Properties

Label 912.2.f.e.113.1
Level $912$
Weight $2$
Character 912.113
Analytic conductor $7.282$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 912.f (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.28235666434\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 114)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 113.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 912.113
Dual form 912.2.f.e.113.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.50000 - 0.866025i) q^{3} +3.46410i q^{5} -1.00000 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(1.50000 - 0.866025i) q^{3} +3.46410i q^{5} -1.00000 q^{7} +(1.50000 - 2.59808i) q^{9} +3.46410i q^{11} -1.73205i q^{13} +(3.00000 + 5.19615i) q^{15} +1.73205i q^{17} +(4.00000 - 1.73205i) q^{19} +(-1.50000 + 0.866025i) q^{21} +5.19615i q^{23} -7.00000 q^{25} -5.19615i q^{27} +9.00000 q^{29} +10.3923i q^{31} +(3.00000 + 5.19615i) q^{33} -3.46410i q^{35} +6.92820i q^{37} +(-1.50000 - 2.59808i) q^{39} -2.00000 q^{43} +(9.00000 + 5.19615i) q^{45} -3.46410i q^{47} -6.00000 q^{49} +(1.50000 + 2.59808i) q^{51} -9.00000 q^{53} -12.0000 q^{55} +(4.50000 - 6.06218i) q^{57} +3.00000 q^{59} -8.00000 q^{61} +(-1.50000 + 2.59808i) q^{63} +6.00000 q^{65} -8.66025i q^{67} +(4.50000 + 7.79423i) q^{69} +12.0000 q^{71} +11.0000 q^{73} +(-10.5000 + 6.06218i) q^{75} -3.46410i q^{77} -6.92820i q^{79} +(-4.50000 - 7.79423i) q^{81} -10.3923i q^{83} -6.00000 q^{85} +(13.5000 - 7.79423i) q^{87} +6.00000 q^{89} +1.73205i q^{91} +(9.00000 + 15.5885i) q^{93} +(6.00000 + 13.8564i) q^{95} -13.8564i q^{97} +(9.00000 + 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 3 q^{3} - 2 q^{7} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 3 q^{3} - 2 q^{7} + 3 q^{9} + 6 q^{15} + 8 q^{19} - 3 q^{21} - 14 q^{25} + 18 q^{29} + 6 q^{33} - 3 q^{39} - 4 q^{43} + 18 q^{45} - 12 q^{49} + 3 q^{51} - 18 q^{53} - 24 q^{55} + 9 q^{57} + 6 q^{59} - 16 q^{61} - 3 q^{63} + 12 q^{65} + 9 q^{69} + 24 q^{71} + 22 q^{73} - 21 q^{75} - 9 q^{81} - 12 q^{85} + 27 q^{87} + 12 q^{89} + 18 q^{93} + 12 q^{95} + 18 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(799\)
\(\chi(n)\) \(-1\) \(1\) \(-1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.50000 0.866025i 0.866025 0.500000i
\(4\) 0 0
\(5\) 3.46410i 1.54919i 0.632456 + 0.774597i \(0.282047\pi\)
−0.632456 + 0.774597i \(0.717953\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964 −0.188982 0.981981i \(-0.560519\pi\)
−0.188982 + 0.981981i \(0.560519\pi\)
\(8\) 0 0
\(9\) 1.50000 2.59808i 0.500000 0.866025i
\(10\) 0 0
\(11\) 3.46410i 1.04447i 0.852803 + 0.522233i \(0.174901\pi\)
−0.852803 + 0.522233i \(0.825099\pi\)
\(12\) 0 0
