Properties

Label 570.2.c.e.569.5
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 569.5
Root \(0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 570.569
Dual form 570.2.c.e.569.1

$q$-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} +(1.03528 + 3.73205i) 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} +(-3.73205 + 1.03528i) 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} +(2.26795 - 6.31319i) 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} +(-7.38891 - 1.55051i) q^{57} +2.44949i q^{58} -4.89898 q^{59} +(-1.03528 - 3.73205i) 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} +(3.48477 - 7.92820i) 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} +(6.31319 + 2.26795i) 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 \(-0.931611\pi\)
0.977008 0.213201i \(-0.0683888\pi\)
\(12\) 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
\(15\) 1.03528 + 3.73205i 0.267307 + 0.963611i
\(16\) 1.00000 0.250000
\(17\) 6.92820 1.68034 0.840168 0.542326i \(-0.182456\pi\)
0.840168 + 0.542326i \(0.182456\pi\)
\(18\) −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 \(-0.382382\pi\)
0.361158 + 0.932505i \(0.382382\pi\)
\(24\) −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 \(-0.426968\pi\)
0.227429 + 0.973795i \(0.426968\pi\)
\(30\) −3.73205 + 1.03528i −0.681376 + 0.189015i
\(31\) 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 \(-0.0943788\pi\)
0.956365 + 0.292174i \(0.0943788\pi\)
\(42\) 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
\(45\) 2.26795 6.31319i 0.338086 0.941115i
\(46\) 3.46410i 0.510754i
\(47\) −3.46410 −0.505291 −0.252646 0.967559i \(-0.581301\pi\)
−0.252646 + 0.967559i \(0.581301\pi\)
\(48\) −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 \(-0.864802\pi\)
0.911147 0.412082i \(-0.135198\pi\)
\(54\) 5.00000 + 1.41421i 0.680414 + 0.192450i
\(55\) −2.00000 + 2.44949i −0.269680 + 0.330289i
\(56\) 2.44949 0.327327
\(57\) −7.38891 1.55051i −0.978684 0.205370i
\(58\) 2.44949i 0.321634i
\(59\) −4.89898 −0.637793 −0.318896 0.947790i \(-0.603312\pi\)
−0.318896 + 0.947790i \(0.603312\pi\)
\(60\) −1.03528 3.73205i −0.133654 0.481806i
\(61\) −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 \(-0.593888\pi\)
−0.290701 + 0.956814i \(0.593888\pi\)
\(72\) 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
\(75\) 3.48477 7.92820i 0.402386 0.915470i
\(76\) −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 \(-0.306807\pi\)
0.570352 + 0.821401i \(0.306807\pi\)
\(84\) −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 \(-0.541441\pi\)
−0.129823 + 0.991537i \(0.541441\pi\)
\(90\) 6.31319 + 2.26795i 0.665469 + 0.239063i
\(91\) 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 \(0.0449416\pi\)
−0.990050 + 0.140720i \(0.955058\pi\)
\(102\) 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
\(105\) −9.14162 + 2.53590i −0.892131 + 0.247478i
\(106\) 6.00000 0.582772
\(107\) 18.0000i 1.74013i 0.492941 + 0.870063i \(0.335922\pi\)
−0.492941 + 0.870063i \(0.664078\pi\)
\(108\) −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 \(-0.678617\pi\)
0.532152 0.846649i \(-0.321383\pi\)
\(114\) 1.55051 7.38891i 0.145219 0.692034i
\(115\) −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
\(120\) 3.73205 1.03528i 0.340688 0.0945074i
\(121\) 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 \(0.0196778\pi\)
−0.998090 + 0.0617802i \(0.980322\pi\)
\(132\) 1.41421 2.00000i 0.123091 0.174078i
\(133\) 4.24264 + 9.79796i 0.367884 + 0.849591i
\(134\) 0 0
\(135\) −9.52056 + 6.66025i −0.819399 + 0.573223i
\(136\) 6.92820i 0.594089i
\(137\) −17.3205 −1.47979 −0.739895 0.672722i \(-0.765125\pi\)
