Properties

Label 570.2.c.a.569.1
Level $570$
Weight $2$
Character 570.569
Analytic conductor $4.551$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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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: \(4\)
Coefficient field: \(\Q(\zeta_{8})\)
Defining polynomial: \(x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 569.1
Root \(-0.707107 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 570.569
Dual form 570.2.c.a.569.3

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} +(-1.41421 - 1.00000i) q^{3} -1.00000 q^{4} +(2.12132 + 0.707107i) q^{5} +(-1.00000 + 1.41421i) q^{6} +1.00000i q^{8} +(1.00000 + 2.82843i) q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +(-1.41421 - 1.00000i) q^{3} -1.00000 q^{4} +(2.12132 + 0.707107i) q^{5} +(-1.00000 + 1.41421i) q^{6} +1.00000i q^{8} +(1.00000 + 2.82843i) q^{9} +(0.707107 - 2.12132i) q^{10} +2.82843i q^{11} +(1.41421 + 1.00000i) q^{12} +4.24264 q^{13} +(-2.29289 - 3.12132i) q^{15} +1.00000 q^{16} +(2.82843 - 1.00000i) q^{18} +(1.00000 + 4.24264i) q^{19} +(-2.12132 - 0.707107i) q^{20} +2.82843 q^{22} +4.24264 q^{23} +(1.00000 - 1.41421i) q^{24} +(4.00000 + 3.00000i) q^{25} -4.24264i q^{26} +(1.41421 - 5.00000i) q^{27} -6.00000 q^{29} +(-3.12132 + 2.29289i) q^{30} -4.24264i q^{31} -1.00000i q^{32} +(2.82843 - 4.00000i) q^{33} +(-1.00000 - 2.82843i) q^{36} +4.24264 q^{37} +(4.24264 - 1.00000i) q^{38} +(-6.00000 - 4.24264i) q^{39} +(-0.707107 + 2.12132i) q^{40} +6.00000 q^{41} -12.0000i q^{43} -2.82843i q^{44} +(0.121320 + 6.70711i) q^{45} -4.24264i q^{46} -12.7279 q^{47} +(-1.41421 - 1.00000i) q^{48} +7.00000 q^{49} +(3.00000 - 4.00000i) q^{50} -4.24264 q^{52} +6.00000i q^{53} +(-5.00000 - 1.41421i) q^{54} +(-2.00000 + 6.00000i) q^{55} +(2.82843 - 7.00000i) q^{57} +6.00000i q^{58} -6.00000 q^{59} +(2.29289 + 3.12132i) q^{60} +10.0000 q^{61} -4.24264 q^{62} -1.00000 q^{64} +(9.00000 + 3.00000i) q^{65} +(-4.00000 - 2.82843i) q^{66} +(-6.00000 - 4.24264i) q^{69} +12.0000 q^{71} +(-2.82843 + 1.00000i) q^{72} -6.00000i q^{73} -4.24264i q^{74} +(-2.65685 - 8.24264i) q^{75} +(-1.00000 - 4.24264i) q^{76} +(-4.24264 + 6.00000i) q^{78} +12.7279i q^{79} +(2.12132 + 0.707107i) q^{80} +(-7.00000 + 5.65685i) q^{81} -6.00000i q^{82} -12.0000 q^{86} +(8.48528 + 6.00000i) q^{87} -2.82843 q^{88} -12.0000 q^{89} +(6.70711 - 0.121320i) q^{90} -4.24264 q^{92} +(-4.24264 + 6.00000i) q^{93} +12.7279i q^{94} +(-0.878680 + 9.70711i) q^{95} +(-1.00000 + 1.41421i) q^{96} -7.00000i q^{98} +(-8.00000 + 2.82843i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{4} - 4q^{6} + 4q^{9} + O(q^{10}) \) \( 4q - 4q^{4} - 4q^{6} + 4q^{9} - 12q^{15} + 4q^{16} + 4q^{19} + 4q^{24} + 16q^{25} - 24q^{29} - 4q^{30} - 4q^{36} - 24q^{39} + 24q^{41} - 8q^{45} + 28q^{49} + 12q^{50} - 20q^{54} - 8q^{55} - 24q^{59} + 12q^{60} + 40q^{61} - 4q^{64} + 36q^{65} - 16q^{66} - 24q^{69} + 48q^{71} + 12q^{75} - 4q^{76} - 28q^{81} - 48q^{86} - 48q^{89} + 24q^{90} - 12q^{95} - 4q^{96} - 32q^{99} + O(q^{100}) \)

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
\(5\) 2.12132 + 0.707107i 0.948683 + 0.316228i
\(6\) −1.00000 + 1.41421i −0.408248 + 0.577350i
\(7\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 1.00000 + 2.82843i 0.333333 + 0.942809i
\(10\) 0.707107 2.12132i 0.223607 0.670820i
\(11\) 2.82843i 0.852803i 0.904534 + 0.426401i \(0.140219\pi\)
−0.904534 + 0.426401i \(0.859781\pi\)
\(12\) 1.41421 + 1.00000i 0.408248 + 0.288675i
\(13\) 4.24264 1.17670 0.588348 0.808608i \(-0.299778\pi\)
0.588348 + 0.808608i \(0.299778\pi\)
\(14\) 0 0
\(15\) −2.29289 3.12132i −0.592022 0.805921i
\(16\) 1.00000 0.250000
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 2.82843 1.00000i 0.666667 0.235702i
\(19\) 1.00000 + 4.24264i 0.229416 + 0.973329i
\(20\) −2.12132 0.707107i −0.474342 0.158114i
\(21\) 0 0
\(22\) 2.82843 0.603023
\(23\) 4.24264 0.884652 0.442326 0.896854i \(-0.354153\pi\)
0.442326 + 0.896854i \(0.354153\pi\)
\(24\) 1.00000 1.41421i 0.204124 0.288675i
\(25\) 4.00000 + 3.00000i 0.800000 + 0.600000i
\(26\) 4.24264i 0.832050i
\(27\) 1.41421 5.00000i 0.272166 0.962250i
\(28\) 0 0
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) −3.12132 + 2.29289i −0.569873 + 0.418623i
\(31\) 4.24264i 0.762001i −0.924575 0.381000i \(-0.875580\pi\)
0.924575 0.381000i \(-0.124420\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 2.82843 4.00000i 0.492366 0.696311i
\(34\) 0 0
\(35\) 0 0
\(36\) −1.00000 2.82843i −0.166667 0.471405i
\(37\) 4.24264 0.697486 0.348743 0.937218i \(-0.386609\pi\)
0.348743 + 0.937218i \(0.386609\pi\)
