0.457330 1.61690i
\(460\) 6.00000 + 4.89898i 0.279751 + 0.228416i
\(461\) 22.6274i 1.05386i −0.849907 0.526932i \(-0.823342\pi\)
0.849907 0.526932i \(-0.176658\pi\)
\(462\) −3.46410 4.89898i −0.161165 0.227921i
\(463\) 12.2474i 0.569187i −0.958648 0.284594i \(-0.908141\pi\)
0.958648 0.284594i \(-0.0918587\pi\)
\(464\) −2.44949 −0.113715
\(465\) 1.85641 26.7685i 0.0860888 1.24136i
\(466\) 10.3923i 0.481414i
\(467\) −24.2487 −1.12210 −0.561048 0.827783i \(-0.689602\pi\)
−0.561048 + 0.827783i \(0.689602\pi\)
\(468\) 4.24264 12.0000i 0.196116 0.554700i
\(469\) 0 0
\(470\) 4.89898 6.00000i 0.225973 0.276759i
\(471\) 14.6969 + 20.7846i 0.677199 + 0.957704i
\(472\) 4.89898i 0.225494i
\(473\) −10.3923 −0.477839
\(474\) −14.6969 + 10.3923i −0.675053 + 0.477334i
\(475\) 12.4853 + 17.8639i 0.572864 + 0.819650i
\(476\) 16.9706i 0.777844i
\(477\) 16.9706 + 6.00000i 0.777029 + 0.274721i
\(478\) −1.41421 −0.0646846
\(479\) 9.89949i 0.452319i 0.974090 + 0.226160i \(0.0726171\pi\)
−0.974090 + 0.226160i \(0.927383\pi\)
\(480\) −0.267949 + 3.86370i −0.0122302 + 0.176353i
\(481\) −18.0000 −0.820729
\(482\) 13.8564 0.631142
\(483\) 8.48528 + 12.0000i 0.386094 + 0.546019i
\(484\) −9.00000 −0.409091
\(485\) 22.0454 + 18.0000i 1.00103 + 0.817338i
\(486\) 1.00000 15.5563i 0.0453609 0.705650i
\(487\) −33.9411 −1.53802 −0.769010 0.639237i \(-0.779250\pi\)
−0.769010 + 0.639237i \(0.779250\pi\)
\(488\) 8.00000i 0.362143i
\(489\) −12.2474 17.3205i −0.553849 0.783260i
\(490\) 1.41421 1.73205i 0.0638877 0.0782461i
\(491\) 7.07107i 0.319113i 0.987189 + 0.159556i \(0.0510064\pi\)
−0.987189 + 0.159556i \(0.948994\pi\)
\(492\) −17.3205 + 12.2474i −0.780869 + 0.552158i
\(493\) 16.9706 0.764316
\(494\) 7.34847 + 16.9706i 0.330623 + 0.763542i
\(495\) 4.92820 + 8.10634i 0.221506 + 0.364353i
\(496\) 6.92820i 0.311086i
\(497\) 12.0000i 0.538274i
\(498\) −10.3923 14.6969i −0.465690 0.658586i
\(499\) −20.0000 −0.895323 −0.447661 0.894203i \(-0.647743\pi\)
−0.447661 + 0.894203i \(0.647743\pi\)
\(500\) 5.19615 9.89949i 0.232379 0.442719i
\(501\) 0 0
\(502\) −1.41421 −0.0631194
\(503\) 17.3205 0.772283 0.386142 0.922440i \(-0.373808\pi\)
0.386142 + 0.922440i \(0.373808\pi\)
\(504\) −2.44949 + 6.92820i −0.109109 + 0.308607i
\(505\) 4.00000 4.89898i 0.177998 0.218002i
\(506\) −4.89898 −0.217786
\(507\) −7.07107 + 5.00000i −0.314037 + 0.222058i
\(508\) 0 0
\(509\) −22.0454 −0.977146 −0.488573 0.872523i \(-0.662482\pi\)
−0.488573 + 0.872523i \(0.662482\pi\)
\(510\) 1.85641 26.7685i 0.0822031 1.18533i
\(511\) 36.0000 1.59255