−0.739895 + 0.672722i \(0.765125\pi\)
\(138\) 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 \(0.153381\pi\)
−0.886135 + 0.463428i \(0.846619\pi\)
\(150\) 7.92820 + 3.48477i 0.647335 + 0.284530i
\(151\) 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
\(165\) 5.27792 1.46410i 0.410885 0.113980i
\(166\) 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
\(171\) 8.89898 + 9.58166i 0.680522 + 0.732728i
\(172\) 7.34847i 0.560316i
\(173\) 6.00000i 0.456172i −0.973641 0.228086i \(-0.926753\pi\)
0.973641 0.228086i \(-0.0732467\pi\)
\(174\) 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 \(-0.558608\pi\)
−0.183083 + 0.983097i \(0.558608\pi\)
\(180\) −2.26795 + 6.31319i −0.169043 + 0.470558i
\(181\) 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 \(-0.664251\pi\)
0.493412 0.869796i \(-0.335749\pi\)
\(192\) 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
\(195\) −4.39230 15.8338i −0.314539 1.13388i
\(196\) −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
\(210\) −2.53590 9.14162i −0.174994 0.630832i
\(211\) 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
\(225\) −12.8564 + 7.72741i −0.857094 + 0.515160i
\(226\) 18.0000 1.19734
\(227\) 12.0000i 0.796468i 0.917284 + 0.398234i \(0.130377\pi\)
−0.917284 + 0.398234i \(0.869623\pi\)
\(228\) 7.38891 + 1.55051i 0.489342 + 0.102685i
\(229\) 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 \(-0.610566\pi\)
−0.340411 + 0.940277i \(0.610566\pi\)
\(234\) 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 \(0.0145642\pi\)
−0.998953 + 0.0457389i \(0.985436\pi\)
\(240\) 1.03528 + 3.73205i 0.0668268 + 0.240903i
\(241\) 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 \(0.0142116\pi\)
−0.999003 + 0.0446322i \(0.985788\pi\)
\(252\) 6.92820 2.44949i 0.436436 0.154303i
\(253\) 4.89898i 0.307996i
\(254\) 0 0
\(255\) 7.17260 + 25.8564i 0.449166 + 1.61919i
\(256\) 1.00000 0.0625000
\(257\) 6.00000i 0.374270i 0.982334 + 0.187135i \(0.0599201\pi\)
−0.982334 + 0.187135i \(0.940080\pi\)
\(258\) 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 \(-0.534061\pi\)
−0.106803 + 0.994280i \(0.534061\pi\)
\(264\) 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 \(-0.324918\pi\)
0.522718 + 0.852506i \(0.324918\pi\)
\(270\) −6.66025 9.52056i −0.405330 0.579403i
\(271\) 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 \(-0.429660\pi\)
0.219186 + 0.975683i \(0.429660\pi\)
\(282\) −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
\(285\) 10.6052 + 13.1351i 0.628198 + 0.778053i
\(286\) −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 \(0.0560772\pi\)
−0.984522 + 0.175262i \(0.943923\pi\)
\(294\) 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
\(300\) −3.48477 + 7.92820i −0.201193 + 0.457735i
\(301\) −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 \(-0.724301\pi\)
0.647776 0.761831i \(-0.275699\pi\)
\(312\) 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
\(315\) 15.4641 + 5.55532i 0.871303 + 0.313007i
\(316\) 10.3923i 0.584613i
\(317\) 18.0000i 1.01098i 0.862832 + 0.505490i \(0.168688\pi\)
−0.862832 + 0.505490i \(0.831312\pi\)
\(318\) −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
\(330\) 1.46410 + 5.27792i 0.0805961 + 0.290540i
\(331\) 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
\(342\) −9.58166 + 8.89898i −0.518117 + 0.481202i
\(343\) 19.5959i 1.05808i
\(344\) 7.34847 0.396203
\(345\) 3.58630 + 12.9282i 0.193080 + 0.696031i
\(346\) 6.00000 0.322562
\(347\) −24.2487 −1.30174 −0.650870 0.759190i \(-0.725596\pi\)
−0.650870 + 0.759190i \(0.725596\pi\)
\(348\) 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 \(-0.347513\pi\)
