Properties

Label 114.2.b.d.113.1
Level $114$
Weight $2$
Character 114.113
Analytic conductor $0.910$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 114 = 2 \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 114.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.910294583043\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{-2}) \)
Defining polynomial: \(x^{2} + 2\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 113.1
Root \(-1.41421i\) of defining polynomial
Character \(\chi\) \(=\) 114.113
Dual form 114.2.b.d.113.2

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +(1.00000 - 1.41421i) q^{3} +1.00000 q^{4} +1.41421i q^{5} +(1.00000 - 1.41421i) q^{6} -4.00000 q^{7} +1.00000 q^{8} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +(1.00000 - 1.41421i) q^{3} +1.00000 q^{4} +1.41421i q^{5} +(1.00000 - 1.41421i) q^{6} -4.00000 q^{7} +1.00000 q^{8} +(-1.00000 - 2.82843i) q^{9} +1.41421i q^{10} +5.65685i q^{11} +(1.00000 - 1.41421i) q^{12} -4.24264i q^{13} -4.00000 q^{14} +(2.00000 + 1.41421i) q^{15} +1.00000 q^{16} -2.82843i q^{17} +(-1.00000 - 2.82843i) q^{18} +(1.00000 + 4.24264i) q^{19} +1.41421i q^{20} +(-4.00000 + 5.65685i) q^{21} +5.65685i q^{22} +1.41421i q^{23} +(1.00000 - 1.41421i) q^{24} +3.00000 q^{25} -4.24264i q^{26} +(-5.00000 - 1.41421i) q^{27} -4.00000 q^{28} -6.00000 q^{29} +(2.00000 + 1.41421i) q^{30} -4.24264i q^{31} +1.00000 q^{32} +(8.00000 + 5.65685i) q^{33} -2.82843i q^{34} -5.65685i q^{35} +(-1.00000 - 2.82843i) q^{36} -4.24264i q^{37} +(1.00000 + 4.24264i) q^{38} +(-6.00000 - 4.24264i) q^{39} +1.41421i q^{40} +(-4.00000 + 5.65685i) q^{42} +2.00000 q^{43} +5.65685i q^{44} +(4.00000 - 1.41421i) q^{45} +1.41421i q^{46} +1.41421i q^{47} +(1.00000 - 1.41421i) q^{48} +9.00000 q^{49} +3.00000 q^{50} +(-4.00000 - 2.82843i) q^{51} -4.24264i q^{52} +6.00000 q^{53} +(-5.00000 - 1.41421i) q^{54} -8.00000 q^{55} -4.00000 q^{56} +(7.00000 + 2.82843i) q^{57} -6.00000 q^{58} +12.0000 q^{59} +(2.00000 + 1.41421i) q^{60} +2.00000 q^{61} -4.24264i q^{62} +(4.00000 + 11.3137i) q^{63} +1.00000 q^{64} +6.00000 q^{65} +(8.00000 + 5.65685i) q^{66} -2.82843i q^{68} +(2.00000 + 1.41421i) q^{69} -5.65685i q^{70} -12.0000 q^{71} +(-1.00000 - 2.82843i) q^{72} -4.00000 q^{73} -4.24264i q^{74} +(3.00000 - 4.24264i) q^{75} +(1.00000 + 4.24264i) q^{76} -22.6274i q^{77} +(-6.00000 - 4.24264i) q^{78} -4.24264i q^{79} +1.41421i q^{80} +(-7.00000 + 5.65685i) q^{81} -2.82843i q^{83} +(-4.00000 + 5.65685i) q^{84} +4.00000 q^{85} +2.00000 q^{86} +(-6.00000 + 8.48528i) q^{87} +5.65685i q^{88} +6.00000 q^{89} +(4.00000 - 1.41421i) q^{90} +16.9706i q^{91} +1.41421i q^{92} +(-6.00000 - 4.24264i) q^{93} +1.41421i q^{94} +(-6.00000 + 1.41421i) q^{95} +(1.00000 - 1.41421i) q^{96} +8.48528i q^{97} +9.00000 q^{98} +(16.0000 - 5.65685i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{2} + 2q^{3} + 2q^{4} + 2q^{6} - 8q^{7} + 2q^{8} - 2q^{9} + O(q^{10}) \) \( 2q + 2q^{2} + 2q^{3} + 2q^{4} + 2q^{6} - 8q^{7} + 2q^{8} - 2q^{9} + 2q^{12} - 8q^{14} + 4q^{15} + 2q^{16} - 2q^{18} + 2q^{19} - 8q^{21} + 2q^{24} + 6q^{25} - 10q^{27} - 8q^{28} - 12q^{29} + 4q^{30} + 2q^{32} + 16q^{33} - 2q^{36} + 2q^{38} - 12q^{39} - 8q^{42} + 4q^{43} + 8q^{45} + 2q^{48} + 18q^{49} + 6q^{50} - 8q^{51} + 12q^{53} - 10q^{54} - 16q^{55} - 8q^{56} + 14q^{57} - 12q^{58} + 24q^{59} + 4q^{60} + 4q^{61} + 8q^{63} + 2q^{64} + 12q^{65} + 16q^{66} + 4q^{69} - 24q^{71} - 2q^{72} - 8q^{73} + 6q^{75} + 2q^{76} - 12q^{78} - 14q^{81} - 8q^{84} + 8q^{85} + 4q^{86} - 12q^{87} + 12q^{89} + 8q^{90} - 12q^{93} - 12q^{95} + 2q^{96} + 18q^{98} + 32q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/114\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(97\)
\(\chi(n)\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 1.00000 1.41421i 0.577350 0.816497i
\(4\) 1.00000 0.500000
\(5\) 1.41421i 0.632456i 0.948683 + 0.316228i \(0.102416\pi\)
−0.948683 + 0.316228i \(0.897584\pi\)
\(6\) 1.00000 1.41421i 0.408248 0.577350i
\(7\) −4.00000 −1.51186 −0.755929 0.654654i \(-0.772814\pi\)
−0.755929 + 0.654654i \(0.772814\pi\)
\(8\) 1.00000 0.353553
\(9\) −1.00000 2.82843i −0.333333 0.942809i
\(10\) 1.41421i 0.447214i
\(11\) 5.65685i 1.70561i 0.522233 + 0.852803i \(0.325099\pi\)
−0.522233 + 0.852803i \(0.674901\pi\)
\(12\) 1.00000 1.41421i 0.288675 0.408248i
\(13\) 4.24264i 1.17670i −0.808608 0.588348i \(-0.799778\pi\)
0.808608 0.588348i \(-0.200222\pi\)
\(14\) −4.00000 −1.06904
\(15\) 2.00000 + 1.41421i 0.516398 + 0.365148i
\(16\) 1.00000 0.250000
\(17\) 2.82843i 0.685994i −0.939336 0.342997i \(-0.888558\pi\)
0.939336 0.342997i \(-0.111442\pi\)
\(18\) −1.00000 2.82843i −0.235702 0.666667i
\(19\) 1.00000 + 4.24264i 0.229416 + 0.973329i
\(20\) 1.41421i 0.316228i
\(21\) −4.00000 + 5.65685i −0.872872 + 1.23443i
\(22\) 5.65685i 1.20605i
\(23\) 1.41421i 0.294884i 0.989071 + 0.147442i \(0.0471040\pi\)
−0.989071 + 0.147442i \(0.952896\pi\)