\(38\) 4.24264 1.00000i 0.688247 0.162221i
\(39\) −6.00000 4.24264i −0.960769 0.679366i
\(40\) −0.707107 + 2.12132i −0.111803 + 0.335410i
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 0 0
\(43\) 12.0000i 1.82998i −0.403473 0.914991i \(-0.632197\pi\)
0.403473 0.914991i \(-0.367803\pi\)
\(44\) 2.82843i 0.426401i
\(45\) 0.121320 + 6.70711i 0.0180854 + 0.999836i
\(46\) 4.24264i 0.625543i
\(47\) −12.7279 −1.85656 −0.928279 0.371884i \(-0.878712\pi\)
−0.928279 + 0.371884i \(0.878712\pi\)
\(48\) −1.41421 1.00000i −0.204124 0.144338i
\(49\) 7.00000 1.00000
\(50\) 3.00000 4.00000i 0.424264 0.565685i
\(51\) 0 0
\(52\) −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 + 6.00000i −0.269680 + 0.809040i
\(56\) 0 0
\(57\) 2.82843 7.00000i 0.374634 0.927173i
\(58\) 6.00000i 0.787839i
\(59\) −6.00000 −0.781133 −0.390567 0.920575i \(-0.627721\pi\)
−0.390567 + 0.920575i \(0.627721\pi\)
\(60\) 2.29289 + 3.12132i 0.296011 + 0.402961i
\(61\) 10.0000 1.28037 0.640184 0.768221i \(-0.278858\pi\)
0.640184 + 0.768221i \(0.278858\pi\)
\(62\) −4.24264 −0.538816
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 9.00000 + 3.00000i 1.11631 + 0.372104i
\(66\) −4.00000 2.82843i −0.492366 0.348155i
\(67\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(68\) 0 0
\(69\) −6.00000 4.24264i −0.722315 0.510754i
\(70\) 0 0
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) −2.82843 + 1.00000i −0.333333 + 0.117851i
\(73\) 6.00000i 0.702247i −0.936329 0.351123i \(-0.885800\pi\)
0.936329 0.351123i \(-0.114200\pi\)
\(74\) 4.24264i 0.493197i
\(75\) −2.65685 8.24264i −0.306787 0.951778i
\(76\) −1.00000 4.24264i −0.114708 0.486664i
\(77\) 0 0
\(78\) −4.24264 + 6.00000i −0.480384 + 0.679366i
\(79\) 12.7279i 1.43200i 0.698099 + 0.716002i \(0.254030\pi\)
−0.698099 + 0.716002i \(0.745970\pi\)
\(80\) 2.12132 + 0.707107i 0.237171 + 0.0790569i
\(81\) −7.00000 + 5.65685i −0.777778 + 0.628539i
\(82\) 6.00000i 0.662589i
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −12.0000 −1.29399
\(87\) 8.48528 + 6.00000i 0.909718 + 0.643268i
\(88\) −2.82843 −0.301511
\(89\) −12.0000 −1.27200 −0.635999 0.771690i \(-0.719412\pi\)
−0.635999 + 0.771690i \(0.719412\pi\)
\(90\) 6.70711 0.121320i 0.706991 0.0127883i
\(91\) 0 0
\(92\) −4.24264 −0.442326
\(93\) −4.24264 + 6.00000i −0.439941 + 0.622171i
\(94\) 12.7279i 1.31278i
\(95\) −0.878680 + 9.70711i −0.0901506 + 0.995928i
\(96\) −1.00000 + 1.41421i −0.102062 + 0.144338i
\(97\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(98\) 7.00000i 0.707107i
\(99\) −8.00000 + 2.82843i −0.804030 + 0.284268i
\(100\) −4.00000 3.00000i −0.400000 0.300000i
\(101\) 15.5563i 1.54791i 0.633238 + 0.773957i \(0.281726\pi\)
−0.633238 + 0.773957i \(0.718274\pi\)
\(102\) 0 0
\(103\) −4.24264 −0.418040 −0.209020 0.977911i \(-0.567027\pi\)
−0.209020 + 0.977911i \(0.567027\pi\)
\(104\) 4.24264i 0.416025i
\(105\) 0 0
\(106\) 6.00000 0.582772
\(107\) 12.0000i 1.16008i 0.814587 + 0.580042i \(0.196964\pi\)
−0.814587 + 0.580042i \(0.803036\pi\)
\(108\) −1.41421 + 5.00000i −0.136083 + 0.481125i
\(109\) 4.24264i 0.406371i −0.979140 0.203186i \(-0.934871\pi\)
0.979140 0.203186i \(-0.0651295\pi\)
\(110\) 6.00000 + 2.00000i 0.572078 + 0.190693i
\(111\) −6.00000 4.24264i −0.569495 0.402694i
\(112\) 0 0
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) −7.00000 2.82843i −0.655610 0.264906i
\(115\) 9.00000 + 3.00000i 0.839254 + 0.279751i
\(116\) 6.00000 0.557086
\(117\) 4.24264 + 12.0000i 0.392232 + 1.10940i
\(118\) 6.00000i 0.552345i
\(119\) 0 0
\(120\) 3.12132 2.29289i 0.284936 0.209312i
\(121\) 3.00000 0.272727
\(122\) 10.0000i 0.905357i
\(123\) −8.48528 6.00000i −0.765092 0.541002i
\(124\) 4.24264i 0.381000i
\(125\) 6.36396 + 9.19239i 0.569210 + 0.822192i
\(126\) 0 0
\(127\) −12.7279 −1.12942 −0.564710 0.825289i \(-0.691012\pi\)
−0.564710 + 0.825289i \(0.691012\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −12.0000 + 16.9706i −1.05654 + 1.49417i
\(130\) 3.00000 9.00000i 0.263117 0.789352i
\(131\) 11.3137i 0.988483i −0.869325 0.494242i \(-0.835446\pi\)
0.869325 0.494242i \(-0.164554\pi\)
\(132\) −2.82843 + 4.00000i −0.246183 + 0.348155i
\(133\) 0 0
\(134\) 0 0
\(135\) 6.53553 9.60660i 0.562489 0.826805i
\(136\) 0 0
\(137\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(138\) −4.24264 + 6.00000i −0.361158 + 0.510754i
\(139\) 4.00000 0.339276 0.169638 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 0 0
\(141\) 18.0000 + 12.7279i 1.51587 + 1.07188i
\(142\) 12.0000i 1.00702i
\(143\) 12.0000i 1.00349i
\(144\) 1.00000 + 2.82843i 0.0833333 + 0.235702i
\(145\) −12.7279 4.24264i −1.05700 0.352332i