\(13\) 1.73205i 0.480384i −0.970725 0.240192i \(-0.922790\pi\)
0.970725 0.240192i \(-0.0772105\pi\)
\(14\) 0 0
\(15\) 3.00000 + 5.19615i 0.774597 + 1.34164i
\(16\) 0 0
\(17\) 1.73205i 0.420084i 0.977692 + 0.210042i \(0.0673601\pi\)
−0.977692 + 0.210042i \(0.932640\pi\)
\(18\) 0 0
\(19\) 4.00000 1.73205i 0.917663 0.397360i
\(20\) 0 0
\(21\) −1.50000 + 0.866025i −0.327327 + 0.188982i
\(22\) 0 0
\(23\) 5.19615i 1.08347i 0.840548 + 0.541736i \(0.182233\pi\)
−0.840548 + 0.541736i \(0.817767\pi\)
\(24\) 0 0
\(25\) −7.00000 −1.40000
\(26\) 0 0
\(27\) 5.19615i 1.00000i
\(28\) 0 0
\(29\) 9.00000 1.67126 0.835629 0.549294i \(-0.185103\pi\)
0.835629 + 0.549294i \(0.185103\pi\)
\(30\) 0 0
\(31\) 10.3923i 1.86651i 0.359211 + 0.933257i \(0.383046\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 0 0
\(33\) 3.00000 + 5.19615i 0.522233 + 0.904534i
\(34\) 0 0
\(35\) 3.46410i 0.585540i
\(36\) 0 0
\(37\) 6.92820i 1.13899i 0.821995 + 0.569495i \(0.192861\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) 0 0
\(39\) −1.50000 2.59808i −0.240192 0.416025i
\(40\) 0 0
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) −2.00000 −0.304997 −0.152499 0.988304i \(-0.548732\pi\)
−0.152499 + 0.988304i \(0.548732\pi\)
\(44\) 0 0
\(45\) 9.00000 + 5.19615i 1.34164 + 0.774597i
\(46\) 0 0
\(47\) 3.46410i 0.505291i −0.967559 0.252646i \(-0.918699\pi\)
0.967559 0.252646i \(-0.0813007\pi\)
\(48\) 0 0
\(49\) −6.00000 −0.857143
\(50\) 0 0
\(51\) 1.50000 + 2.59808i 0.210042 + 0.363803i
\(52\) 0 0
\(53\) −9.00000 −1.23625 −0.618123 0.786082i \(-0.712106\pi\)
−0.618123 + 0.786082i \(0.712106\pi\)
\(54\) 0 0
\(55\) −12.0000 −1.61808
\(56\) 0 0
\(57\) 4.50000 6.06218i 0.596040 0.802955i
\(58\) 0 0
\(59\) 3.00000 0.390567 0.195283 0.980747i \(-0.437437\pi\)
0.195283 + 0.980747i \(0.437437\pi\)
\(60\) 0 0
\(61\) −8.00000 −1.02430 −0.512148 0.858898i \(-0.671150\pi\)
−0.512148 + 0.858898i \(0.671150\pi\)
\(62\) 0 0
\(63\) −1.50000 + 2.59808i −0.188982 + 0.327327i
\(64\) 0 0
\(65\) 6.00000 0.744208
\(66\) 0 0
\(67\) 8.66025i 1.05802i −0.848616 0.529009i \(-0.822564\pi\)
0.848616 0.529009i \(-0.177436\pi\)
\(68\) 0 0
\(69\) 4.50000 + 7.79423i 0.541736 + 0.938315i
\(70\) 0 0
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) 0 0
\(73\) 11.0000 1.28745 0.643726 0.765256i \(-0.277388\pi\)
0.643726 + 0.765256i \(0.277388\pi\)
\(74\) 0 0
\(75\) −10.5000 + 6.06218i −1.21244 + 0.700000i
\(76\) 0 0
\(77\) 3.46410i 0.394771i
\(78\) 0 0
\(79\) 6.92820i 0.779484i −0.920924 0.389742i \(-0.872564\pi\)
0.920924 0.389742i \(-0.127436\pi\)
\(80\) 0 0
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) 0 0
\(83\) 10.3923i 1.14070i −0.821401 0.570352i \(-0.806807\pi\)
0.821401 0.570352i \(-0.193193\pi\)
\(84\) 0 0