\(24\) 1.00000 1.41421i 0.204124 0.288675i
\(25\) 3.00000 0.600000
\(26\) 4.24264i 0.832050i
\(27\) −5.00000 1.41421i −0.962250 0.272166i
\(28\) −4.00000 −0.755929
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) 2.00000 + 1.41421i 0.365148 + 0.258199i
\(31\) 4.24264i 0.762001i −0.924575 0.381000i \(-0.875580\pi\)
0.924575 0.381000i \(-0.124420\pi\)
\(32\) 1.00000 0.176777
\(33\) 8.00000 + 5.65685i 1.39262 + 0.984732i
\(34\) 2.82843i 0.485071i
\(35\) 5.65685i 0.956183i
\(36\) −1.00000 2.82843i −0.166667 0.471405i
\(37\) 4.24264i 0.697486i −0.937218 0.348743i \(-0.886609\pi\)
0.937218 0.348743i \(-0.113391\pi\)
\(38\) 1.00000 + 4.24264i 0.162221 + 0.688247i
\(39\) −6.00000 4.24264i −0.960769 0.679366i
\(40\) 1.41421i 0.223607i
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) −4.00000 + 5.65685i −0.617213 + 0.872872i
\(43\) 2.00000 0.304997 0.152499 0.988304i \(-0.451268\pi\)
0.152499 + 0.988304i \(0.451268\pi\)
\(44\) 5.65685i 0.852803i
\(45\) 4.00000 1.41421i 0.596285 0.210819i
\(46\) 1.41421i 0.208514i
\(47\) 1.41421i 0.206284i 0.994667 + 0.103142i \(0.0328896\pi\)
−0.994667 + 0.103142i \(0.967110\pi\)
\(48\) 1.00000 1.41421i 0.144338 0.204124i
\(49\) 9.00000 1.28571
\(50\) 3.00000 0.424264
\(51\) −4.00000 2.82843i −0.560112 0.396059i
\(52\) 4.24264i 0.588348i
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) −5.00000 1.41421i −0.680414 0.192450i
\(55\) −8.00000 −1.07872
\(56\) −4.00000 −0.534522
\(57\) 7.00000 + 2.82843i 0.927173 + 0.374634i
\(58\) −6.00000 −0.787839
\(59\) 12.0000 1.56227 0.781133 0.624364i \(-0.214642\pi\)
0.781133 + 0.624364i \(0.214642\pi\)
\(60\) 2.00000 + 1.41421i 0.258199 + 0.182574i
\(61\) 2.00000 0.256074 0.128037 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) 4.24264i 0.538816i
\(63\) 4.00000 + 11.3137i 0.503953 + 1.42539i
\(64\) 1.00000 0.125000
\(65\) 6.00000 0.744208
\(66\) 8.00000 + 5.65685i 0.984732 + 0.696311i
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 2.82843i 0.342997i
\(69\) 2.00000 + 1.41421i 0.240772 + 0.170251i
\(70\) 5.65685i 0.676123i
\(71\) −12.0000 −1.42414 −0.712069 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) −1.00000 2.82843i −0.117851 0.333333i
\(73\) −4.00000 −0.468165 −0.234082 0.972217i \(-0.575209\pi\)
−0.234082 + 0.972217i \(0.575209\pi\)
\(74\) 4.24264i 0.493197i
\(75\) 3.00000 4.24264i 0.346410 0.489898i
\(76\) 1.00000 + 4.24264i 0.114708 + 0.486664i
\(77\) 22.6274i 2.57863i
\(78\) −6.00000 4.24264i −0.679366 0.480384i
\(79\) 4.24264i 0.477334i −0.971101 0.238667i \(-0.923290\pi\)
0.971101 0.238667i \(-0.0767105\pi\)
\(80\) 1.41421i 0.158114i
\(81\) −7.00000 + 5.65685i −0.777778 + 0.628539i
\(82\) 0 0
\(83\) 2.82843i 0.310460i −0.987878 0.155230i \(-0.950388\pi\)
0.987878 0.155230i \(-0.0496119\pi\)
\(84\) −4.00000 + 5.65685i −0.436436 + 0.617213i
\(85\) 4.00000 0.433861
\(86\) 2.00000 0.215666
\(87\) −6.00000 + 8.48528i −0.643268 + 0.909718i
\(88\) 5.65685i 0.603023i
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) 4.00000 1.41421i 0.421637 0.149071i
\(91\) 16.9706i 1.77900i
\(92\) 1.41421i 0.147442i
\(93\) −6.00000 4.24264i −0.622171 0.439941i
\(94\) 1.41421i 0.145865i
\(95\) −6.00000 + 1.41421i −0.615587 + 0.145095i
\(96\) 1.00000 1.41421i 0.102062 0.144338i
\(97\) 8.48528i 0.861550i 0.902459 + 0.430775i \(0.141760\pi\)
−0.902459 + 0.430775i \(0.858240\pi\)
\(98\) 9.00000 0.909137
\(99\) 16.0000 5.65685i 1.60806 0.568535i
\(100\) 3.00000 0.300000
\(101\) 9.89949i 0.985037i 0.870302 + 0.492518i \(0.163924\pi\)
−0.870302 + 0.492518i \(0.836076\pi\)
\(102\) −4.00000 2.82843i −0.396059 0.280056i
\(103\) 12.7279i 1.25412i −0.778971 0.627060i \(-0.784258\pi\)
0.778971 0.627060i \(-0.215742\pi\)
\(104\) 4.24264i 0.416025i
\(105\) −8.00000 5.65685i −0.780720 0.552052i
\(106\) 6.00000 0.582772
\(107\) −12.0000 −1.16008 −0.580042 0.814587i \(-0.696964\pi\)
−0.580042 + 0.814587i \(0.696964\pi\)
\(108\) −5.00000 1.41421i −0.481125 0.136083i
\(109\) 4.24264i 0.406371i 0.979140 + 0.203186i \(0.0651295\pi\)
−0.979140 + 0.203186i \(0.934871\pi\)
\(110\) −8.00000 −0.762770
\(111\) −6.00000 4.24264i −0.569495 0.402694i
\(112\) −4.00000 −0.377964
\(113\) −12.0000 −1.12887 −0.564433 0.825479i \(-0.690905\pi\)
−0.564433 + 0.825479i \(0.690905\pi\)
\(114\) 7.00000 + 2.82843i 0.655610 + 0.264906i
\(115\) −2.00000 −0.186501
\(116\) −6.00000 −0.557086
\(117\) −12.0000 + 4.24264i −1.10940 + 0.392232i
\(118\) 12.0000 1.10469
\(119\) 11.3137i 1.03713i
\(120\) 2.00000 + 1.41421i 0.182574 + 0.129099i
\(121\) −21.0000 −1.90909
\(122\) 2.00000 0.181071
\(123\) 0 0
\(124\) 4.24264i 0.381000i
\(125\) 11.3137i 1.01193i
\(126\) 4.00000 + 11.3137i 0.356348 + 1.00791i
\(127\) 21.2132i 1.88237i 0.337895 + 0.941184i \(0.390285\pi\)
−0.337895 + 0.941184i \(0.609715\pi\)
\(128\) 1.00000 0.0883883
\(129\) 2.00000 2.82843i 0.176090 0.249029i
\(130\) 6.00000 0.526235
\(131\) 19.7990i 1.72985i −0.501905 0.864923i \(-0.667367\pi\)