\(146\) −6.00000 −0.496564
\(147\) −9.89949 7.00000i −0.816497 0.577350i
\(148\) −4.24264 −0.348743
\(149\) 1.41421i 0.115857i −0.998321 0.0579284i \(-0.981550\pi\)
0.998321 0.0579284i \(-0.0184495\pi\)
\(150\) −8.24264 + 2.65685i −0.673009 + 0.216931i
\(151\) 4.24264i 0.345261i 0.984987 + 0.172631i \(0.0552267\pi\)
−0.984987 + 0.172631i \(0.944773\pi\)
\(152\) −4.24264 + 1.00000i −0.344124 + 0.0811107i
\(153\) 0 0
\(154\) 0 0
\(155\) 3.00000 9.00000i 0.240966 0.722897i
\(156\) 6.00000 + 4.24264i 0.480384 + 0.339683i
\(157\) 18.0000i 1.43656i −0.695756 0.718278i \(-0.744931\pi\)
0.695756 0.718278i \(-0.255069\pi\)
\(158\) 12.7279 1.01258
\(159\) 6.00000 8.48528i 0.475831 0.672927i
\(160\) 0.707107 2.12132i 0.0559017 0.167705i
\(161\) 0 0
\(162\) 5.65685 + 7.00000i 0.444444 + 0.549972i
\(163\) 6.00000i 0.469956i 0.972001 + 0.234978i \(0.0755019\pi\)
−0.972001 + 0.234978i \(0.924498\pi\)
\(164\) −6.00000 −0.468521
\(165\) 8.82843 6.48528i 0.687292 0.504878i
\(166\) 0 0
\(167\) 12.0000i 0.928588i −0.885681 0.464294i \(-0.846308\pi\)
0.885681 0.464294i \(-0.153692\pi\)
\(168\) 0 0
\(169\) 5.00000 0.384615
\(170\) 0 0
\(171\) −11.0000 + 7.07107i −0.841191 + 0.540738i
\(172\) 12.0000i 0.914991i
\(173\) 6.00000i 0.456172i −0.973641 0.228086i \(-0.926753\pi\)
0.973641 0.228086i \(-0.0732467\pi\)
\(174\) 6.00000 8.48528i 0.454859 0.643268i
\(175\) 0 0
\(176\) 2.82843i 0.213201i
\(177\) 8.48528 + 6.00000i 0.637793 + 0.450988i
\(178\) 12.0000i 0.899438i
\(179\) 12.0000 0.896922 0.448461 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) −0.121320 6.70711i −0.00904268 0.499918i
\(181\) 4.24264i 0.315353i −0.987491 0.157676i \(-0.949600\pi\)
0.987491 0.157676i \(-0.0504003\pi\)
\(182\) 0 0
\(183\) −14.1421 10.0000i −1.04542 0.739221i
\(184\) 4.24264i 0.312772i
\(185\) 9.00000 + 3.00000i 0.661693 + 0.220564i
\(186\) 6.00000 + 4.24264i 0.439941 + 0.311086i
\(187\) 0 0
\(188\) 12.7279 0.928279
\(189\) 0 0
\(190\) 9.70711 + 0.878680i 0.704228 + 0.0637461i
\(191\) 15.5563i 1.12562i −0.826587 0.562809i \(-0.809721\pi\)
0.826587 0.562809i \(-0.190279\pi\)
\(192\) 1.41421 + 1.00000i 0.102062 + 0.0721688i
\(193\) −16.9706 −1.22157 −0.610784 0.791797i \(-0.709146\pi\)
−0.610784 + 0.791797i \(0.709146\pi\)
\(194\) 0 0
\(195\) −9.72792 13.2426i −0.696631 0.948325i
\(196\) −7.00000 −0.500000
\(197\) −12.7279 −0.906827 −0.453413 0.891300i \(-0.649794\pi\)
−0.453413 + 0.891300i \(0.649794\pi\)
\(198\) 2.82843 + 8.00000i 0.201008 + 0.568535i
\(199\) −16.0000 −1.13421 −0.567105 0.823646i \(-0.691937\pi\)
−0.567105 + 0.823646i \(0.691937\pi\)
\(200\) −3.00000 + 4.00000i −0.212132 + 0.282843i
\(201\) 0 0
\(202\) 15.5563 1.09454
\(203\) 0 0
\(204\) 0 0
\(205\) 12.7279 + 4.24264i 0.888957 + 0.296319i
\(206\) 4.24264i 0.295599i
\(207\) 4.24264 + 12.0000i 0.294884 + 0.834058i
\(208\) 4.24264 0.294174
\(209\) −12.0000 + 2.82843i −0.830057 + 0.195646i
\(210\) 0 0
\(211\) 8.48528i 0.584151i −0.956395 0.292075i \(-0.905654\pi\)
0.956395 0.292075i \(-0.0943458\pi\)
\(212\) 6.00000i 0.412082i
\(213\) −16.9706 12.0000i −1.16280 0.822226i
\(214\) 12.0000 0.820303
\(215\) 8.48528 25.4558i 0.578691 1.73607i
\(216\) 5.00000 + 1.41421i 0.340207 + 0.0962250i
\(217\) 0 0
\(218\) −4.24264 −0.287348
\(219\) −6.00000 + 8.48528i −0.405442 + 0.573382i
\(220\) 2.00000 6.00000i 0.134840 0.404520i
\(221\) 0 0
\(222\) −4.24264 + 6.00000i −0.284747 + 0.402694i
\(223\) 21.2132 1.42054 0.710271 0.703929i \(-0.248573\pi\)
0.710271 + 0.703929i \(0.248573\pi\)
\(224\) 0 0
\(225\) −4.48528 + 14.3137i −0.299019 + 0.954247i
\(226\) 0 0
\(227\) 18.0000i 1.19470i 0.801980 + 0.597351i \(0.203780\pi\)
−0.801980 + 0.597351i \(0.796220\pi\)
\(228\) −2.82843 + 7.00000i −0.187317 + 0.463586i
\(229\) −14.0000 −0.925146 −0.462573 0.886581i \(-0.653074\pi\)
−0.462573 + 0.886581i \(0.653074\pi\)
\(230\) 3.00000 9.00000i 0.197814 0.593442i
\(231\) 0 0
\(232\) 6.00000i 0.393919i
\(233\) −8.48528 −0.555889 −0.277945 0.960597i \(-0.589653\pi\)
−0.277945 + 0.960597i \(0.589653\pi\)
\(234\) 12.0000 4.24264i 0.784465 0.277350i
\(235\) −27.0000 9.00000i −1.76129 0.587095i
\(236\) 6.00000 0.390567
\(237\) 12.7279 18.0000i 0.826767 1.16923i
\(238\) 0 0
\(239\) 24.0416i 1.55512i −0.628806 0.777562i \(-0.716456\pi\)
0.628806 0.777562i \(-0.283544\pi\)
\(240\) −2.29289 3.12132i −0.148006 0.201480i
\(241\) 8.48528i 0.546585i −0.961931 0.273293i \(-0.911887\pi\)
0.961931 0.273293i \(-0.0881127\pi\)
\(242\) 3.00000i 0.192847i
\(243\) 15.5563 1.00000i 0.997940 0.0641500i
\(244\) −10.0000 −0.640184
\(245\) 14.8492 + 4.94975i 0.948683 + 0.316228i