\(85\) −6.00000 −0.650791
\(86\) 0 0
\(87\) 13.5000 7.79423i 1.44735 0.835629i
\(88\) 0 0
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) 0 0
\(91\) 1.73205i 0.181568i
\(92\) 0 0
\(93\) 9.00000 + 15.5885i 0.933257 + 1.61645i
\(94\) 0 0
\(95\) 6.00000 + 13.8564i 0.615587 + 1.42164i
\(96\) 0 0
\(97\) 13.8564i 1.40690i −0.710742 0.703452i \(-0.751641\pi\)
0.710742 0.703452i \(-0.248359\pi\)
\(98\) 0 0
\(99\) 9.00000 + 5.19615i 0.904534 + 0.522233i
\(100\) 0 0
\(101\) 10.3923i 1.03407i −0.855963 0.517036i \(-0.827035\pi\)
0.855963 0.517036i \(-0.172965\pi\)
\(102\) 0 0
\(103\) 3.46410i 0.341328i −0.985329 0.170664i \(-0.945409\pi\)
0.985329 0.170664i \(-0.0545913\pi\)
\(104\) 0 0
\(105\) −3.00000 5.19615i −0.292770 0.507093i
\(106\) 0 0
\(107\) −3.00000 −0.290021 −0.145010 0.989430i \(-0.546322\pi\)
−0.145010 + 0.989430i \(0.546322\pi\)
\(108\) 0 0
\(109\) 15.5885i 1.49310i −0.665327 0.746552i \(-0.731708\pi\)
0.665327 0.746552i \(-0.268292\pi\)
\(110\) 0 0
\(111\) 6.00000 + 10.3923i 0.569495 + 0.986394i
\(112\) 0 0
\(113\) −12.0000 −1.12887 −0.564433 0.825479i \(-0.690905\pi\)
−0.564433 + 0.825479i \(0.690905\pi\)
\(114\) 0 0
\(115\) −18.0000 −1.67851
\(116\) 0 0
\(117\) −4.50000 2.59808i −0.416025 0.240192i
\(118\) 0 0
\(119\) 1.73205i 0.158777i
\(120\) 0 0
\(121\) −1.00000 −0.0909091
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 6.92820i 0.619677i
\(126\) 0 0
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) 0 0
\(129\) −3.00000 + 1.73205i −0.264135 + 0.152499i
\(130\) 0 0
\(131\) 3.46410i 0.302660i −0.988483 0.151330i \(-0.951644\pi\)
0.988483 0.151330i \(-0.0483556\pi\)
\(132\) 0 0
\(133\) −4.00000 + 1.73205i −0.346844 + 0.150188i
\(134\) 0 0
\(135\) 18.0000 1.54919
\(136\) 0 0
\(137\) 8.66025i 0.739895i 0.929053 + 0.369948i \(0.120624\pi\)
−0.929053 + 0.369948i \(0.879376\pi\)
\(138\) 0 0
\(139\) 14.0000 1.18746 0.593732 0.804663i \(-0.297654\pi\)
0.593732 + 0.804663i \(0.297654\pi\)
\(140\) 0 0
\(141\) −3.00000 5.19615i −0.252646 0.437595i
\(142\) 0 0
\(143\) 6.00000 0.501745
\(144\) 0 0
\(145\) 31.1769i 2.58910i
\(146\) 0 0
\(147\) −9.00000 + 5.19615i −0.742307 + 0.428571i
\(148\) 0 0
\(149\) 6.92820i 0.567581i 0.958886 + 0.283790i \(0.0915919\pi\)
−0.958886 + 0.283790i \(0.908408\pi\)
\(150\) 0 0
\(151\) 3.46410i 0.281905i 0.990016 + 0.140952i \(0.0450164\pi\)
−0.990016 + 0.140952i \(0.954984\pi\)
\(152\) 0 0
\(153\) 4.50000 + 2.59808i 0.363803 + 0.210042i
\(154\) 0 0
\(155\) −36.0000 −2.89159
\(156\) 0 0
\(157\) 4.00000 0.319235 0.159617 0.987179i \(-0.448974\pi\)
0.159617 + 0.987179i \(0.448974\pi\)
\(158\) 0 0
\(159\) −13.5000 + 7.79423i −1.07062 + 0.618123i
\(160\) 0 0
\(161\) 5.19615i 0.409514i
\(162\) 0 0