\(512\) 1.00000i 0.0441942i
\(513\) 14.3171 + 17.5505i 0.632116 + 0.774874i
\(514\) −6.00000 −0.264649
\(515\) 14.6969 + 12.0000i 0.647624 + 0.528783i
\(516\) 7.34847 + 10.3923i 0.323498 + 0.457496i
\(517\) 4.89898i 0.215457i
\(518\) 10.3923 0.456612
\(519\) −6.00000 8.48528i −0.263371 0.372463i
\(520\) 6.00000 7.34847i 0.263117 0.322252i
\(521\) 22.0454 0.965827 0.482913 0.875668i \(-0.339579\pi\)
0.482913 + 0.875668i \(0.339579\pi\)
\(522\) 6.92820 + 2.44949i 0.303239 + 0.107211i
\(523\) −16.9706 −0.742071 −0.371035 0.928619i \(-0.620997\pi\)
−0.371035 + 0.928619i \(0.620997\pi\)
\(524\) 1.41421i 0.0617802i
\(525\) 14.5211 15.4641i 0.633752 0.674909i
\(526\) 3.46410i 0.151042i
\(527\) 48.0000i 2.09091i
\(528\) −1.41421 2.00000i −0.0615457 0.0870388i
\(529\) −11.0000 −0.478261
\(530\) 10.3923 + 8.48528i 0.451413 + 0.368577i
\(531\) 4.89898 13.8564i 0.212598 0.601317i
\(532\) −4.24264 9.79796i −0.183942 0.424795i
\(533\) 51.9615 2.25070
\(534\) 2.44949 + 3.46410i 0.106000 + 0.149906i
\(535\) 25.4558 31.1769i 1.10055 1.34790i
\(536\) 0 0
\(537\) −6.92820 + 4.89898i −0.298974 + 0.211407i
\(538\) 17.1464i 0.739235i
\(539\) 1.41421i 0.0609145i
\(540\) 4.62158 10.6603i 0.198881 0.458744i
\(541\) −2.00000 −0.0859867 −0.0429934 0.999075i \(-0.513689\pi\)
−0.0429934 + 0.999075i \(0.513689\pi\)
\(542\) 4.00000i 0.171815i
\(543\) 13.8564 + 19.5959i 0.594635 + 0.840941i
\(544\) 6.92820i 0.297044i
\(545\) −9.79796 + 12.0000i −0.419698 + 0.514024i
\(546\) 14.6969 10.3923i 0.628971 0.444750i
\(547\) 25.4558 1.08841 0.544207 0.838951i \(-0.316831\pi\)
0.544207 + 0.838951i \(0.316831\pi\)
\(548\) −17.3205 −0.739895
\(549\) −8.00000 + 22.6274i −0.341432 + 0.965715i
\(550\) 1.41421 + 6.92820i 0.0603023 + 0.295420i
\(551\) −9.79796 + 4.24264i −0.417407 + 0.180743i
\(552\) 3.46410 + 4.89898i 0.147442 + 0.208514i
\(553\) −25.4558 −1.08249
\(554\) 19.5959 0.832551
\(555\) −16.3923 1.13681i −0.695815 0.0482550i
\(556\) −4.00000 −0.169638
\(557\) 10.3923 0.440336 0.220168 0.975462i \(-0.429339\pi\)
0.220168 + 0.975462i \(0.429339\pi\)
\(558\) 6.92820 19.5959i 0.293294 0.829561i
\(559\) 31.1769i 1.31864i
\(560\) −3.46410 + 4.24264i −0.146385 + 0.179284i
\(561\) 9.79796 + 13.8564i 0.413670 + 0.585018i
\(562\) 7.34847i 0.309976i
\(563\) 36.0000i 1.51722i 0.651546 + 0.758610i \(0.274121\pi\)
−0.651546 + 0.758610i \(0.725879\pi\)
\(564\) 4.89898 3.46410i 0.206284 0.145865i
\(565\) −25.4558 + 31.1769i −1.07094 + 1.31162i
\(566\) 12.2474 0.514799
\(567\) 13.8564 17.1464i 0.581914 0.720082i
\(568\) 4.89898i 0.205557i