\(246\) −6.00000 + 8.48528i −0.382546 + 0.541002i
\(247\) 4.24264 + 18.0000i 0.269953 + 1.14531i
\(248\) 4.24264 0.269408
\(249\) 0 0
\(250\) 9.19239 6.36396i 0.581378 0.402492i
\(251\) 5.65685i 0.357057i 0.983935 + 0.178529i \(0.0571337\pi\)
−0.983935 + 0.178529i \(0.942866\pi\)
\(252\) 0 0
\(253\) 12.0000i 0.754434i
\(254\) 12.7279i 0.798621i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 18.0000i 1.12281i −0.827541 0.561405i \(-0.810261\pi\)
0.827541 0.561405i \(-0.189739\pi\)
\(258\) 16.9706 + 12.0000i 1.05654 + 0.747087i
\(259\) 0 0
\(260\) −9.00000 3.00000i −0.558156 0.186052i
\(261\) −6.00000 16.9706i −0.371391 1.05045i
\(262\) −11.3137 −0.698963
\(263\) −21.2132 −1.30806 −0.654031 0.756468i \(-0.726923\pi\)
−0.654031 + 0.756468i \(0.726923\pi\)
\(264\) 4.00000 + 2.82843i 0.246183 + 0.174078i
\(265\) −4.24264 + 12.7279i −0.260623 + 0.781870i
\(266\) 0 0
\(267\) 16.9706 + 12.0000i 1.03858 + 0.734388i
\(268\) 0 0
\(269\) −6.00000 −0.365826 −0.182913 0.983129i \(-0.558553\pi\)
−0.182913 + 0.983129i \(0.558553\pi\)
\(270\) −9.60660 6.53553i −0.584639 0.397740i
\(271\) −20.0000 −1.21491 −0.607457 0.794353i \(-0.707810\pi\)
−0.607457 + 0.794353i \(0.707810\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −8.48528 + 11.3137i −0.511682 + 0.682242i
\(276\) 6.00000 + 4.24264i 0.361158 + 0.255377i
\(277\) 18.0000i 1.08152i 0.841178 + 0.540758i \(0.181862\pi\)
−0.841178 + 0.540758i \(0.818138\pi\)
\(278\) 4.00000i 0.239904i
\(279\) 12.0000 4.24264i 0.718421 0.254000i
\(280\) 0 0
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) 12.7279 18.0000i 0.757937 1.07188i
\(283\) 18.0000i 1.06999i 0.844856 + 0.534994i \(0.179686\pi\)
−0.844856 + 0.534994i \(0.820314\pi\)
\(284\) −12.0000 −0.712069
\(285\) 10.9497 12.8492i 0.648607 0.761123i
\(286\) 12.0000 0.709575
\(287\) 0 0
\(288\) 2.82843 1.00000i 0.166667 0.0589256i
\(289\) −17.0000 −1.00000
\(290\) −4.24264 + 12.7279i −0.249136 + 0.747409i
\(291\) 0 0
\(292\) 6.00000i 0.351123i
\(293\) 18.0000i 1.05157i −0.850617 0.525786i \(-0.823771\pi\)
0.850617 0.525786i \(-0.176229\pi\)
\(294\) −7.00000 + 9.89949i −0.408248 + 0.577350i
\(295\) −12.7279 4.24264i −0.741048 0.247016i
\(296\) 4.24264i 0.246598i
\(297\) 14.1421 + 4.00000i 0.820610 + 0.232104i
\(298\) −1.41421 −0.0819232
\(299\) 18.0000 1.04097
\(300\) 2.65685 + 8.24264i 0.153394 + 0.475889i
\(301\) 0 0
\(302\) 4.24264 0.244137
\(303\) 15.5563 22.0000i 0.893689 1.26387i
\(304\) 1.00000 + 4.24264i 0.0573539 + 0.243332i
\(305\) 21.2132 + 7.07107i 1.21466 + 0.404888i
\(306\) 0 0
\(307\) 33.9411 1.93712 0.968561 0.248776i \(-0.0800281\pi\)
0.968561 + 0.248776i \(0.0800281\pi\)
\(308\) 0 0
\(309\) 6.00000 + 4.24264i 0.341328 + 0.241355i
\(310\) −9.00000 3.00000i −0.511166 0.170389i
\(311\) 1.41421i 0.0801927i −0.999196 0.0400963i \(-0.987234\pi\)
0.999196 0.0400963i \(-0.0127665\pi\)
\(312\) 4.24264 6.00000i 0.240192 0.339683i
\(313\) 30.0000i 1.69570i −0.530236 0.847850i \(-0.677897\pi\)
0.530236 0.847850i \(-0.322103\pi\)
\(314\) −18.0000 −1.01580
\(315\) 0 0
\(316\) 12.7279i 0.716002i
\(317\) 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
\(319\) 16.9706i 0.950169i
\(320\) −2.12132 0.707107i −0.118585 0.0395285i
\(321\) 12.0000 16.9706i 0.669775 0.947204i
\(322\) 0 0
\(323\) 0 0
\(324\) 7.00000 5.65685i 0.388889 0.314270i
\(325\) 16.9706 + 12.7279i 0.941357 + 0.706018i
\(326\) 6.00000 0.332309
\(327\) −4.24264 + 6.00000i −0.234619 + 0.331801i
\(328\) 6.00000i 0.331295i
\(329\) 0 0
\(330\) −6.48528 8.82843i −0.357003 0.485989i
\(331\) 33.9411i 1.86557i −0.360429 0.932786i \(-0.617370\pi\)
0.360429 0.932786i \(-0.382630\pi\)
\(332\) 0 0
\(333\) 4.24264 + 12.0000i 0.232495 + 0.657596i
\(334\) −12.0000 −0.656611
\(335\) 0 0
\(336\) 0 0
\(337\) −25.4558 −1.38667 −0.693334 0.720616i \(-0.743859\pi\)
−0.693334 + 0.720616i \(0.743859\pi\)
\(338\) 5.00000i 0.271964i
\(339\) 0 0
\(340\) 0 0
\(341\) 12.0000 0.649836
\(342\) 7.07107 + 11.0000i 0.382360 + 0.594812i
\(343\) 0 0
\(344\) 12.0000 0.646997
\(345\) −9.72792 13.2426i −0.523734 0.712960i
\(346\) −6.00000 −0.322562
\(347\) −8.48528 −0.455514 −0.227757 0.973718i \(-0.573139\pi\)
−0.227757 + 0.973718i \(0.573139\pi\)
\(348\) −8.48528 6.00000i −0.454859 0.321634i
\(349\) 26.0000 1.39175 0.695874 0.718164i \(-0.255017\pi\)
0.695874 + 0.718164i \(0.255017\pi\)
\(350\) 0 0
\(351\) 6.00000 21.2132i 0.320256 1.13228i
\(352\) 2.82843 0.150756
\(353\) 8.48528 0.451626 0.225813 0.974171i \(-0.427496\pi\)
0.225813 + 0.974171i \(0.427496\pi\)
\(354\) 6.00000 8.48528i 0.318896 0.450988i
\(355\) 25.4558 + 8.48528i 1.35106 + 0.450352i
\(356\) 12.0000 0.635999