\(163\) −10.0000 −0.783260 −0.391630 0.920123i \(-0.628089\pi\)
−0.391630 + 0.920123i \(0.628089\pi\)
\(164\) 0 0
\(165\) −18.0000 + 10.3923i −1.40130 + 0.809040i
\(166\) 0 0
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) 10.0000 0.769231
\(170\) 0 0
\(171\) 1.50000 12.9904i 0.114708 0.993399i
\(172\) 0 0
\(173\) 6.00000 0.456172 0.228086 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) 0 0
\(175\) 7.00000 0.529150
\(176\) 0 0
\(177\) 4.50000 2.59808i 0.338241 0.195283i
\(178\) 0 0
\(179\) −12.0000 −0.896922 −0.448461 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 0 0
\(181\) 13.8564i 1.02994i −0.857209 0.514969i \(-0.827803\pi\)
0.857209 0.514969i \(-0.172197\pi\)
\(182\) 0 0
\(183\) −12.0000 + 6.92820i −0.887066 + 0.512148i
\(184\) 0 0
\(185\) −24.0000 −1.76452
\(186\) 0 0
\(187\) −6.00000 −0.438763
\(188\) 0 0
\(189\) 5.19615i 0.377964i
\(190\) 0 0
\(191\) 19.0526i 1.37859i −0.724479 0.689297i \(-0.757919\pi\)
0.724479 0.689297i \(-0.242081\pi\)
\(192\) 0 0
\(193\) 3.46410i 0.249351i −0.992198 0.124676i \(-0.960211\pi\)
0.992198 0.124676i \(-0.0397891\pi\)
\(194\) 0 0
\(195\) 9.00000 5.19615i 0.644503 0.372104i
\(196\) 0 0
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) −11.0000 −0.779769 −0.389885 0.920864i \(-0.627485\pi\)
−0.389885 + 0.920864i \(0.627485\pi\)
\(200\) 0 0
\(201\) −7.50000 12.9904i −0.529009 0.916271i
\(202\) 0 0
\(203\) −9.00000 −0.631676
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 13.5000 + 7.79423i 0.938315 + 0.541736i
\(208\) 0 0
\(209\) 6.00000 + 13.8564i 0.415029 + 0.958468i
\(210\) 0 0
\(211\) 12.1244i 0.834675i −0.908752 0.417338i \(-0.862963\pi\)
0.908752 0.417338i \(-0.137037\pi\)
\(212\) 0 0
\(213\) 18.0000 10.3923i 1.23334 0.712069i
\(214\) 0 0
\(215\) 6.92820i 0.472500i
\(216\) 0 0
\(217\) 10.3923i 0.705476i
\(218\) 0 0
\(219\) 16.5000 9.52628i 1.11497 0.643726i
\(220\) 0 0
\(221\) 3.00000 0.201802
\(222\) 0 0
\(223\) 10.3923i 0.695920i −0.937509 0.347960i \(-0.886874\pi\)
0.937509 0.347960i \(-0.113126\pi\)
\(224\) 0 0
\(225\) −10.5000 + 18.1865i −0.700000 + 1.21244i
\(226\) 0 0
\(227\) 3.00000 0.199117 0.0995585 0.995032i \(-0.468257\pi\)
0.0995585 + 0.995032i \(0.468257\pi\)
\(228\) 0 0
\(229\) −8.00000 −0.528655 −0.264327 0.964433i \(-0.585150\pi\)
−0.264327 + 0.964433i \(0.585150\pi\)
\(230\) 0 0
\(231\) −3.00000 5.19615i −0.197386 0.341882i
\(232\) 0 0
\(233\) 6.92820i 0.453882i 0.973909 + 0.226941i \(0.0728724\pi\)
−0.973909 + 0.226941i \(0.927128\pi\)
\(234\) 0 0
\(235\) 12.0000 0.782794
\(236\) 0 0
\(237\) −6.00000 10.3923i −0.389742 0.675053i
\(238\) 0 0
\(239\) 12.1244i 0.784259i 0.919910 + 0.392130i \(0.128262\pi\)
−0.919910 + 0.392130i \(0.871738\pi\)