0.501905 0.864923i \(-0.332633\pi\)
\(132\) 8.00000 + 5.65685i 0.696311 + 0.492366i
\(133\) −4.00000 16.9706i −0.346844 1.47153i
\(134\) 0 0
\(135\) 2.00000 7.07107i 0.172133 0.608581i
\(136\) 2.82843i 0.242536i
\(137\) 14.1421i 1.20824i 0.796892 + 0.604122i \(0.206476\pi\)
−0.796892 + 0.604122i \(0.793524\pi\)
\(138\) 2.00000 + 1.41421i 0.170251 + 0.120386i
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 5.65685i 0.478091i
\(141\) 2.00000 + 1.41421i 0.168430 + 0.119098i
\(142\) −12.0000 −1.00702
\(143\) 24.0000 2.00698
\(144\) −1.00000 2.82843i −0.0833333 0.235702i
\(145\) 8.48528i 0.704664i
\(146\) −4.00000 −0.331042
\(147\) 9.00000 12.7279i 0.742307 1.04978i
\(148\) 4.24264i 0.348743i
\(149\) 9.89949i 0.810998i 0.914095 + 0.405499i \(0.132902\pi\)
−0.914095 + 0.405499i \(0.867098\pi\)
\(150\) 3.00000 4.24264i 0.244949 0.346410i
\(151\) 12.7279i 1.03578i 0.855446 + 0.517892i \(0.173283\pi\)
−0.855446 + 0.517892i \(0.826717\pi\)
\(152\) 1.00000 + 4.24264i 0.0811107 + 0.344124i
\(153\) −8.00000 + 2.82843i −0.646762 + 0.228665i
\(154\) 22.6274i 1.82337i
\(155\) 6.00000 0.481932
\(156\) −6.00000 4.24264i −0.480384 0.339683i
\(157\) 14.0000 1.11732 0.558661 0.829396i \(-0.311315\pi\)
0.558661 + 0.829396i \(0.311315\pi\)
\(158\) 4.24264i 0.337526i
\(159\) 6.00000 8.48528i 0.475831 0.672927i
\(160\) 1.41421i 0.111803i
\(161\) 5.65685i 0.445823i
\(162\) −7.00000 + 5.65685i −0.549972 + 0.444444i
\(163\) 20.0000 1.56652 0.783260 0.621694i \(-0.213555\pi\)
0.783260 + 0.621694i \(0.213555\pi\)
\(164\) 0 0
\(165\) −8.00000 + 11.3137i −0.622799 + 0.880771i
\(166\) 2.82843i 0.219529i
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) −4.00000 + 5.65685i −0.308607 + 0.436436i
\(169\) −5.00000 −0.384615
\(170\) 4.00000 0.306786
\(171\) 11.0000 7.07107i 0.841191 0.540738i
\(172\) 2.00000 0.152499
\(173\) 6.00000 0.456172 0.228086 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) −6.00000 + 8.48528i −0.454859 + 0.643268i
\(175\) −12.0000 −0.907115
\(176\) 5.65685i 0.426401i
\(177\) 12.0000 16.9706i 0.901975 1.27559i
\(178\) 6.00000 0.449719
\(179\) −18.0000 −1.34538 −0.672692 0.739923i \(-0.734862\pi\)
−0.672692 + 0.739923i \(0.734862\pi\)
\(180\) 4.00000 1.41421i 0.298142 0.105409i
\(181\) 12.7279i 0.946059i −0.881047 0.473029i \(-0.843160\pi\)
0.881047 0.473029i \(-0.156840\pi\)
\(182\) 16.9706i 1.25794i
\(183\) 2.00000 2.82843i 0.147844 0.209083i
\(184\) 1.41421i 0.104257i
\(185\) 6.00000 0.441129
\(186\) −6.00000 4.24264i −0.439941 0.311086i
\(187\) 16.0000 1.17004
\(188\) 1.41421i 0.103142i
\(189\) 20.0000 + 5.65685i 1.45479 + 0.411476i
\(190\) −6.00000 + 1.41421i −0.435286 + 0.102598i
\(191\) 18.3848i 1.33028i 0.746721 + 0.665138i \(0.231627\pi\)
−0.746721 + 0.665138i \(0.768373\pi\)
\(192\) 1.00000 1.41421i 0.0721688 0.102062i
\(193\) 8.48528i 0.610784i −0.952227 0.305392i \(-0.901213\pi\)
0.952227 0.305392i \(-0.0987875\pi\)
\(194\) 8.48528i 0.609208i
\(195\) 6.00000 8.48528i 0.429669 0.607644i
\(196\) 9.00000 0.642857
\(197\) 7.07107i 0.503793i −0.967754 0.251896i \(-0.918946\pi\)
0.967754 0.251896i \(-0.0810542\pi\)
\(198\) 16.0000 5.65685i 1.13707 0.402015i
\(199\) −4.00000 −0.283552 −0.141776 0.989899i \(-0.545281\pi\)
−0.141776 + 0.989899i \(0.545281\pi\)
\(200\) 3.00000 0.212132
\(201\) 0 0
\(202\) 9.89949i 0.696526i
\(203\) 24.0000 1.68447
\(204\) −4.00000 2.82843i −0.280056 0.198030i
\(205\) 0 0
\(206\) 12.7279i 0.886796i
\(207\) 4.00000 1.41421i 0.278019 0.0982946i
\(208\) 4.24264i 0.294174i
\(209\) −24.0000 + 5.65685i −1.66011 + 0.391293i
\(210\) −8.00000 5.65685i −0.552052 0.390360i
\(211\) 8.48528i 0.584151i 0.956395 + 0.292075i \(0.0943458\pi\)
−0.956395 + 0.292075i \(0.905654\pi\)
\(212\) 6.00000 0.412082
\(213\) −12.0000 + 16.9706i −0.822226 + 1.16280i
\(214\) −12.0000 −0.820303
\(215\) 2.82843i 0.192897i
\(216\) −5.00000 1.41421i −0.340207 0.0962250i
\(217\) 16.9706i 1.15204i
\(218\) 4.24264i 0.287348i
\(219\) −4.00000 + 5.65685i −0.270295 + 0.382255i
\(220\) −8.00000 −0.539360
\(221\) −12.0000 −0.807207
\(222\) −6.00000 4.24264i −0.402694 0.284747i
\(223\) 4.24264i 0.284108i 0.989859 + 0.142054i \(0.0453707\pi\)
−0.989859 + 0.142054i \(0.954629\pi\)
\(224\) −4.00000 −0.267261
\(225\) −3.00000 8.48528i −0.200000 0.565685i
\(226\) −12.0000 −0.798228
\(227\) −18.0000 −1.19470 −0.597351 0.801980i \(-0.703780\pi\)
−0.597351 + 0.801980i \(0.703780\pi\)
\(228\) 7.00000 + 2.82843i 0.463586 + 0.187317i
\(229\) 2.00000 0.132164 0.0660819 0.997814i \(-0.478950\pi\)
0.0660819 + 0.997814i \(0.478950\pi\)
\(230\) −2.00000 −0.131876
\(231\) −32.0000 22.6274i −2.10545 1.48877i
\(232\) −6.00000 −0.393919
\(233\) 11.3137i 0.741186i −0.928795 0.370593i \(-0.879155\pi\)
0.928795 0.370593i \(-0.120845\pi\)
\(234\) −12.0000 + 4.24264i −0.784465 + 0.277350i
\(235\) −2.00000 −0.130466
\(236\) 12.0000 0.781133
\(237\) −6.00000 4.24264i −0.389742 0.275589i