\(357\) 0 0
\(358\) 12.0000i 0.634220i
\(359\) 7.07107i 0.373197i 0.982436 + 0.186598i \(0.0597463\pi\)
−0.982436 + 0.186598i \(0.940254\pi\)
\(360\) −6.70711 + 0.121320i −0.353496 + 0.00639414i
\(361\) −17.0000 + 8.48528i −0.894737 + 0.446594i
\(362\) −4.24264 −0.222988
\(363\) −4.24264 3.00000i −0.222681 0.157459i
\(364\) 0 0
\(365\) 4.24264 12.7279i 0.222070 0.666210i
\(366\) −10.0000 + 14.1421i −0.522708 + 0.739221i
\(367\) 24.0000i 1.25279i 0.779506 + 0.626395i \(0.215470\pi\)
−0.779506 + 0.626395i \(0.784530\pi\)
\(368\) 4.24264 0.221163
\(369\) 6.00000 + 16.9706i 0.312348 + 0.883452i
\(370\) 3.00000 9.00000i 0.155963 0.467888i
\(371\) 0 0
\(372\) 4.24264 6.00000i 0.219971 0.311086i
\(373\) 21.2132 1.09838 0.549189 0.835698i \(-0.314937\pi\)
0.549189 + 0.835698i \(0.314937\pi\)
\(374\) 0 0
\(375\) 0.192388 19.3640i 0.00993488 0.999951i
\(376\) 12.7279i 0.656392i
\(377\) −25.4558 −1.31104
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0.878680 9.70711i 0.0450753 0.497964i
\(381\) 18.0000 + 12.7279i 0.922168 + 0.652071i
\(382\) −15.5563 −0.795932
\(383\) 12.0000i 0.613171i 0.951843 + 0.306586i \(0.0991866\pi\)
−0.951843 + 0.306586i \(0.900813\pi\)
\(384\) 1.00000 1.41421i 0.0510310 0.0721688i
\(385\) 0 0
\(386\) 16.9706i 0.863779i
\(387\) 33.9411 12.0000i 1.72532 0.609994i
\(388\) 0 0
\(389\) 9.89949i 0.501924i 0.967997 + 0.250962i \(0.0807470\pi\)
−0.967997 + 0.250962i \(0.919253\pi\)
\(390\) −13.2426 + 9.72792i −0.670567 + 0.492592i
\(391\) 0 0
\(392\) 7.00000i 0.353553i
\(393\) −11.3137 + 16.0000i −0.570701 + 0.807093i
\(394\) 12.7279i 0.641223i
\(395\) −9.00000 + 27.0000i −0.452839 + 1.35852i
\(396\) 8.00000 2.82843i 0.402015 0.142134i
\(397\) 30.0000i 1.50566i 0.658217 + 0.752828i \(0.271311\pi\)
−0.658217 + 0.752828i \(0.728689\pi\)
\(398\) 16.0000i 0.802008i
\(399\) 0 0
\(400\) 4.00000 + 3.00000i 0.200000 + 0.150000i
\(401\) −18.0000 −0.898877 −0.449439 0.893311i \(-0.648376\pi\)
−0.449439 + 0.893311i \(0.648376\pi\)
\(402\) 0 0
\(403\) 18.0000i 0.896644i
\(404\) 15.5563i 0.773957i
\(405\) −18.8492 + 7.05025i −0.936626 + 0.350330i
\(406\) 0 0
\(407\) 12.0000i 0.594818i
\(408\) 0 0
\(409\) 25.4558i 1.25871i −0.777118 0.629355i \(-0.783319\pi\)
0.777118 0.629355i \(-0.216681\pi\)
\(410\) 4.24264 12.7279i 0.209529 0.628587i
\(411\) 0 0
\(412\) 4.24264 0.209020
\(413\) 0 0
\(414\) 12.0000 4.24264i 0.589768 0.208514i
\(415\) 0 0
\(416\) 4.24264i 0.208013i
\(417\) −5.65685 4.00000i −0.277017 0.195881i
\(418\) 2.82843 + 12.0000i 0.138343 + 0.586939i
\(419\) 14.1421i 0.690889i 0.938439 + 0.345444i \(0.112272\pi\)
−0.938439 + 0.345444i \(0.887728\pi\)
\(420\) 0 0
\(421\) 29.6985i 1.44742i 0.690107 + 0.723708i \(0.257564\pi\)
−0.690107 + 0.723708i \(0.742436\pi\)
\(422\) −8.48528 −0.413057
\(423\) −12.7279 36.0000i −0.618853 1.75038i
\(424\) −6.00000 −0.291386
\(425\) 0 0
\(426\) −12.0000 + 16.9706i −0.581402 + 0.822226i
\(427\) 0 0
\(428\) 12.0000i 0.580042i
\(429\) 12.0000 16.9706i 0.579365 0.819346i
\(430\) −25.4558 8.48528i −1.22759 0.409197i
\(431\) 12.0000 0.578020 0.289010 0.957326i \(-0.406674\pi\)
0.289010 + 0.957326i \(0.406674\pi\)
\(432\) 1.41421 5.00000i 0.0680414 0.240563i
\(433\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(434\) 0 0
\(435\) 13.7574 + 18.7279i 0.659615 + 0.897935i
\(436\) 4.24264i 0.203186i
\(437\) 4.24264 + 18.0000i 0.202953 + 0.861057i
\(438\) 8.48528 + 6.00000i 0.405442 + 0.286691i
\(439\) 4.24264i 0.202490i 0.994862 + 0.101245i \(0.0322826\pi\)
−0.994862 + 0.101245i \(0.967717\pi\)
\(440\) −6.00000 2.00000i −0.286039 0.0953463i
\(441\) 7.00000 + 19.7990i 0.333333 + 0.942809i
\(442\) 0 0
\(443\) −8.48528 −0.403148 −0.201574 0.979473i \(-0.564606\pi\)
−0.201574 + 0.979473i \(0.564606\pi\)
\(444\) 6.00000 + 4.24264i 0.284747 + 0.201347i
\(445\) −25.4558 8.48528i −1.20672 0.402241i
\(446\) 21.2132i 1.00447i
\(447\) −1.41421 + 2.00000i −0.0668900 + 0.0945968i
\(448\) 0 0
\(449\) 24.0000 1.13263 0.566315 0.824189i \(-0.308369\pi\)
0.566315 + 0.824189i \(0.308369\pi\)
\(450\) 14.3137 + 4.48528i 0.674755 + 0.211438i
\(451\) 16.9706i 0.799113i
\(452\) 0 0
\(453\) 4.24264 6.00000i 0.199337 0.281905i
\(454\) 18.0000 0.844782
\(455\) 0 0
\(456\) 7.00000 + 2.82843i 0.327805 + 0.132453i
\(457\) 12.0000i 0.561336i −0.959805 0.280668i \(-0.909444\pi\)
0.959805 0.280668i \(-0.0905560\pi\)
\(458\) 14.0000i 0.654177i
\(459\) 0 0
\(460\) −9.00000 3.00000i −0.419627 0.139876i
\(461\) 15.5563i 0.724531i −0.932075 0.362266i \(-0.882003\pi\)
0.932075 0.362266i \(-0.117997\pi\)
\(462\) 0 0
\(463\) 36.0000i 1.67306i −0.547920 0.836531i \(-0.684580\pi\)