\(240\) 0 0
\(241\) 13.8564i 0.892570i 0.894891 + 0.446285i \(0.147253\pi\)
−0.894891 + 0.446285i \(0.852747\pi\)
\(242\) 0 0
\(243\) −13.5000 7.79423i −0.866025 0.500000i
\(244\) 0 0
\(245\) 20.7846i 1.32788i
\(246\) 0 0
\(247\) −3.00000 6.92820i −0.190885 0.440831i
\(248\) 0 0
\(249\) −9.00000 15.5885i −0.570352 0.987878i
\(250\) 0 0
\(251\) 13.8564i 0.874609i 0.899314 + 0.437304i \(0.144067\pi\)
−0.899314 + 0.437304i \(0.855933\pi\)
\(252\) 0 0
\(253\) −18.0000 −1.13165
\(254\) 0 0
\(255\) −9.00000 + 5.19615i −0.563602 + 0.325396i
\(256\) 0 0
\(257\) 6.00000 0.374270 0.187135 0.982334i \(-0.440080\pi\)
0.187135 + 0.982334i \(0.440080\pi\)
\(258\) 0 0
\(259\) 6.92820i 0.430498i
\(260\) 0 0
\(261\) 13.5000 23.3827i 0.835629 1.44735i
\(262\) 0 0
\(263\) 3.46410i 0.213606i 0.994280 + 0.106803i \(0.0340614\pi\)
−0.994280 + 0.106803i \(0.965939\pi\)
\(264\) 0 0
\(265\) 31.1769i 1.91518i
\(266\) 0 0
\(267\) 9.00000 5.19615i 0.550791 0.317999i
\(268\) 0 0
\(269\) 18.0000 1.09748 0.548740 0.835993i \(-0.315108\pi\)
0.548740 + 0.835993i \(0.315108\pi\)
\(270\) 0 0
\(271\) 1.00000 0.0607457 0.0303728 0.999539i \(-0.490331\pi\)
0.0303728 + 0.999539i \(0.490331\pi\)
\(272\) 0 0
\(273\) 1.50000 + 2.59808i 0.0907841 + 0.157243i
\(274\) 0 0
\(275\) 24.2487i 1.46225i
\(276\) 0 0
\(277\) −2.00000 −0.120168 −0.0600842 0.998193i \(-0.519137\pi\)
−0.0600842 + 0.998193i \(0.519137\pi\)
\(278\) 0 0
\(279\) 27.0000 + 15.5885i 1.61645 + 0.933257i
\(280\) 0 0
\(281\) −12.0000 −0.715860 −0.357930 0.933748i \(-0.616517\pi\)
−0.357930 + 0.933748i \(0.616517\pi\)
\(282\) 0 0
\(283\) 10.0000 0.594438 0.297219 0.954809i \(-0.403941\pi\)
0.297219 + 0.954809i \(0.403941\pi\)
\(284\) 0 0
\(285\) 21.0000 + 15.5885i 1.24393 + 0.923381i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 14.0000 0.823529
\(290\) 0 0
\(291\) −12.0000 20.7846i −0.703452 1.21842i
\(292\) 0 0
\(293\) −21.0000 −1.22683 −0.613417 0.789760i \(-0.710205\pi\)
−0.613417 + 0.789760i \(0.710205\pi\)
\(294\) 0 0
\(295\) 10.3923i 0.605063i
\(296\) 0 0
\(297\) 18.0000 1.04447
\(298\) 0 0
\(299\) 9.00000 0.520483
\(300\) 0 0
\(301\) 2.00000 0.115278
\(302\) 0 0
\(303\) −9.00000 15.5885i −0.517036 0.895533i
\(304\) 0 0
\(305\) 27.7128i 1.58683i
\(306\) 0 0
\(307\) 10.3923i 0.593120i −0.955014 0.296560i \(-0.904160\pi\)
0.955014 0.296560i \(-0.0958395\pi\)
\(308\) 0 0
\(309\) −3.00000 5.19615i −0.170664 0.295599i
\(310\) 0 0
\(311\) 22.5167i 1.27680i 0.769704 + 0.638401i \(0.220404\pi\)
−0.769704 + 0.638401i \(0.779596\pi\)
\(312\) 0 0
\(313\) 13.0000 0.734803 0.367402 0.930062i \(-0.380247\pi\)
0.367402 + 0.930062i \(0.380247\pi\)
\(314\) 0 0
\(315\) −9.00000 5.19615i −0.507093 0.292770i
\(316\) 0 0