\(238\) 11.3137i 0.733359i
\(239\) 15.5563i 1.00626i −0.864212 0.503128i \(-0.832182\pi\)
0.864212 0.503128i \(-0.167818\pi\)
\(240\) 2.00000 + 1.41421i 0.129099 + 0.0912871i
\(241\) 8.48528i 0.546585i −0.961931 0.273293i \(-0.911887\pi\)
0.961931 0.273293i \(-0.0881127\pi\)
\(242\) −21.0000 −1.34993
\(243\) 1.00000 + 15.5563i 0.0641500 + 0.997940i
\(244\) 2.00000 0.128037
\(245\) 12.7279i 0.813157i
\(246\) 0 0
\(247\) 18.0000 4.24264i 1.14531 0.269953i
\(248\) 4.24264i 0.269408i
\(249\) −4.00000 2.82843i −0.253490 0.179244i
\(250\) 11.3137i 0.715542i
\(251\) 19.7990i 1.24970i −0.780744 0.624851i \(-0.785160\pi\)
0.780744 0.624851i \(-0.214840\pi\)
\(252\) 4.00000 + 11.3137i 0.251976 + 0.712697i
\(253\) −8.00000 −0.502956
\(254\) 21.2132i 1.33103i
\(255\) 4.00000 5.65685i 0.250490 0.354246i
\(256\) 1.00000 0.0625000
\(257\) 6.00000 0.374270 0.187135 0.982334i \(-0.440080\pi\)
0.187135 + 0.982334i \(0.440080\pi\)
\(258\) 2.00000 2.82843i 0.124515 0.176090i
\(259\) 16.9706i 1.05450i
\(260\) 6.00000 0.372104
\(261\) 6.00000 + 16.9706i 0.371391 + 1.05045i
\(262\) 19.7990i 1.22319i
\(263\) 15.5563i 0.959246i −0.877475 0.479623i \(-0.840774\pi\)
0.877475 0.479623i \(-0.159226\pi\)
\(264\) 8.00000 + 5.65685i 0.492366 + 0.348155i
\(265\) 8.48528i 0.521247i
\(266\) −4.00000 16.9706i −0.245256 1.04053i
\(267\) 6.00000 8.48528i 0.367194 0.519291i
\(268\) 0 0
\(269\) 18.0000 1.09748 0.548740 0.835993i \(-0.315108\pi\)
0.548740 + 0.835993i \(0.315108\pi\)
\(270\) 2.00000 7.07107i 0.121716 0.430331i
\(271\) −16.0000 −0.971931 −0.485965 0.873978i \(-0.661532\pi\)
−0.485965 + 0.873978i \(0.661532\pi\)
\(272\) 2.82843i 0.171499i
\(273\) 24.0000 + 16.9706i 1.45255 + 1.02711i
\(274\) 14.1421i 0.854358i
\(275\) 16.9706i 1.02336i
\(276\) 2.00000 + 1.41421i 0.120386 + 0.0851257i
\(277\) −22.0000 −1.32185 −0.660926 0.750451i \(-0.729836\pi\)
−0.660926 + 0.750451i \(0.729836\pi\)
\(278\) −4.00000 −0.239904
\(279\) −12.0000 + 4.24264i −0.718421 + 0.254000i
\(280\) 5.65685i 0.338062i
\(281\) −12.0000 −0.715860 −0.357930 0.933748i \(-0.616517\pi\)
−0.357930 + 0.933748i \(0.616517\pi\)
\(282\) 2.00000 + 1.41421i 0.119098 + 0.0842152i
\(283\) 20.0000 1.18888 0.594438 0.804141i \(-0.297374\pi\)
0.594438 + 0.804141i \(0.297374\pi\)
\(284\) −12.0000 −0.712069
\(285\) −4.00000 + 9.89949i −0.236940 + 0.586395i
\(286\) 24.0000 1.41915
\(287\) 0 0
\(288\) −1.00000 2.82843i −0.0589256 0.166667i
\(289\) 9.00000 0.529412
\(290\) 8.48528i 0.498273i
\(291\) 12.0000 + 8.48528i 0.703452 + 0.497416i
\(292\) −4.00000 −0.234082
\(293\) −6.00000 −0.350524 −0.175262 0.984522i \(-0.556077\pi\)
−0.175262 + 0.984522i \(0.556077\pi\)
\(294\) 9.00000 12.7279i 0.524891 0.742307i
\(295\) 16.9706i 0.988064i
\(296\) 4.24264i 0.246598i
\(297\) 8.00000 28.2843i 0.464207 1.64122i
\(298\) 9.89949i 0.573462i
\(299\) 6.00000 0.346989
\(300\) 3.00000 4.24264i 0.173205 0.244949i
\(301\) −8.00000 −0.461112
\(302\) 12.7279i 0.732410i
\(303\) 14.0000 + 9.89949i 0.804279 + 0.568711i
\(304\) 1.00000 + 4.24264i 0.0573539 + 0.243332i
\(305\) 2.82843i 0.161955i
\(306\) −8.00000 + 2.82843i −0.457330 + 0.161690i
\(307\) 16.9706i 0.968561i −0.874913 0.484281i \(-0.839081\pi\)
0.874913 0.484281i \(-0.160919\pi\)
\(308\) 22.6274i 1.28932i
\(309\) −18.0000 12.7279i −1.02398 0.724066i
\(310\) 6.00000 0.340777
\(311\) 1.41421i 0.0801927i 0.999196 + 0.0400963i \(0.0127665\pi\)
−0.999196 + 0.0400963i \(0.987234\pi\)
\(312\) −6.00000 4.24264i −0.339683 0.240192i
\(313\) 8.00000 0.452187 0.226093 0.974106i \(-0.427405\pi\)
0.226093 + 0.974106i \(0.427405\pi\)
\(314\) 14.0000 0.790066
\(315\) −16.0000 + 5.65685i −0.901498 + 0.318728i
\(316\) 4.24264i 0.238667i
\(317\) 18.0000 1.01098 0.505490 0.862832i \(-0.331312\pi\)
0.505490 + 0.862832i \(0.331312\pi\)
\(318\) 6.00000 8.48528i 0.336463 0.475831i
\(319\) 33.9411i 1.90034i
\(320\) 1.41421i 0.0790569i
\(321\) −12.0000 + 16.9706i −0.669775 + 0.947204i
\(322\) 5.65685i 0.315244i
\(323\) 12.0000 2.82843i 0.667698 0.157378i
\(324\) −7.00000 + 5.65685i −0.388889 + 0.314270i
\(325\) 12.7279i 0.706018i
\(326\) 20.0000 1.10770
\(327\) 6.00000 + 4.24264i 0.331801 + 0.234619i
\(328\) 0 0
\(329\) 5.65685i 0.311872i
\(330\) −8.00000 + 11.3137i −0.440386 + 0.622799i
\(331\) 16.9706i 0.932786i −0.884577 0.466393i \(-0.845553\pi\)
0.884577 0.466393i \(-0.154447\pi\)
\(332\) 2.82843i 0.155230i
\(333\) −12.0000 + 4.24264i −0.657596 + 0.232495i
\(334\) 0 0
\(335\) 0 0
\(336\) −4.00000 + 5.65685i −0.218218 + 0.308607i
\(337\) 16.9706i 0.924445i 0.886764 + 0.462223i \(0.152948\pi\)
−0.886764 + 0.462223i \(0.847052\pi\)
\(338\) −5.00000 −0.271964
\(339\) −12.0000 + 16.9706i −0.651751 + 0.921714i
\(340\) 4.00000 0.216930
\(341\) 24.0000 1.29967
\(342\) 11.0000 7.07107i 0.594812 0.382360i
\(343\) −8.00000 −0.431959
\(344\) 2.00000 0.107833
\(345\) −2.00000 + 2.82843i −0.107676 + 0.152277i
\(346\) 6.00000 0.322562
\(347\) 11.3137i 0.607352i −0.952775 0.303676i \(-0.901786\pi\)