\(569\) 46.5403 1.95107 0.975536 0.219842i \(-0.0705541\pi\)
0.975536 + 0.219842i \(0.0705541\pi\)
\(570\) 5.62033 + 15.9189i 0.235410 + 0.666770i
\(571\) 4.00000 0.167395 0.0836974 0.996491i \(-0.473327\pi\)
0.0836974 + 0.996491i \(0.473327\pi\)
\(572\) 6.00000i 0.250873i
\(573\) −24.0416 34.0000i −1.00435 1.42037i
\(574\) −30.0000 −1.25218
\(575\) −3.46410 16.9706i −0.144463 0.707721i
\(576\) −1.00000 + 2.82843i −0.0416667 + 0.117851i
\(577\) 24.4949i 1.01974i −0.860253 0.509868i \(-0.829694\pi\)
0.860253 0.509868i \(-0.170306\pi\)
\(578\) 31.0000i 1.28943i
\(579\) −18.0000 + 12.7279i −0.748054 + 0.528954i
\(580\) 4.24264 + 3.46410i 0.176166 + 0.143839i
\(581\) 25.4558i 1.05609i
\(582\) 12.7279 + 18.0000i 0.527589 + 0.746124i
\(583\) −8.48528 −0.351424
\(584\) 14.6969 0.608164
\(585\) −24.3190 + 14.7846i −1.00547 + 0.611268i
\(586\) −6.00000 −0.247858
\(587\) 3.46410 0.142979 0.0714894 0.997441i \(-0.477225\pi\)
0.0714894 + 0.997441i \(0.477225\pi\)
\(588\) 1.41421 1.00000i 0.0583212 0.0412393i
\(589\) 12.0000 + 27.7128i 0.494451 + 1.14189i
\(590\) 6.92820 8.48528i 0.285230 0.349334i
\(591\) 0 0
\(592\) 4.24264 0.174371
\(593\) 3.46410 0.142254 0.0711268 0.997467i \(-0.477341\pi\)
0.0711268 + 0.997467i \(0.477341\pi\)
\(594\) 2.00000 + 7.07107i 0.0820610 + 0.290129i
\(595\) 24.0000 29.3939i 0.983904 1.20503i
\(596\) 11.3137i 0.463428i
\(597\) 22.6274 16.0000i 0.926079 0.654836i
\(598\) 14.6969i 0.601003i
\(599\) 4.89898 0.200167 0.100083 0.994979i \(-0.468089\pi\)
0.100083 + 0.994979i \(0.468089\pi\)
\(600\) 5.92820 6.31319i 0.242018 0.257735i
\(601\) 6.92820i 0.282607i −0.989966 0.141304i \(-0.954871\pi\)
0.989966 0.141304i \(-0.0451294\pi\)
\(602\) 18.0000i 0.733625i
\(603\) 0 0
\(604\) 13.8564i 0.563809i
\(605\) 15.5885 + 12.7279i 0.633761 + 0.517464i
\(606\) 4.00000 2.82843i 0.162489 0.114897i
\(607\) 16.9706 0.688814 0.344407 0.938820i \(-0.388080\pi\)
0.344407 + 0.938820i \(0.388080\pi\)
\(608\) −1.73205 4.00000i −0.0702439 0.162221i
\(609\) 6.00000 + 8.48528i 0.243132 + 0.343841i
\(610\) −11.3137 + 13.8564i −0.458079 + 0.561029i
\(611\) −14.6969 −0.594574
\(612\) 6.92820 19.5959i 0.280056 0.792118i
\(613\) 44.0908i 1.78081i −0.455168 0.890406i \(-0.650421\pi\)
0.455168 0.890406i \(-0.349579\pi\)
\(614\) 25.4558i 1.02731i
\(615\) 47.3205 + 3.28169i 1.90815 + 0.132331i
\(616\) 3.46410i 0.139573i
\(617\) 20.7846 0.836757 0.418378 0.908273i \(-0.362599\pi\)
0.418378 + 0.908273i \(0.362599\pi\)
\(618\) 8.48528 + 12.0000i 0.341328 + 0.482711i
\(619\) 16.0000 0.643094 0.321547 0.946894i \(-0.395797\pi\)