0.460939 + 0.887432i \(0.347513\pi\)
\(354\) −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 \(-0.838763\pi\)
0.874428 0.485156i \(-0.161237\pi\)
\(360\) −6.31319 2.26795i −0.332734 0.119531i
\(361\) 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
\(375\) −17.2480 + 8.80385i −0.890681 + 0.454629i
\(376\) 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 \(-0.951012\pi\)
0.988181 0.153293i \(-0.0489878\pi\)
\(384\) −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 \(-0.832626\pi\)
0.864912 0.501924i \(-0.167374\pi\)
\(390\) 15.8338 4.39230i 0.801773 0.222413i
\(391\) 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
\(399\) 3.79796 18.0990i 0.190136 0.906086i
\(400\) 1.00000 + 4.89898i 0.0500000 + 0.244949i
\(401\) 22.0454 1.10090 0.550448 0.834870i \(-0.314457\pi\)
0.550448 + 0.834870i \(0.314457\pi\)
\(402\) 0 0
\(403\) 29.3939i 1.46421i
\(404\) 2.82843i 0.140720i
\(405\) 20.1244 + 0.101536i 0.999987 + 0.00504536i
\(406\) −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 \(0.0777414\pi\)
−0.970323 + 0.241811i \(0.922259\pi\)
\(420\) 9.14162 2.53590i 0.446065 0.123739i
\(421\) 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 \(-0.656450\pi\)
−0.471951 + 0.881625i \(0.656450\pi\)
\(432\) 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
\(435\) 2.53590 + 9.14162i 0.121587 + 0.438307i
\(436\) 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 \(-0.365019\pi\)
0.411461 + 0.911427i \(0.365019\pi\)
\(444\) 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 \(-0.406678\pi\)
0.288996 + 0.957330i \(0.406678\pi\)
\(450\) −7.72741 12.8564i −0.364273 0.606057i
\(451\) 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
\(456\) −1.55051 + 7.38891i −0.0726093 + 0.346017i
\(457\) 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 \(0.176658\pi\)
−0.849907 + 0.526932i \(0.823342\pi\)
\(462\) 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
\(465\) −25.8564 + 7.17260i −1.19906 + 0.332622i
\(466\) 10.3923i 0.481414i
\(467\) 24.2487 1.12210 0.561048 0.827783i \(-0.310398\pi\)
0.561048 + 0.827783i \(0.310398\pi\)
\(468\) 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 \(-0.927383\pi\)
0.974090 0.226160i \(-0.0726171\pi\)
\(480\) −3.73205 + 1.03528i −0.170344 + 0.0472537i
\(481\) −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 \(-0.948994\pi\)
0.987189 0.159556i \(-0.0510064\pi\)
\(492\) 17.3205 + 12.2474i 0.780869 + 0.552158i
\(493\) 16.9706 0.764316
\(494\) −7.34847 16.9706i −0.330623 0.763542i
\(495\) −8.92820 3.20736i −0.401293 0.144160i
\(496\) 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 \(-0.626192\pi\)
−0.386142 + 0.922440i \(0.626192\pi\)
\(504\) 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 \(-0.337518\pi\)
0.488573 + 0.872523i \(0.337518\pi\)
\(510\) −25.8564 + 7.17260i −1.14494 + 0.317608i
\(511\) 36.0000 1.59255
\(512\) 1.00000i 0.0441942i
\(513\) −3.00340 22.4495i −0.132603 0.991169i
\(514\) −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 \(-0.660421\pi\)
−0.482913 + 0.875668i \(0.660421\pi\)
\(522\) −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
\(525\) 19.4201 + 8.53590i 0.847561 + 0.372537i
\(526\) 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
\(540\) 9.52056 6.66025i 0.409700 0.286612i
\(541\) −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
\(555\) 4.39230 + 15.8338i 0.186443 + 0.672105i
\(556\) −4.00000 −0.169638
\(557\) −10.3923 −0.440336 −0.220168 0.975462i \(-0.570661\pi\)
−0.220168 + 0.975462i \(0.570661\pi\)
\(558\) −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 \(-0.725879\pi\)
0.651546 0.758610i \(-0.274121\pi\)