0.952775 0.303676i \(-0.0982140\pi\)
\(348\) −6.00000 + 8.48528i −0.321634 + 0.454859i
\(349\) 2.00000 0.107058 0.0535288 0.998566i \(-0.482953\pi\)
0.0535288 + 0.998566i \(0.482953\pi\)
\(350\) −12.0000 −0.641427
\(351\) −6.00000 + 21.2132i −0.320256 + 1.13228i
\(352\) 5.65685i 0.301511i
\(353\) 28.2843i 1.50542i −0.658352 0.752710i \(-0.728746\pi\)
0.658352 0.752710i \(-0.271254\pi\)
\(354\) 12.0000 16.9706i 0.637793 0.901975i
\(355\) 16.9706i 0.900704i
\(356\) 6.00000 0.317999
\(357\) 16.0000 + 11.3137i 0.846810 + 0.598785i
\(358\) −18.0000 −0.951330
\(359\) 18.3848i 0.970311i 0.874428 + 0.485156i \(0.161237\pi\)
−0.874428 + 0.485156i \(0.838763\pi\)
\(360\) 4.00000 1.41421i 0.210819 0.0745356i
\(361\) −17.0000 + 8.48528i −0.894737 + 0.446594i
\(362\) 12.7279i 0.668965i
\(363\) −21.0000 + 29.6985i −1.10221 + 1.55877i
\(364\) 16.9706i 0.889499i
\(365\) 5.65685i 0.296093i
\(366\) 2.00000 2.82843i 0.104542 0.147844i
\(367\) −28.0000 −1.46159 −0.730794 0.682598i \(-0.760850\pi\)
−0.730794 + 0.682598i \(0.760850\pi\)
\(368\) 1.41421i 0.0737210i
\(369\) 0 0
\(370\) 6.00000 0.311925
\(371\) −24.0000 −1.24602
\(372\) −6.00000 4.24264i −0.311086 0.219971i
\(373\) 29.6985i 1.53773i −0.639412 0.768865i \(-0.720822\pi\)
0.639412 0.768865i \(-0.279178\pi\)
\(374\) 16.0000 0.827340
\(375\) 16.0000 + 11.3137i 0.826236 + 0.584237i
\(376\) 1.41421i 0.0729325i
\(377\) 25.4558i 1.31104i
\(378\) 20.0000 + 5.65685i 1.02869 + 0.290957i
\(379\) 33.9411i 1.74344i −0.490006 0.871719i \(-0.663005\pi\)
0.490006 0.871719i \(-0.336995\pi\)
\(380\) −6.00000 + 1.41421i −0.307794 + 0.0725476i
\(381\) 30.0000 + 21.2132i 1.53695 + 1.08679i
\(382\) 18.3848i 0.940647i
\(383\) −24.0000 −1.22634 −0.613171 0.789950i \(-0.710106\pi\)
−0.613171 + 0.789950i \(0.710106\pi\)
\(384\) 1.00000 1.41421i 0.0510310 0.0721688i
\(385\) 32.0000 1.63087
\(386\) 8.48528i 0.431889i
\(387\) −2.00000 5.65685i −0.101666 0.287554i
\(388\) 8.48528i 0.430775i
\(389\) 15.5563i 0.788738i −0.918952 0.394369i \(-0.870963\pi\)
0.918952 0.394369i \(-0.129037\pi\)
\(390\) 6.00000 8.48528i 0.303822 0.429669i
\(391\) 4.00000 0.202289
\(392\) 9.00000 0.454569
\(393\) −28.0000 19.7990i −1.41241 0.998727i
\(394\) 7.07107i 0.356235i
\(395\) 6.00000 0.301893
\(396\) 16.0000 5.65685i 0.804030 0.284268i
\(397\) 38.0000 1.90717 0.953583 0.301131i \(-0.0973643\pi\)
0.953583 + 0.301131i \(0.0973643\pi\)
\(398\) −4.00000 −0.200502
\(399\) −28.0000 11.3137i −1.40175 0.566394i
\(400\) 3.00000 0.150000
\(401\) 24.0000 1.19850 0.599251 0.800561i \(-0.295465\pi\)
0.599251 + 0.800561i \(0.295465\pi\)
\(402\) 0 0
\(403\) −18.0000 −0.896644
\(404\) 9.89949i 0.492518i
\(405\) −8.00000 9.89949i −0.397523 0.491910i
\(406\) 24.0000 1.19110
\(407\) 24.0000 1.18964
\(408\) −4.00000 2.82843i −0.198030 0.140028i
\(409\) 8.48528i 0.419570i 0.977748 + 0.209785i \(0.0672764\pi\)
−0.977748 + 0.209785i \(0.932724\pi\)
\(410\) 0 0
\(411\) 20.0000 + 14.1421i 0.986527 + 0.697580i
\(412\) 12.7279i 0.627060i
\(413\) −48.0000 −2.36193
\(414\) 4.00000 1.41421i 0.196589 0.0695048i
\(415\) 4.00000 0.196352
\(416\) 4.24264i 0.208013i
\(417\) −4.00000 + 5.65685i −0.195881 + 0.277017i
\(418\) −24.0000 + 5.65685i −1.17388 + 0.276686i
\(419\) 39.5980i 1.93449i 0.253849 + 0.967244i \(0.418303\pi\)
−0.253849 + 0.967244i \(0.581697\pi\)
\(420\) −8.00000 5.65685i −0.390360 0.276026i
\(421\) 12.7279i 0.620321i 0.950684 + 0.310160i \(0.100383\pi\)
−0.950684 + 0.310160i \(0.899617\pi\)
\(422\) 8.48528i 0.413057i
\(423\) 4.00000 1.41421i 0.194487 0.0687614i
\(424\) 6.00000 0.291386
\(425\) 8.48528i 0.411597i
\(426\) −12.0000 + 16.9706i −0.581402 + 0.822226i
\(427\) −8.00000 −0.387147
\(428\) −12.0000 −0.580042
\(429\) 24.0000 33.9411i 1.15873 1.63869i
\(430\) 2.82843i 0.136399i
\(431\) 12.0000 0.578020 0.289010 0.957326i \(-0.406674\pi\)
0.289010 + 0.957326i \(0.406674\pi\)
\(432\) −5.00000 1.41421i −0.240563 0.0680414i
\(433\) 25.4558i 1.22333i 0.791117 + 0.611665i \(0.209500\pi\)
−0.791117 + 0.611665i \(0.790500\pi\)
\(434\) 16.9706i 0.814613i
\(435\) −12.0000 8.48528i −0.575356 0.406838i
\(436\) 4.24264i 0.203186i
\(437\) −6.00000 + 1.41421i −0.287019 + 0.0676510i
\(438\) −4.00000 + 5.65685i −0.191127 + 0.270295i
\(439\) 12.7279i 0.607471i 0.952756 + 0.303735i \(0.0982338\pi\)
−0.952756 + 0.303735i \(0.901766\pi\)
\(440\) −8.00000 −0.381385
\(441\) −9.00000 25.4558i −0.428571 1.21218i
\(442\) −12.0000 −0.570782
\(443\) 28.2843i 1.34383i −0.740630 0.671913i \(-0.765473\pi\)
0.740630 0.671913i \(-0.234527\pi\)
\(444\) −6.00000 4.24264i −0.284747 0.201347i
\(445\) 8.48528i 0.402241i
\(446\) 4.24264i 0.200895i
\(447\) 14.0000 + 9.89949i 0.662177 + 0.468230i
\(448\) −4.00000 −0.188982
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) −3.00000 8.48528i −0.141421 0.400000i
\(451\) 0 0
\(452\) −12.0000 −0.564433
\(453\) 18.0000 + 12.7279i 0.845714 + 0.598010i