0.321547 + 0.946894i \(0.395797\pi\)
\(620\) 9.79796 12.0000i 0.393496 0.481932i
\(621\) −4.89898 17.3205i −0.196589 0.695048i
\(622\) 26.8701 1.07739
\(623\) 6.00000i 0.240385i
\(624\) 6.00000 4.24264i 0.240192 0.169842i
\(625\) −23.0000 + 9.79796i −0.920000 + 0.391918i
\(626\) 4.89898 0.195803
\(627\) −9.12096 5.55051i −0.364256 0.221666i
\(628\) 14.6969i 0.586472i
\(629\) −29.3939 −1.17201
\(630\) 14.0406 8.53590i 0.559391 0.340078i
\(631\) −44.0000 −1.75161 −0.875806 0.482663i \(-0.839670\pi\)
−0.875806 + 0.482663i \(0.839670\pi\)
\(632\) −10.3923 −0.413384
\(633\) −3.46410 4.89898i −0.137686 0.194717i
\(634\) −18.0000 −0.714871
\(635\) 0 0
\(636\) 6.00000 + 8.48528i 0.237915 + 0.336463i
\(637\) −4.24264 −0.168100
\(638\) −3.46410 −0.137145
\(639\) 4.89898 13.8564i 0.193801 0.548151i
\(640\) −1.41421 + 1.73205i −0.0559017 + 0.0684653i
\(641\) 12.2474 0.483745 0.241873 0.970308i \(-0.422238\pi\)
0.241873 + 0.970308i \(0.422238\pi\)
\(642\) 25.4558 18.0000i 1.00466 0.710403i
\(643\) 7.34847i 0.289795i 0.989447 + 0.144898i \(0.0462853\pi\)
−0.989447 + 0.144898i \(0.953715\pi\)
\(644\) 8.48528i 0.334367i
\(645\) 1.96902 28.3923i 0.0775299 1.11795i
\(646\) 12.0000 + 27.7128i 0.472134 + 1.09035i
\(647\) 10.3923 0.408564 0.204282 0.978912i \(-0.434514\pi\)
0.204282 + 0.978912i \(0.434514\pi\)
\(648\) 5.65685 7.00000i 0.222222 0.274986i
\(649\) 6.92820i 0.271956i
\(650\) −20.7846 + 4.24264i −0.815239 + 0.166410i
\(651\) 24.0000 16.9706i 0.940634 0.665129i
\(652\) 12.2474i 0.479647i
\(653\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(654\) −9.79796 + 6.92820i −0.383131 + 0.270914i
\(655\) 2.00000 2.44949i 0.0781465 0.0957095i
\(656\) −12.2474 −0.478183
\(657\) −41.5692 14.6969i −1.62177 0.573382i
\(658\) 8.48528 0.330791
\(659\) −44.0908 −1.71753 −0.858767 0.512366i \(-0.828769\pi\)
−0.858767 + 0.512366i \(0.828769\pi\)
\(660\) −0.378937 + 5.46410i −0.0147501 + 0.212690i
\(661\) 48.4974i 1.88633i −0.332323 0.943166i \(-0.607832\pi\)
0.332323 0.943166i \(-0.392168\pi\)
\(662\) −6.92820 −0.269272
\(663\) −41.5692 + 29.3939i −1.61441 + 1.14156i
\(664\) 10.3923i 0.403300i
\(665\) −6.50794 + 22.9706i −0.252367 + 0.890760i
\(666\) −12.0000 4.24264i −0.464991 0.164399i
\(667\) 8.48528 0.328551
\(668\) 0 0
\(669\) −36.0000 + 25.4558i −1.39184 + 0.984180i
\(670\) 0 0
\(671\) 11.3137i 0.436761i
\(672\) −3.46410 + 2.44949i −0.133631 + 0.0944911i
\(673\) −12.7279 −0.490625 −0.245313 0.969444i \(-0.578891\pi\)
−0.245313 + 0.969444i \(0.578891\pi\)
\(674\) 4.24264i 0.163420i