0.547920 0.836531i \(-0.315420\pi\)
\(464\) −6.00000 −0.278543
\(465\) −13.2426 + 9.72792i −0.614113 + 0.451122i
\(466\) 8.48528i 0.393073i
\(467\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(468\) −4.24264 12.0000i −0.196116 0.554700i
\(469\) 0 0
\(470\) −9.00000 + 27.0000i −0.415139 + 1.24542i
\(471\) −18.0000 + 25.4558i −0.829396 + 1.17294i
\(472\) 6.00000i 0.276172i
\(473\) 33.9411 1.56061
\(474\) −18.0000 12.7279i −0.826767 0.584613i
\(475\) −8.72792 + 19.9706i −0.400465 + 0.916312i
\(476\) 0 0
\(477\) −16.9706 + 6.00000i −0.777029 + 0.274721i
\(478\) −24.0416 −1.09964
\(479\) 9.89949i 0.452319i −0.974090 0.226160i \(-0.927383\pi\)
0.974090 0.226160i \(-0.0726171\pi\)
\(480\) −3.12132 + 2.29289i −0.142468 + 0.104656i
\(481\) 18.0000 0.820729
\(482\) −8.48528 −0.386494
\(483\) 0 0
\(484\) −3.00000 −0.136364
\(485\) 0 0
\(486\) −1.00000 15.5563i −0.0453609 0.705650i
\(487\) −12.7279 −0.576757 −0.288379 0.957516i \(-0.593116\pi\)
−0.288379 + 0.957516i \(0.593116\pi\)
\(488\) 10.0000i 0.452679i
\(489\) 6.00000 8.48528i 0.271329 0.383718i
\(490\) 4.94975 14.8492i 0.223607 0.670820i
\(491\) 39.5980i 1.78703i 0.449032 + 0.893516i \(0.351769\pi\)
−0.449032 + 0.893516i \(0.648231\pi\)
\(492\) 8.48528 + 6.00000i 0.382546 + 0.270501i
\(493\) 0 0
\(494\) 18.0000 4.24264i 0.809858 0.190885i
\(495\) −18.9706 + 0.343146i −0.852663 + 0.0154233i
\(496\) 4.24264i 0.190500i
\(497\) 0 0
\(498\) 0 0
\(499\) −14.0000 −0.626726 −0.313363 0.949633i \(-0.601456\pi\)
−0.313363 + 0.949633i \(0.601456\pi\)
\(500\) −6.36396 9.19239i −0.284605 0.411096i
\(501\) −12.0000 + 16.9706i −0.536120 + 0.758189i
\(502\) 5.65685 0.252478
\(503\) −21.2132 −0.945850 −0.472925 0.881103i \(-0.656802\pi\)
−0.472925 + 0.881103i \(0.656802\pi\)
\(504\) 0 0
\(505\) −11.0000 + 33.0000i −0.489494 + 1.46848i
\(506\) 12.0000 0.533465
\(507\) −7.07107 5.00000i −0.314037 0.222058i
\(508\) 12.7279 0.564710
\(509\) −18.0000 −0.797836 −0.398918 0.916987i \(-0.630614\pi\)
−0.398918 + 0.916987i \(0.630614\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 22.6274 + 1.00000i 0.999025 + 0.0441511i
\(514\) −18.0000 −0.793946
\(515\) −9.00000 3.00000i −0.396587 0.132196i
\(516\) 12.0000 16.9706i 0.528271 0.747087i
\(517\) 36.0000i 1.58328i
\(518\) 0 0
\(519\) −6.00000 + 8.48528i −0.263371 + 0.372463i
\(520\) −3.00000 + 9.00000i −0.131559 + 0.394676i
\(521\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(522\) −16.9706 + 6.00000i −0.742781 + 0.262613i
\(523\) −16.9706 −0.742071 −0.371035 0.928619i \(-0.620997\pi\)
−0.371035 + 0.928619i \(0.620997\pi\)
\(524\) 11.3137i 0.494242i
\(525\) 0 0
\(526\) 21.2132i 0.924940i
\(527\) 0 0
\(528\) 2.82843 4.00000i 0.123091 0.174078i
\(529\) −5.00000 −0.217391
\(530\) 12.7279 + 4.24264i 0.552866 + 0.184289i
\(531\) −6.00000 16.9706i −0.260378 0.736460i
\(532\) 0 0
\(533\) 25.4558 1.10262
\(534\) 12.0000 16.9706i 0.519291 0.734388i
\(535\) −8.48528 + 25.4558i −0.366851 + 1.10055i
\(536\) 0 0
\(537\) −16.9706 12.0000i −0.732334 0.517838i
\(538\) 6.00000i 0.258678i
\(539\) 19.7990i 0.852803i
\(540\) −6.53553 + 9.60660i −0.281245 + 0.413402i
\(541\) −38.0000 −1.63375 −0.816874 0.576816i \(-0.804295\pi\)
−0.816874 + 0.576816i \(0.804295\pi\)
\(542\) 20.0000i 0.859074i
\(543\) −4.24264 + 6.00000i −0.182069 + 0.257485i
\(544\) 0 0
\(545\) 3.00000 9.00000i 0.128506 0.385518i
\(546\) 0 0
\(547\) −33.9411 −1.45122 −0.725609 0.688107i \(-0.758442\pi\)
−0.725609 + 0.688107i \(0.758442\pi\)
\(548\) 0 0
\(549\) 10.0000 + 28.2843i 0.426790 + 1.20714i
\(550\) 11.3137 + 8.48528i 0.482418 + 0.361814i
\(551\) −6.00000 25.4558i −0.255609 1.08446i
\(552\) 4.24264 6.00000i 0.180579 0.255377i
\(553\) 0 0
\(554\) 18.0000 0.764747
\(555\) −9.72792 13.2426i −0.412927 0.562119i
\(556\) −4.00000 −0.169638
\(557\) −21.2132 −0.898832 −0.449416 0.893323i \(-0.648368\pi\)
−0.449416 + 0.893323i \(0.648368\pi\)
\(558\) −4.24264 12.0000i −0.179605 0.508001i
\(559\) 50.9117i 2.15333i
\(560\) 0 0
\(561\) 0 0
\(562\) 18.0000i 0.759284i
\(563\) 12.0000i 0.505740i 0.967500 + 0.252870i \(0.0813744\pi\)
−0.967500 + 0.252870i \(0.918626\pi\)
\(564\) −18.0000 12.7279i −0.757937 0.535942i
\(565\) 0 0
\(566\) 18.0000 0.756596
\(567\) 0 0
\(568\) 12.0000i 0.503509i
\(569\) 24.0000 1.00613 0.503066 0.864248i \(-0.332205\pi\)
0.503066 + 0.864248i \(0.332205\pi\)
\(570\) −12.8492 10.9497i −0.538196 0.458634i
\(571\) 22.0000 0.920671 0.460336 0.887745i \(-0.347729\pi\)
0.460336 + 0.887745i \(0.347729\pi\)
\(572\) 12.0000i 0.501745i
\(573\) −15.5563 + 22.0000i −0.649876 + 0.919063i
\(574\) 0 0
\(575\) 16.9706 + 12.7279i 0.707721 + 0.530791i