\(454\) −18.0000 −0.844782
\(455\) −24.0000 −1.12514
\(456\) 7.00000 + 2.82843i 0.327805 + 0.132453i
\(457\) −10.0000 −0.467780 −0.233890 0.972263i \(-0.575146\pi\)
−0.233890 + 0.972263i \(0.575146\pi\)
\(458\) 2.00000 0.0934539
\(459\) −4.00000 + 14.1421i −0.186704 + 0.660098i
\(460\) −2.00000 −0.0932505
\(461\) 1.41421i 0.0658665i 0.999458 + 0.0329332i \(0.0104849\pi\)
−0.999458 + 0.0329332i \(0.989515\pi\)
\(462\) −32.0000 22.6274i −1.48877 1.05272i
\(463\) 20.0000 0.929479 0.464739 0.885448i \(-0.346148\pi\)
0.464739 + 0.885448i \(0.346148\pi\)
\(464\) −6.00000 −0.278543
\(465\) 6.00000 8.48528i 0.278243 0.393496i
\(466\) 11.3137i 0.524097i
\(467\) 2.82843i 0.130884i −0.997856 0.0654420i \(-0.979154\pi\)
0.997856 0.0654420i \(-0.0208457\pi\)
\(468\) −12.0000 + 4.24264i −0.554700 + 0.196116i
\(469\) 0 0
\(470\) −2.00000 −0.0922531
\(471\) 14.0000 19.7990i 0.645086 0.912289i
\(472\) 12.0000 0.552345
\(473\) 11.3137i 0.520205i
\(474\) −6.00000 4.24264i −0.275589 0.194871i
\(475\) 3.00000 + 12.7279i 0.137649 + 0.583997i
\(476\) 11.3137i 0.518563i
\(477\) −6.00000 16.9706i −0.274721 0.777029i
\(478\) 15.5563i 0.711531i
\(479\) 9.89949i 0.452319i 0.974090 + 0.226160i \(0.0726171\pi\)
−0.974090 + 0.226160i \(0.927383\pi\)
\(480\) 2.00000 + 1.41421i 0.0912871 + 0.0645497i
\(481\) −18.0000 −0.820729
\(482\) 8.48528i 0.386494i
\(483\) −8.00000 5.65685i −0.364013 0.257396i
\(484\) −21.0000 −0.954545
\(485\) −12.0000 −0.544892
\(486\) 1.00000 + 15.5563i 0.0453609 + 0.705650i
\(487\) 12.7279i 0.576757i 0.957516 + 0.288379i \(0.0931162\pi\)
−0.957516 + 0.288379i \(0.906884\pi\)
\(488\) 2.00000 0.0905357
\(489\) 20.0000 28.2843i 0.904431 1.27906i
\(490\) 12.7279i 0.574989i
\(491\) 14.1421i 0.638226i 0.947717 + 0.319113i \(0.103385\pi\)
−0.947717 + 0.319113i \(0.896615\pi\)
\(492\) 0 0
\(493\) 16.9706i 0.764316i
\(494\) 18.0000 4.24264i 0.809858 0.190885i
\(495\) 8.00000 + 22.6274i 0.359573 + 1.01703i
\(496\) 4.24264i 0.190500i
\(497\) 48.0000 2.15309
\(498\) −4.00000 2.82843i −0.179244 0.126745i
\(499\) −10.0000 −0.447661 −0.223831 0.974628i \(-0.571856\pi\)
−0.223831 + 0.974628i \(0.571856\pi\)
\(500\) 11.3137i 0.505964i
\(501\) 0 0
\(502\) 19.7990i 0.883672i
\(503\) 7.07107i 0.315283i −0.987496 0.157642i \(-0.949611\pi\)
0.987496 0.157642i \(-0.0503891\pi\)
\(504\) 4.00000 + 11.3137i 0.178174 + 0.503953i
\(505\) −14.0000 −0.622992
\(506\) −8.00000 −0.355643
\(507\) −5.00000 + 7.07107i −0.222058 + 0.314037i
\(508\) 21.2132i 0.941184i
\(509\) 6.00000 0.265945 0.132973 0.991120i \(-0.457548\pi\)
0.132973 + 0.991120i \(0.457548\pi\)
\(510\) 4.00000 5.65685i 0.177123 0.250490i
\(511\) 16.0000 0.707798
\(512\) 1.00000 0.0441942
\(513\) 1.00000 22.6274i 0.0441511 0.999025i
\(514\) 6.00000 0.264649
\(515\) 18.0000 0.793175
\(516\) 2.00000 2.82843i 0.0880451 0.124515i
\(517\) −8.00000 −0.351840
\(518\) 16.9706i 0.745644i
\(519\) 6.00000 8.48528i 0.263371 0.372463i
\(520\) 6.00000 0.263117
\(521\) 6.00000 0.262865 0.131432 0.991325i \(-0.458042\pi\)
0.131432 + 0.991325i \(0.458042\pi\)
\(522\) 6.00000 + 16.9706i 0.262613 + 0.742781i
\(523\) 16.9706i 0.742071i −0.928619 0.371035i \(-0.879003\pi\)
0.928619 0.371035i \(-0.120997\pi\)
\(524\) 19.7990i 0.864923i
\(525\) −12.0000 + 16.9706i −0.523723 + 0.740656i
\(526\) 15.5563i 0.678289i
\(527\) −12.0000 −0.522728
\(528\) 8.00000 + 5.65685i 0.348155 + 0.246183i
\(529\) 21.0000 0.913043
\(530\) 8.48528i 0.368577i
\(531\) −12.0000 33.9411i −0.520756 1.47292i
\(532\) −4.00000 16.9706i −0.173422 0.735767i
\(533\) 0 0
\(534\) 6.00000 8.48528i 0.259645 0.367194i
\(535\) 16.9706i 0.733701i
\(536\) 0 0
\(537\) −18.0000 + 25.4558i −0.776757 + 1.09850i
\(538\) 18.0000 0.776035
\(539\) 50.9117i 2.19292i
\(540\) 2.00000 7.07107i 0.0860663 0.304290i
\(541\) 38.0000 1.63375 0.816874 0.576816i \(-0.195705\pi\)
0.816874 + 0.576816i \(0.195705\pi\)
\(542\) −16.0000 −0.687259
\(543\) −18.0000 12.7279i −0.772454 0.546207i
\(544\) 2.82843i 0.121268i
\(545\) −6.00000 −0.257012
\(546\) 24.0000 + 16.9706i 1.02711 + 0.726273i
\(547\) 16.9706i 0.725609i 0.931865 + 0.362804i \(0.118181\pi\)
−0.931865 + 0.362804i \(0.881819\pi\)
\(548\) 14.1421i 0.604122i
\(549\) −2.00000 5.65685i −0.0853579 0.241429i
\(550\) 16.9706i 0.723627i
\(551\) −6.00000 25.4558i −0.255609 1.08446i
\(552\) 2.00000 + 1.41421i 0.0851257 + 0.0601929i
\(553\) 16.9706i 0.721662i
\(554\) −22.0000 −0.934690
\(555\) 6.00000 8.48528i 0.254686 0.360180i
\(556\) −4.00000 −0.169638
\(557\) 24.0416i 1.01868i −0.860566 0.509338i \(-0.829890\pi\)
0.860566 0.509338i \(-0.170110\pi\)
\(558\) −12.0000 + 4.24264i −0.508001 + 0.179605i
\(559\) 8.48528i 0.358889i
\(560\) 5.65685i 0.239046i
\(561\) 16.0000 22.6274i 0.675521 0.955330i
\(562\) −12.0000 −0.506189
\(563\) 36.0000 1.51722 0.758610 0.651546i \(-0.225879\pi\)
0.758610 + 0.651546i \(0.225879\pi\)
\(564\) 2.00000 + 1.41421i 0.0842152 + 0.0595491i
\(565\) 16.9706i 0.713957i