\(675\) −23.0807 + 11.9282i −0.888376 + 0.459117i
\(676\) −5.00000 −0.192308
\(677\) 30.0000i 1.15299i 0.817099 + 0.576497i \(0.195581\pi\)
−0.817099 + 0.576497i \(0.804419\pi\)
\(678\) −25.4558 + 18.0000i −0.977626 + 0.691286i
\(679\) 31.1769i 1.19646i
\(680\) 9.79796 12.0000i 0.375735 0.460179i
\(681\) 12.0000 + 16.9706i 0.459841 + 0.650313i
\(682\) 9.79796i 0.375183i
\(683\) 18.0000i 0.688751i −0.938832 0.344375i \(-0.888091\pi\)
0.938832 0.344375i \(-0.111909\pi\)
\(684\) 0.898979 + 13.0458i 0.0343733 + 0.498817i
\(685\) 30.0000 + 24.4949i 1.14624 + 0.935902i
\(686\) 19.5959 0.748176
\(687\) −39.5980 + 28.0000i −1.51076 + 1.06827i
\(688\) 7.34847i 0.280158i
\(689\) 25.4558i 0.969790i
\(690\) 0.928203 13.3843i 0.0353361 0.509530i
\(691\) −20.0000 −0.760836 −0.380418 0.924815i \(-0.624220\pi\)
−0.380418 + 0.924815i \(0.624220\pi\)
\(692\) 6.00000i 0.228086i
\(693\) −3.46410 + 9.79796i −0.131590 + 0.372194i
\(694\) 24.2487i 0.920468i
\(695\) 6.92820 + 5.65685i 0.262802 + 0.214577i
\(696\) 2.44949 + 3.46410i 0.0928477 + 0.131306i
\(697\) 84.8528 3.21403
\(698\) 22.0000i 0.832712i
\(699\) −14.6969 + 10.3923i −0.555889 + 0.393073i
\(700\) 12.0000 2.44949i 0.453557 0.0925820i
\(701\) 28.2843i 1.06828i −0.845395 0.534141i \(-0.820635\pi\)
0.845395 0.534141i \(-0.179365\pi\)
\(702\) −21.2132 + 6.00000i −0.800641 + 0.226455i
\(703\) 16.9706 7.34847i 0.640057 0.277153i
\(704\) 1.41421i 0.0533002i
\(705\) −13.3843 0.928203i −0.504080 0.0349582i
\(706\) 17.3205i 0.651866i
\(707\) 6.92820 0.260562
\(708\) 6.92820 4.89898i 0.260378 0.184115i
\(709\) −16.0000 −0.600893 −0.300446 0.953799i \(-0.597136\pi\)
−0.300446 + 0.953799i \(0.597136\pi\)
\(710\) 6.92820 8.48528i 0.260011 0.318447i
\(711\) 29.3939 + 10.3923i 1.10236 + 0.389742i
\(712\) 2.44949i 0.0917985i
\(713\) 24.0000i 0.898807i
\(714\) 24.0000 16.9706i 0.898177 0.635107i
\(715\) 8.48528 10.3923i 0.317332 0.388650i
\(716\) −4.89898 −0.183083
\(717\) 1.41421 + 2.00000i 0.0528148 + 0.0746914i
\(718\) 18.3848 0.686114
\(719\) 7.07107i 0.263706i −0.991269 0.131853i \(-0.957907\pi\)
0.991269 0.131853i \(-0.0420927\pi\)
\(720\) 5.73205 3.48477i 0.213621 0.129870i
\(721\) 20.7846i 0.774059i
\(722\) −13.8564 13.0000i −0.515682 0.483810i
\(723\) −13.8564 19.5959i −0.515325 0.728780i
\(724\) 13.8564i 0.514969i
\(725\) −2.44949 12.0000i −0.0909718 0.445669i
\(726\) 9.00000 + 12.7279i 0.334021 + 0.472377i
\(727\) 31.8434i 1.18101i 0.807036 + 0.590503i \(0.201070\pi\)
−0.807036 + 0.590503i \(0.798930\pi\)
\(728\) 10.3923 0.385164
\(729\) −23.0000 + 14.1421i −0.851852 + 0.523783i