\(564\) −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 \(-0.929446\pi\)
−0.975536 + 0.219842i \(0.929446\pi\)
\(570\) −13.1351 + 10.6052i −0.550167 + 0.444203i
\(571\) 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
\(585\) −9.62209 + 26.7846i −0.397825 + 1.10741i
\(586\) −6.00000 −0.247858
\(587\) −3.46410 −0.142979 −0.0714894 0.997441i \(-0.522775\pi\)
−0.0714894 + 0.997441i \(0.522775\pi\)
\(588\) 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 \(-0.522659\pi\)
−0.0711268 + 0.997467i \(0.522659\pi\)
\(594\) 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 \(-0.531911\pi\)
−0.100083 + 0.994979i \(0.531911\pi\)
\(600\) −7.92820 3.48477i −0.323668 0.142265i
\(601\) 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
\(615\) 12.6795 + 45.7081i 0.511286 + 1.84313i
\(616\) 3.46410i 0.139573i
\(617\) −20.7846 −0.836757 −0.418378 0.908273i \(-0.637401\pi\)
−0.418378 + 0.908273i \(0.637401\pi\)
\(618\) 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
\(627\) −2.19275 + 10.4495i −0.0875701 + 0.417312i
\(628\) 14.6969i 0.586472i
\(629\) 29.3939 1.17201
\(630\) −5.55532 + 15.4641i −0.221329 + 0.616105i
\(631\) −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 \(-0.577762\pi\)
−0.241873 + 0.970308i \(0.577762\pi\)
\(642\) 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
\(645\) −27.4249 + 7.60770i −1.07985 + 0.299553i
\(646\) 12.0000 + 27.7128i 0.472134 + 1.09035i
\(647\) −10.3923 −0.408564 −0.204282 0.978912i \(-0.565486\pi\)
−0.204282 + 0.978912i \(0.565486\pi\)
\(648\) 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 \(-0.171231\pi\)
0.858767 + 0.512366i \(0.171231\pi\)
\(660\) −5.27792 + 1.46410i −0.205443 + 0.0569901i
\(661\) 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
\(675\) 25.9091 + 1.92820i 0.997242 + 0.0742166i
\(676\) −5.00000 −0.192308
\(677\) 30.0000i 1.15299i −0.817099 0.576497i \(-0.804419\pi\)
0.817099 0.576497i \(-0.195581\pi\)
\(678\) −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 \(0.111909\pi\)
−0.938832 + 0.344375i \(0.888091\pi\)
\(684\) −8.89898 9.58166i −0.340261 0.366364i
\(685\) 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
\(690\) −12.9282 + 3.58630i −0.492168 + 0.136528i
\(691\) −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 \(0.179365\pi\)
−0.845395 + 0.534141i \(0.820635\pi\)
\(702\) −21.2132 6.00000i −0.800641 0.226455i
\(703\) 16.9706 7.34847i 0.640057 0.277153i
\(704\) 1.41421i 0.0533002i
\(705\) −3.58630 12.9282i −0.135068 0.486904i
\(706\) 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 \(0.0420927\pi\)
−0.991269 + 0.131853i \(0.957907\pi\)
\(720\) 2.26795 6.31319i 0.0845215 0.235279i
\(721\) 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
\(735\) 1.03528 + 3.73205i 0.0381867 + 0.137659i
\(736\) 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
\(741\) 31.3485 + 6.57826i 1.15161 + 0.241658i
\(742\) 14.6969i 0.539542i
\(743\) 30.0000i 1.10059i −0.834969 0.550297i \(-0.814515\pi\)
0.834969 0.550297i \(-0.185485\pi\)
\(744\) −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
\(750\) −8.80385 17.2480i −0.321471 0.629807i
\(751\) 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 \(-0.917488\pi\)
0.966590 0.256326i \(-0.0825121\pi\)
\(762\) 0 0
\(763\) −16.9706 −0.614376
\(764\) 24.0416i 0.869796i
\(765\) 15.7128 43.7391i 0.568098 1.58139i
\(766\) 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 \(0.104929\pi\)
−0.946157 + 0.323708i \(0.895071\pi\)
\(774\) −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
\(780\) 4.39230 + 15.8338i 0.157270 + 0.566939i
\(781\) 6.92820i 0.247911i
\(782\) 24.0000i 0.858238i
\(783\) 3.46410 12.2474i 0.123797