\(576\) −1.00000 2.82843i −0.0416667 0.117851i
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) 17.0000i 0.707107i
\(579\) 24.0000 + 16.9706i 0.997406 + 0.705273i
\(580\) 12.7279 + 4.24264i 0.528498 + 0.176166i
\(581\) 0 0
\(582\) 0 0
\(583\) −16.9706 −0.702849
\(584\) 6.00000 0.248282
\(585\) 0.514719 + 28.4558i 0.0212810 + 1.17650i
\(586\) −18.0000 −0.743573
\(587\) 42.4264 1.75113 0.875563 0.483105i \(-0.160491\pi\)
0.875563 + 0.483105i \(0.160491\pi\)
\(588\) 9.89949 + 7.00000i 0.408248 + 0.288675i
\(589\) 18.0000 4.24264i 0.741677 0.174815i
\(590\) −4.24264 + 12.7279i −0.174667 + 0.524000i
\(591\) 18.0000 + 12.7279i 0.740421 + 0.523557i
\(592\) 4.24264 0.174371
\(593\) 8.48528 0.348449 0.174224 0.984706i \(-0.444258\pi\)
0.174224 + 0.984706i \(0.444258\pi\)
\(594\) 4.00000 14.1421i 0.164122 0.580259i
\(595\) 0 0
\(596\) 1.41421i 0.0579284i
\(597\) 22.6274 + 16.0000i 0.926079 + 0.654836i
\(598\) 18.0000i 0.736075i
\(599\) 48.0000 1.96123 0.980613 0.195952i \(-0.0627798\pi\)
0.980613 + 0.195952i \(0.0627798\pi\)
\(600\) 8.24264 2.65685i 0.336504 0.108466i
\(601\) 16.9706i 0.692244i 0.938190 + 0.346122i \(0.112502\pi\)
−0.938190 + 0.346122i \(0.887498\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 4.24264i 0.172631i
\(605\) 6.36396 + 2.12132i 0.258732 + 0.0862439i
\(606\) −22.0000 15.5563i −0.893689 0.631933i
\(607\) 4.24264 0.172203 0.0861017 0.996286i \(-0.472559\pi\)
0.0861017 + 0.996286i \(0.472559\pi\)
\(608\) 4.24264 1.00000i 0.172062 0.0405554i
\(609\) 0 0
\(610\) 7.07107 21.2132i 0.286299 0.858898i
\(611\) −54.0000 −2.18461
\(612\) 0 0
\(613\) 6.00000i 0.242338i −0.992632 0.121169i \(-0.961336\pi\)
0.992632 0.121169i \(-0.0386643\pi\)
\(614\) 33.9411i 1.36975i
\(615\) −13.7574 18.7279i −0.554750 0.755183i
\(616\) 0 0
\(617\) −42.4264 −1.70802 −0.854011 0.520254i \(-0.825837\pi\)
−0.854011 + 0.520254i \(0.825837\pi\)
\(618\) 4.24264 6.00000i 0.170664 0.241355i
\(619\) 10.0000 0.401934 0.200967 0.979598i \(-0.435592\pi\)
0.200967 + 0.979598i \(0.435592\pi\)
\(620\) −3.00000 + 9.00000i −0.120483 + 0.361449i
\(621\) 6.00000 21.2132i 0.240772 0.851257i
\(622\) −1.41421 −0.0567048
\(623\) 0 0
\(624\) −6.00000 4.24264i −0.240192 0.169842i
\(625\) 7.00000 + 24.0000i 0.280000 + 0.960000i
\(626\) −30.0000 −1.19904
\(627\) 19.7990 + 8.00000i 0.790695 + 0.319489i
\(628\) 18.0000i 0.718278i
\(629\) 0 0
\(630\) 0 0
\(631\) −20.0000 −0.796187 −0.398094 0.917345i \(-0.630328\pi\)
−0.398094 + 0.917345i \(0.630328\pi\)
\(632\) −12.7279 −0.506290
\(633\) −8.48528 + 12.0000i −0.337260 + 0.476957i
\(634\) −18.0000 −0.714871
\(635\) −27.0000 9.00000i −1.07146 0.357154i
\(636\) −6.00000 + 8.48528i −0.237915 + 0.336463i
\(637\) 29.6985 1.17670
\(638\) −16.9706 −0.671871
\(639\) 12.0000 + 33.9411i 0.474713 + 1.34269i
\(640\) −0.707107 + 2.12132i −0.0279508 + 0.0838525i
\(641\) −24.0000 −0.947943 −0.473972 0.880540i \(-0.657180\pi\)
−0.473972 + 0.880540i \(0.657180\pi\)
\(642\) −16.9706 12.0000i −0.669775 0.473602i
\(643\) 6.00000i 0.236617i −0.992977 0.118308i \(-0.962253\pi\)
0.992977 0.118308i \(-0.0377472\pi\)
\(644\) 0 0
\(645\) −37.4558 + 27.5147i −1.47482 + 1.08339i
\(646\) 0 0
\(647\) 4.24264 0.166795 0.0833977 0.996516i \(-0.473423\pi\)
0.0833977 + 0.996516i \(0.473423\pi\)
\(648\) −5.65685 7.00000i −0.222222 0.274986i
\(649\) 16.9706i 0.666153i
\(650\) 12.7279 16.9706i 0.499230 0.665640i
\(651\) 0 0
\(652\) 6.00000i 0.234978i
\(653\) −21.2132 −0.830137 −0.415068 0.909790i \(-0.636242\pi\)
−0.415068 + 0.909790i \(0.636242\pi\)
\(654\) 6.00000 + 4.24264i 0.234619 + 0.165900i
\(655\) 8.00000 24.0000i 0.312586 0.937758i
\(656\) 6.00000 0.234261
\(657\) 16.9706 6.00000i 0.662085 0.234082i
\(658\) 0 0
\(659\) 36.0000 1.40236 0.701180 0.712984i \(-0.252657\pi\)
0.701180 + 0.712984i \(0.252657\pi\)
\(660\) −8.82843 + 6.48528i −0.343646 + 0.252439i
\(661\) 4.24264i 0.165020i 0.996590 + 0.0825098i \(0.0262936\pi\)
−0.996590 + 0.0825098i \(0.973706\pi\)
\(662\) −33.9411 −1.31916
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 12.0000 4.24264i 0.464991 0.164399i
\(667\) −25.4558 −0.985654
\(668\) 12.0000i 0.464294i
\(669\) −30.0000 21.2132i −1.15987 0.820150i
\(670\) 0 0
\(671\) 28.2843i 1.09190i
\(672\) 0 0
\(673\) −16.9706 −0.654167 −0.327084 0.944995i \(-0.606066\pi\)
−0.327084 + 0.944995i \(0.606066\pi\)
\(674\) 25.4558i 0.980522i
\(675\) 20.6569 15.7574i 0.795083 0.606501i
\(676\) −5.00000 −0.192308
\(677\) 42.0000i 1.61419i −0.590421 0.807096i \(-0.701038\pi\)
0.590421 0.807096i \(-0.298962\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 18.0000 25.4558i 0.689761 0.975470i