\(730\) −25.4558 20.7846i −0.942163 0.769273i
\(731\) 50.9117i 1.88304i
\(732\) −11.3137 + 8.00000i −0.418167 + 0.295689i
\(733\) 4.89898i 0.180948i 0.995899 + 0.0904740i \(0.0288382\pi\)
−0.995899 + 0.0904740i \(0.971162\pi\)
\(734\) −31.8434 −1.17536
\(735\) −3.86370 0.267949i −0.142515 0.00988345i
\(736\) 3.46410i 0.127688i
\(737\) 0 0
\(738\) 34.6410 + 12.2474i 1.27515 + 0.450835i
\(739\) 20.0000 0.735712 0.367856 0.929883i \(-0.380092\pi\)
0.367856 + 0.929883i \(0.380092\pi\)
\(740\) −7.34847 6.00000i −0.270135 0.220564i
\(741\) 16.6515 27.3629i 0.611709 1.00520i
\(742\) 14.6969i 0.539542i
\(743\) 30.0000i 1.10059i 0.834969 + 0.550297i \(0.185485\pi\)
−0.834969 + 0.550297i \(0.814515\pi\)
\(744\) 9.79796 6.92820i 0.359211 0.254000i
\(745\) 16.0000 19.5959i 0.586195 0.717939i
\(746\) 12.7279i 0.466002i
\(747\) −10.3923 + 29.3939i −0.380235 + 1.07547i
\(748\) 9.79796i 0.358249i
\(749\) 44.0908 1.61104
\(750\) −19.1962 + 2.55103i −0.700944 + 0.0931503i
\(751\) 41.5692i 1.51688i 0.651741 + 0.758441i \(0.274039\pi\)
−0.651741 + 0.758441i \(0.725961\pi\)
\(752\) 3.46410 0.126323
\(753\) 1.41421 + 2.00000i 0.0515368 + 0.0728841i
\(754\) 10.3923i 0.378465i
\(755\) −19.5959 + 24.0000i −0.713168 + 0.873449i
\(756\) 12.2474 3.46410i 0.445435 0.125988i
\(757\) 9.79796i 0.356113i −0.984020 0.178056i \(-0.943019\pi\)
0.984020 0.178056i \(-0.0569810\pi\)
\(758\) −20.7846 −0.754931
\(759\) 4.89898 + 6.92820i 0.177822 + 0.251478i
\(760\) −2.65685 + 9.37769i −0.0963742 + 0.340165i
\(761\) 14.1421i 0.512652i 0.966590 + 0.256326i \(0.0825121\pi\)
−0.966590 + 0.256326i \(0.917488\pi\)
\(762\) 0 0
\(763\) −16.9706 −0.614376
\(764\) 24.0416i 0.869796i
\(765\) −39.7128 + 24.1432i −1.43582 + 0.872898i
\(766\) 6.00000 0.216789
\(767\) −20.7846 −0.750489
\(768\) −1.41421 + 1.00000i −0.0510310 + 0.0360844i
\(769\) −14.0000 −0.504853 −0.252426 0.967616i \(-0.581229\pi\)
−0.252426 + 0.967616i \(0.581229\pi\)
\(770\) −4.89898 + 6.00000i −0.176547 + 0.216225i
\(771\) 6.00000 + 8.48528i 0.216085 + 0.305590i
\(772\) −12.7279 −0.458088
\(773\) 18.0000i 0.647415i −0.946157 0.323708i \(-0.895071\pi\)
0.946157 0.323708i \(-0.104929\pi\)
\(774\) 7.34847 20.7846i 0.264135 0.747087i
\(775\) −33.9411 + 6.92820i −1.21920 + 0.248868i
\(776\) 12.7279i 0.456906i
\(777\) −10.3923 14.6969i −0.372822 0.527250i
\(778\) 19.7990 0.709828
\(779\) −48.9898 + 21.2132i −1.75524 + 0.760042i
\(780\) −16.3923 1.13681i −0.586939 0.0407044i
\(781\) 6.92820i 0.247911i
\(782\) 24.0000i 0.858238i
\(783\) −3.46410 12.2474i −0.123797