\(317\) 3.00000 0.168497 0.0842484 0.996445i \(-0.473151\pi\)
0.0842484 + 0.996445i \(0.473151\pi\)
\(318\) 0 0
\(319\) 31.1769i 1.74557i
\(320\) 0 0
\(321\) −4.50000 + 2.59808i −0.251166 + 0.145010i
\(322\) 0 0
\(323\) 3.00000 + 6.92820i 0.166924 + 0.385496i
\(324\) 0 0
\(325\) 12.1244i 0.672538i
\(326\) 0 0
\(327\) −13.5000 23.3827i −0.746552 1.29307i
\(328\) 0 0
\(329\) 3.46410i 0.190982i
\(330\) 0 0
\(331\) 19.0526i 1.04722i −0.851957 0.523612i \(-0.824584\pi\)
0.851957 0.523612i \(-0.175416\pi\)
\(332\) 0 0
\(333\) 18.0000 + 10.3923i 0.986394 + 0.569495i
\(334\) 0 0
\(335\) 30.0000 1.63908
\(336\) 0 0
\(337\) 24.2487i 1.32091i 0.750865 + 0.660456i \(0.229637\pi\)
−0.750865 + 0.660456i \(0.770363\pi\)
\(338\) 0 0
\(339\) −18.0000 + 10.3923i −0.977626 + 0.564433i
\(340\) 0 0
\(341\) −36.0000 −1.94951
\(342\) 0 0
\(343\) 13.0000 0.701934
\(344\) 0 0
\(345\) −27.0000 + 15.5885i −1.45363 + 0.839254i
\(346\) 0 0
\(347\) 27.7128i 1.48770i 0.668346 + 0.743851i \(0.267003\pi\)
−0.668346 + 0.743851i \(0.732997\pi\)
\(348\) 0 0
\(349\) −28.0000 −1.49881 −0.749403 0.662114i \(-0.769659\pi\)
−0.749403 + 0.662114i \(0.769659\pi\)
\(350\) 0 0
\(351\) −9.00000 −0.480384
\(352\) 0 0
\(353\) 25.9808i 1.38282i 0.722464 + 0.691408i \(0.243009\pi\)
−0.722464 + 0.691408i \(0.756991\pi\)
\(354\) 0 0
\(355\) 41.5692i 2.20627i
\(356\) 0 0
\(357\) −1.50000 2.59808i −0.0793884 0.137505i
\(358\) 0 0
\(359\) 19.0526i 1.00556i −0.864416 0.502778i \(-0.832311\pi\)
0.864416 0.502778i \(-0.167689\pi\)
\(360\) 0 0
\(361\) 13.0000 13.8564i 0.684211 0.729285i
\(362\) 0 0
\(363\) −1.50000 + 0.866025i −0.0787296 + 0.0454545i
\(364\) 0 0
\(365\) 38.1051i 1.99451i
\(366\) 0 0
\(367\) −32.0000 −1.67039 −0.835193 0.549957i \(-0.814644\pi\)
−0.835193 + 0.549957i \(0.814644\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 9.00000 0.467257
\(372\) 0 0
\(373\) 29.4449i 1.52460i −0.647225 0.762299i \(-0.724071\pi\)
0.647225 0.762299i \(-0.275929\pi\)
\(374\) 0 0
\(375\) −6.00000 10.3923i −0.309839 0.536656i
\(376\) 0 0
\(377\) 15.5885i 0.802846i
\(378\) 0 0
\(379\) 12.1244i 0.622786i −0.950281 0.311393i \(-0.899204\pi\)
0.950281 0.311393i \(-0.100796\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −6.00000 −0.306586 −0.153293 0.988181i \(-0.548988\pi\)
−0.153293 + 0.988181i \(0.548988\pi\)
\(384\) 0 0
\(385\) 12.0000 0.611577
\(386\) 0 0
\(387\) −3.00000 + 5.19615i −0.152499 + 0.264135i
\(388\) 0 0
\(389\) 3.46410i 0.175637i −0.996136 0.0878185i \(-0.972010\pi\)
0.996136 0.0878185i \(-0.0279895\pi\)
\(390\) 0 0
\(391\) −9.00000 −0.455150
\(392\) 0 0
\(393\) −3.00000 5.19615i −0.151330 0.262111i
\(394\) 0 0
\(395\) 24.0000 1.20757
\(396\) 0 0
\(397\) −22.0000 −1.10415 −0.552074 0.833795i \(-0.686163\pi\)