\(566\) 20.0000 0.840663
\(567\) 28.0000 22.6274i 1.17589 0.950262i
\(568\) −12.0000 −0.503509
\(569\) −6.00000 −0.251533 −0.125767 0.992060i \(-0.540139\pi\)
−0.125767 + 0.992060i \(0.540139\pi\)
\(570\) −4.00000 + 9.89949i −0.167542 + 0.414644i
\(571\) 14.0000 0.585882 0.292941 0.956131i \(-0.405366\pi\)
0.292941 + 0.956131i \(0.405366\pi\)
\(572\) 24.0000 1.00349
\(573\) 26.0000 + 18.3848i 1.08617 + 0.768035i
\(574\) 0 0
\(575\) 4.24264i 0.176930i
\(576\) −1.00000 2.82843i −0.0416667 0.117851i
\(577\) −10.0000 −0.416305 −0.208153 0.978096i \(-0.566745\pi\)
−0.208153 + 0.978096i \(0.566745\pi\)
\(578\) 9.00000 0.374351
\(579\) −12.0000 8.48528i −0.498703 0.352636i
\(580\) 8.48528i 0.352332i
\(581\) 11.3137i 0.469372i
\(582\) 12.0000 + 8.48528i 0.497416 + 0.351726i
\(583\) 33.9411i 1.40570i
\(584\) −4.00000 −0.165521
\(585\) −6.00000 16.9706i −0.248069 0.701646i
\(586\) −6.00000 −0.247858
\(587\) 22.6274i 0.933933i 0.884275 + 0.466967i \(0.154653\pi\)
−0.884275 + 0.466967i \(0.845347\pi\)
\(588\) 9.00000 12.7279i 0.371154 0.524891i
\(589\) 18.0000 4.24264i 0.741677 0.174815i
\(590\) 16.9706i 0.698667i
\(591\) −10.0000 7.07107i −0.411345 0.290865i
\(592\) 4.24264i 0.174371i
\(593\) 5.65685i 0.232299i 0.993232 + 0.116150i \(0.0370552\pi\)
−0.993232 + 0.116150i \(0.962945\pi\)
\(594\) 8.00000 28.2843i 0.328244 1.16052i
\(595\) −16.0000 −0.655936
\(596\) 9.89949i 0.405499i
\(597\) −4.00000 + 5.65685i −0.163709 + 0.231520i
\(598\) 6.00000 0.245358
\(599\) 12.0000 0.490307 0.245153 0.969484i \(-0.421162\pi\)
0.245153 + 0.969484i \(0.421162\pi\)
\(600\) 3.00000 4.24264i 0.122474 0.173205i
\(601\) 16.9706i 0.692244i −0.938190 0.346122i \(-0.887498\pi\)
0.938190 0.346122i \(-0.112502\pi\)
\(602\) −8.00000 −0.326056
\(603\) 0 0
\(604\) 12.7279i 0.517892i
\(605\) 29.6985i 1.20742i
\(606\) 14.0000 + 9.89949i 0.568711 + 0.402139i
\(607\) 38.1838i 1.54983i −0.632065 0.774916i \(-0.717792\pi\)
0.632065 0.774916i \(-0.282208\pi\)
\(608\) 1.00000 + 4.24264i 0.0405554 + 0.172062i
\(609\) 24.0000 33.9411i 0.972529 1.37536i
\(610\) 2.82843i 0.114520i
\(611\) 6.00000 0.242734
\(612\) −8.00000 + 2.82843i −0.323381 + 0.114332i
\(613\) −22.0000 −0.888572 −0.444286 0.895885i \(-0.646543\pi\)
−0.444286 + 0.895885i \(0.646543\pi\)
\(614\) 16.9706i 0.684876i
\(615\) 0 0
\(616\) 22.6274i 0.911685i
\(617\) 22.6274i 0.910946i 0.890250 + 0.455473i \(0.150530\pi\)
−0.890250 + 0.455473i \(0.849470\pi\)
\(618\) −18.0000 12.7279i −0.724066 0.511992i
\(619\) −46.0000 −1.84890 −0.924448 0.381308i \(-0.875474\pi\)
−0.924448 + 0.381308i \(0.875474\pi\)
\(620\) 6.00000 0.240966
\(621\) 2.00000 7.07107i 0.0802572 0.283752i
\(622\) 1.41421i 0.0567048i
\(623\) −24.0000 −0.961540
\(624\) −6.00000 4.24264i −0.240192 0.169842i
\(625\) −1.00000 −0.0400000
\(626\) 8.00000 0.319744
\(627\) −16.0000 + 39.5980i −0.638978 + 1.58139i
\(628\) 14.0000 0.558661
\(629\) −12.0000 −0.478471
\(630\) −16.0000 + 5.65685i −0.637455 + 0.225374i
\(631\) −4.00000 −0.159237 −0.0796187 0.996825i \(-0.525370\pi\)
−0.0796187 + 0.996825i \(0.525370\pi\)
\(632\) 4.24264i 0.168763i
\(633\) 12.0000 + 8.48528i 0.476957 + 0.337260i
\(634\) 18.0000 0.714871
\(635\) −30.0000 −1.19051
\(636\) 6.00000 8.48528i 0.237915 0.336463i
\(637\) 38.1838i 1.51290i
\(638\) 33.9411i 1.34374i
\(639\) 12.0000 + 33.9411i 0.474713 + 1.34269i
\(640\) 1.41421i 0.0559017i
\(641\) 30.0000 1.18493 0.592464 0.805597i \(-0.298155\pi\)
0.592464 + 0.805597i \(0.298155\pi\)
\(642\) −12.0000 + 16.9706i −0.473602 + 0.669775i
\(643\) −28.0000 −1.10421 −0.552106 0.833774i \(-0.686176\pi\)
−0.552106 + 0.833774i \(0.686176\pi\)
\(644\) 5.65685i 0.222911i
\(645\) 4.00000 + 2.82843i 0.157500 + 0.111369i
\(646\) 12.0000 2.82843i 0.472134 0.111283i
\(647\) 24.0416i 0.945174i −0.881284 0.472587i \(-0.843320\pi\)
0.881284 0.472587i \(-0.156680\pi\)
\(648\) −7.00000 + 5.65685i −0.274986 + 0.222222i
\(649\) 67.8823i 2.66461i
\(650\) 12.7279i 0.499230i
\(651\) 24.0000 + 16.9706i 0.940634 + 0.665129i
\(652\) 20.0000 0.783260
\(653\) 35.3553i 1.38356i 0.722108 + 0.691781i \(0.243173\pi\)
−0.722108 + 0.691781i \(0.756827\pi\)
\(654\) 6.00000 + 4.24264i 0.234619 + 0.165900i
\(655\) 28.0000 1.09405
\(656\) 0 0
\(657\) 4.00000 + 11.3137i 0.156055 + 0.441390i
\(658\) 5.65685i 0.220527i
\(659\) −18.0000 −0.701180 −0.350590 0.936529i \(-0.614019\pi\)
−0.350590 + 0.936529i \(0.614019\pi\)
\(660\) −8.00000 + 11.3137i −0.311400 + 0.440386i
\(661\) 29.6985i 1.15514i 0.816342 + 0.577569i \(0.195998\pi\)
−0.816342 + 0.577569i \(0.804002\pi\)
\(662\) 16.9706i 0.659580i
\(663\) −12.0000 + 16.9706i −0.466041 + 0.659082i
\(664\) 2.82843i 0.109764i
\(665\) 24.0000 5.65685i 0.930680 0.219363i
\(666\) −12.0000 + 4.24264i −0.464991 + 0.164399i
\(667\) 8.48528i 0.328551i
\(668\) 0 0
\(669\) 6.00000 + 4.24264i 0.231973 + 0.164030i
\(670\) 0 0
\(671\) 11.3137i 0.436761i
\(672\) −4.00000 + 5.65685i −0.154303 + 0.218218i