\(682\) 12.0000i 0.459504i
\(683\) 18.0000i 0.688751i −0.938832 0.344375i \(-0.888091\pi\)
0.938832 0.344375i \(-0.111909\pi\)
\(684\) 11.0000 7.07107i 0.420596 0.270369i
\(685\) 0 0
\(686\) 0 0
\(687\) 19.7990 + 14.0000i 0.755379 + 0.534133i
\(688\) 12.0000i 0.457496i
\(689\) 25.4558i 0.969790i
\(690\) −13.2426 + 9.72792i −0.504139 + 0.370336i
\(691\) 46.0000 1.74992 0.874961 0.484193i \(-0.160887\pi\)
0.874961 + 0.484193i \(0.160887\pi\)
\(692\) 6.00000i 0.228086i
\(693\) 0 0
\(694\) 8.48528i 0.322097i
\(695\) 8.48528 + 2.82843i 0.321865 + 0.107288i
\(696\) −6.00000 + 8.48528i −0.227429 + 0.321634i
\(697\) 0 0
\(698\) 26.0000i 0.984115i
\(699\) 12.0000 + 8.48528i 0.453882 + 0.320943i
\(700\) 0 0
\(701\) 43.8406i 1.65584i −0.560848 0.827919i \(-0.689525\pi\)
0.560848 0.827919i \(-0.310475\pi\)
\(702\) −21.2132 6.00000i −0.800641 0.226455i
\(703\) 4.24264 + 18.0000i 0.160014 + 0.678883i
\(704\) 2.82843i 0.106600i
\(705\) 29.1838 + 39.7279i 1.09912 + 1.49624i
\(706\) 8.48528i 0.319348i
\(707\) 0 0
\(708\) −8.48528 6.00000i −0.318896 0.225494i
\(709\) −10.0000 −0.375558 −0.187779 0.982211i \(-0.560129\pi\)
−0.187779 + 0.982211i \(0.560129\pi\)
\(710\) 8.48528 25.4558i 0.318447 0.955341i
\(711\) −36.0000 + 12.7279i −1.35011 + 0.477334i
\(712\) 12.0000i 0.449719i
\(713\) 18.0000i 0.674105i
\(714\) 0 0
\(715\) −8.48528 + 25.4558i −0.317332 + 0.951995i
\(716\) −12.0000 −0.448461
\(717\) −24.0416 + 34.0000i −0.897851 + 1.26975i
\(718\) 7.07107 0.263890
\(719\) 18.3848i 0.685636i −0.939402 0.342818i \(-0.888619\pi\)
0.939402 0.342818i \(-0.111381\pi\)
\(720\) 0.121320 + 6.70711i 0.00452134 + 0.249959i
\(721\) 0 0
\(722\) 8.48528 + 17.0000i 0.315789 + 0.632674i
\(723\) −8.48528 + 12.0000i −0.315571 + 0.446285i
\(724\) 4.24264i 0.157676i
\(725\) −24.0000 18.0000i −0.891338 0.668503i
\(726\) −3.00000 + 4.24264i −0.111340 + 0.157459i
\(727\) 12.0000i 0.445055i −0.974926 0.222528i \(-0.928569\pi\)
0.974926 0.222528i \(-0.0714308\pi\)
\(728\) 0 0
\(729\) −23.0000 14.1421i −0.851852 0.523783i
\(730\) −12.7279 4.24264i −0.471082 0.157027i
\(731\) 0 0
\(732\) 14.1421 + 10.0000i 0.522708 + 0.369611i
\(733\) 42.0000i 1.55131i 0.631160 + 0.775653i \(0.282579\pi\)
−0.631160 + 0.775653i \(0.717421\pi\)
\(734\) 24.0000 0.885856
\(735\) −16.0503 21.8492i −0.592022 0.805921i
\(736\) 4.24264i 0.156386i
\(737\) 0 0
\(738\) 16.9706 6.00000i 0.624695 0.220863i
\(739\) 20.0000 0.735712 0.367856 0.929883i \(-0.380092\pi\)
0.367856 + 0.929883i \(0.380092\pi\)
\(740\) −9.00000 3.00000i −0.330847 0.110282i
\(741\) 12.0000 29.6985i 0.440831 1.09100i
\(742\) 0 0
\(743\) 24.0000i 0.880475i 0.897881 + 0.440237i \(0.145106\pi\)
−0.897881 + 0.440237i \(0.854894\pi\)
\(744\) −6.00000 4.24264i −0.219971 0.155543i
\(745\) 1.00000 3.00000i 0.0366372 0.109911i
\(746\) 21.2132i 0.776671i
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) −19.3640 0.192388i −0.707072 0.00702502i
\(751\) 12.7279i 0.464448i −0.972662 0.232224i \(-0.925400\pi\)
0.972662 0.232224i \(-0.0746003\pi\)
\(752\) −12.7279 −0.464140
\(753\) 5.65685 8.00000i 0.206147 0.291536i
\(754\) 25.4558i 0.927047i
\(755\) −3.00000 + 9.00000i −0.109181 + 0.327544i
\(756\) 0 0
\(757\) 42.0000i 1.52652i −0.646094 0.763258i \(-0.723599\pi\)
0.646094 0.763258i \(-0.276401\pi\)
\(758\) 0 0
\(759\) 12.0000 16.9706i 0.435572 0.615992i
\(760\) −9.70711 0.878680i −0.352114 0.0318731i
\(761\) 14.1421i 0.512652i −0.966590 0.256326i \(-0.917488\pi\)
0.966590 0.256326i \(-0.0825121\pi\)
\(762\) 12.7279 18.0000i 0.461084 0.652071i
\(763\) 0 0
\(764\) 15.5563i 0.562809i
\(765\) 0 0
\(766\) 12.0000 0.433578
\(767\) −25.4558 −0.919157
\(768\) −1.41421 1.00000i −0.0510310 0.0360844i
\(769\) 40.0000 1.44244 0.721218 0.692708i \(-0.243582\pi\)
0.721218 + 0.692708i \(0.243582\pi\)
\(770\) 0 0
\(771\) −18.0000 + 25.4558i −0.648254 + 0.916770i
\(772\) 16.9706 0.610784
\(773\) 6.00000i 0.215805i −0.994161 0.107903i \(-0.965587\pi\)
0.994161 0.107903i \(-0.0344134\pi\)
\(774\) −12.0000 33.9411i −0.431331 1.21999i
\(775\) 12.7279 16.9706i 0.457200 0.609601i
\(776\) 0 0
\(777\) 0 0
\(778\) 9.89949 0.354914
\(779\) 6.00000 + 25.4558i 0.214972 + 0.912050i
\(780\) 9.72792 + 13.2426i 0.348315 + 0.474163i
\(781\) 33.9411i 1.21451i
\(782\) 0 0
\(783\) −8.48528 + 30.0000i −0.303239 + 1.07211i
\(784\) 7.00000 0.250000
\(785\) 12.7279 38.1838i 0.454279 1.36284i
\(786\) 16.0000 + 11.3137i 0.570701 + 0.403547i
\(787\) 25.4558 0.907403 0.453701 0.891154i \(-0.350103\pi\)
0.453701 + 0.891154i \(0.350103\pi\)
\(788\) 12.7279 0.453413
\(789\) 30.0000 + 21.2132i 1.06803 + 0.755210i