\(673\) 8.48528i 0.327084i 0.986536 + 0.163542i \(0.0522919\pi\)
−0.986536 + 0.163542i \(0.947708\pi\)
\(674\) 16.9706i 0.653682i
\(675\) −15.0000 4.24264i −0.577350 0.163299i
\(676\) −5.00000 −0.192308
\(677\) −30.0000 −1.15299 −0.576497 0.817099i \(-0.695581\pi\)
−0.576497 + 0.817099i \(0.695581\pi\)
\(678\) −12.0000 + 16.9706i −0.460857 + 0.651751i
\(679\) 33.9411i 1.30254i
\(680\) 4.00000 0.153393
\(681\) −18.0000 + 25.4558i −0.689761 + 0.975470i
\(682\) 24.0000 0.919007
\(683\) −18.0000 −0.688751 −0.344375 0.938832i \(-0.611909\pi\)
−0.344375 + 0.938832i \(0.611909\pi\)
\(684\) 11.0000 7.07107i 0.420596 0.270369i
\(685\) −20.0000 −0.764161
\(686\) −8.00000 −0.305441
\(687\) 2.00000 2.82843i 0.0763048 0.107911i
\(688\) 2.00000 0.0762493
\(689\) 25.4558i 0.969790i
\(690\) −2.00000 + 2.82843i −0.0761387 + 0.107676i
\(691\) −10.0000 −0.380418 −0.190209 0.981744i \(-0.560917\pi\)
−0.190209 + 0.981744i \(0.560917\pi\)
\(692\) 6.00000 0.228086
\(693\) −64.0000 + 22.6274i −2.43116 + 0.859544i
\(694\) 11.3137i 0.429463i
\(695\) 5.65685i 0.214577i
\(696\) −6.00000 + 8.48528i −0.227429 + 0.321634i
\(697\) 0 0
\(698\) 2.00000 0.0757011
\(699\) −16.0000 11.3137i −0.605176 0.427924i
\(700\) −12.0000 −0.453557
\(701\) 7.07107i 0.267071i −0.991044 0.133535i \(-0.957367\pi\)
0.991044 0.133535i \(-0.0426329\pi\)
\(702\) −6.00000 + 21.2132i −0.226455 + 0.800641i
\(703\) 18.0000 4.24264i 0.678883 0.160014i
\(704\) 5.65685i 0.213201i
\(705\) −2.00000 + 2.82843i −0.0753244 + 0.106525i
\(706\) 28.2843i 1.06449i
\(707\) 39.5980i 1.48924i
\(708\) 12.0000 16.9706i 0.450988 0.637793i
\(709\) 26.0000 0.976450 0.488225 0.872718i \(-0.337644\pi\)
0.488225 + 0.872718i \(0.337644\pi\)
\(710\) 16.9706i 0.636894i
\(711\) −12.0000 + 4.24264i −0.450035 + 0.159111i
\(712\) 6.00000 0.224860
\(713\) 6.00000 0.224702
\(714\) 16.0000 + 11.3137i 0.598785 + 0.423405i
\(715\) 33.9411i 1.26933i
\(716\) −18.0000 −0.672692
\(717\) −22.0000 15.5563i −0.821605 0.580963i
\(718\) 18.3848i 0.686114i
\(719\) 7.07107i 0.263706i −0.991269 0.131853i \(-0.957907\pi\)
0.991269 0.131853i \(-0.0420927\pi\)
\(720\) 4.00000 1.41421i 0.149071 0.0527046i
\(721\) 50.9117i 1.89605i
\(722\) −17.0000 + 8.48528i −0.632674 + 0.315789i
\(723\) −12.0000 8.48528i −0.446285 0.315571i
\(724\) 12.7279i 0.473029i
\(725\) −18.0000 −0.668503
\(726\) −21.0000 + 29.6985i −0.779383 + 1.10221i
\(727\) 8.00000 0.296704 0.148352 0.988935i \(-0.452603\pi\)
0.148352 + 0.988935i \(0.452603\pi\)
\(728\) 16.9706i 0.628971i
\(729\) 23.0000 + 14.1421i 0.851852 + 0.523783i
\(730\) 5.65685i 0.209370i
\(731\) 5.65685i 0.209226i
\(732\) 2.00000 2.82843i 0.0739221 0.104542i
\(733\) −22.0000 −0.812589 −0.406294 0.913742i \(-0.633179\pi\)
−0.406294 + 0.913742i \(0.633179\pi\)
\(734\) −28.0000 −1.03350
\(735\) 18.0000 + 12.7279i 0.663940 + 0.469476i
\(736\) 1.41421i 0.0521286i
\(737\) 0 0
\(738\) 0 0
\(739\) 20.0000 0.735712 0.367856 0.929883i \(-0.380092\pi\)
0.367856 + 0.929883i \(0.380092\pi\)
\(740\) 6.00000 0.220564
\(741\) 12.0000 29.6985i 0.440831 1.09100i
\(742\) −24.0000 −0.881068
\(743\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(744\) −6.00000 4.24264i −0.219971 0.155543i
\(745\) −14.0000 −0.512920
\(746\) 29.6985i 1.08734i
\(747\) −8.00000 + 2.82843i −0.292705 + 0.103487i
\(748\) 16.0000 0.585018
\(749\) 48.0000 1.75388
\(750\) 16.0000 + 11.3137i 0.584237 + 0.413118i
\(751\) 38.1838i 1.39335i 0.717389 + 0.696673i \(0.245337\pi\)
−0.717389 + 0.696673i \(0.754663\pi\)
\(752\) 1.41421i 0.0515711i
\(753\) −28.0000 19.7990i −1.02038 0.721515i
\(754\) 25.4558i 0.927047i
\(755\) −18.0000 −0.655087
\(756\) 20.0000 + 5.65685i 0.727393 + 0.205738i
\(757\) −34.0000 −1.23575 −0.617876 0.786276i \(-0.712006\pi\)
−0.617876 + 0.786276i \(0.712006\pi\)
\(758\) 33.9411i 1.23280i
\(759\) −8.00000 + 11.3137i −0.290382 + 0.410662i
\(760\) −6.00000 + 1.41421i −0.217643 + 0.0512989i
\(761\) 14.1421i 0.512652i 0.966590 + 0.256326i \(0.0825121\pi\)
−0.966590 + 0.256326i \(0.917488\pi\)
\(762\) 30.0000 + 21.2132i 1.08679 + 0.768473i
\(763\) 16.9706i 0.614376i
\(764\) 18.3848i 0.665138i
\(765\) −4.00000 11.3137i −0.144620 0.409048i
\(766\) −24.0000 −0.867155
\(767\) 50.9117i 1.83831i
\(768\) 1.00000 1.41421i 0.0360844 0.0510310i
\(769\) −16.0000 −0.576975 −0.288487 0.957484i \(-0.593152\pi\)
−0.288487 + 0.957484i \(0.593152\pi\)
\(770\) 32.0000 1.15320
\(771\) 6.00000 8.48528i 0.216085 0.305590i
\(772\) 8.48528i 0.305392i
\(773\) −18.0000 −0.647415 −0.323708 0.946157i \(-0.604929\pi\)
−0.323708 + 0.946157i \(0.604929\pi\)
\(774\) −2.00000 5.65685i −0.0718885 0.203331i
\(775\) 12.7279i 0.457200i
\(776\) 8.48528i 0.304604i
\(777\) 24.0000 + 16.9706i 0.860995 + 0.608816i
\(778\) 15.5563i 0.557722i
\(779\) 0 0
\(780\) 6.00000 8.48528i 0.214834 0.303822i
\(781\) 67.8823i 2.42902i
\(782\) 4.00000 0.143040
\(783\) 30.0000 + 8.48528i 1.07211 + 0.303239i
\(784\) 9.00000 0.321429
\(785\) 19.7990i