−0.552074 + 0.833795i \(0.686163\pi\)
\(398\) 0 0
\(399\) −4.50000 + 6.06218i −0.225282 + 0.303488i
\(400\) 0 0
\(401\) 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
\(404\) 0 0
\(405\) 27.0000 15.5885i 1.34164 0.774597i
\(406\) 0 0
\(407\) −24.0000 −1.18964
\(408\) 0 0
\(409\) 38.1051i 1.88418i 0.335365 + 0.942088i \(0.391140\pi\)
−0.335365 + 0.942088i \(0.608860\pi\)
\(410\) 0 0
\(411\) 7.50000 + 12.9904i 0.369948 + 0.640768i
\(412\) 0 0
\(413\) −3.00000 −0.147620
\(414\) 0 0
\(415\) 36.0000 1.76717
\(416\) 0 0
\(417\) 21.0000 12.1244i 1.02837 0.593732i
\(418\) 0 0
\(419\) 10.3923i 0.507697i −0.967244 0.253849i \(-0.918303\pi\)
0.967244 0.253849i \(-0.0816965\pi\)
\(420\) 0 0
\(421\) 12.1244i 0.590905i −0.955357 0.295452i \(-0.904530\pi\)
0.955357 0.295452i \(-0.0954704\pi\)
\(422\) 0 0
\(423\) −9.00000 5.19615i −0.437595 0.252646i
\(424\) 0 0
\(425\) 12.1244i 0.588118i
\(426\) 0 0
\(427\) 8.00000 0.387147
\(428\) 0 0
\(429\) 9.00000 5.19615i 0.434524 0.250873i
\(430\) 0 0
\(431\) −12.0000 −0.578020 −0.289010 0.957326i \(-0.593326\pi\)
−0.289010 + 0.957326i \(0.593326\pi\)
\(432\) 0 0
\(433\) 10.3923i 0.499422i 0.968320 + 0.249711i \(0.0803357\pi\)
−0.968320 + 0.249711i \(0.919664\pi\)
\(434\) 0 0
\(435\) 27.0000 + 46.7654i 1.29455 + 2.24223i
\(436\) 0 0
\(437\) 9.00000 + 20.7846i 0.430528 + 0.994263i
\(438\) 0 0
\(439\) 20.7846i 0.991995i 0.868324 + 0.495998i \(0.165198\pi\)
−0.868324 + 0.495998i \(0.834802\pi\)
\(440\) 0 0
\(441\) −9.00000 + 15.5885i −0.428571 + 0.742307i
\(442\) 0 0
\(443\) 17.3205i 0.822922i 0.911427 + 0.411461i \(0.134981\pi\)
−0.911427 + 0.411461i \(0.865019\pi\)
\(444\) 0 0
\(445\) 20.7846i 0.985285i
\(446\) 0 0
\(447\) 6.00000 + 10.3923i 0.283790 + 0.491539i
\(448\) 0 0
\(449\) 30.0000 1.41579 0.707894 0.706319i \(-0.249646\pi\)
0.707894 + 0.706319i \(0.249646\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 3.00000 + 5.19615i 0.140952 + 0.244137i
\(454\) 0 0
\(455\) −6.00000 −0.281284
\(456\) 0 0
\(457\) −25.0000 −1.16945 −0.584725 0.811231i \(-0.698798\pi\)
−0.584725 + 0.811231i \(0.698798\pi\)
\(458\) 0 0
\(459\) 9.00000 0.420084
\(460\) 0 0
\(461\) 13.8564i 0.645357i −0.946509 0.322679i \(-0.895417\pi\)
0.946509 0.322679i \(-0.104583\pi\)
\(462\) 0 0
\(463\) 40.0000 1.85896 0.929479 0.368875i \(-0.120257\pi\)
0.929479 + 0.368875i \(0.120257\pi\)
\(464\) 0 0
\(465\) −54.0000 + 31.1769i −2.50419 + 1.44579i
\(466\) 0 0
\(467\) 27.7128i 1.28240i −0.767375 0.641198i \(-0.778438\pi\)
0.767375 0.641198i \(-0.221562\pi\)
\(468\) 0 0
\(469\) 8.66025i 0.399893i
\(470\) 0 0
\(471\) 6.00000 3.46410i 0.276465 0.159617i
\(472\) 0 0
\(473\) 6.92820i 0.318559i
\(474\) 0 0
\(475\) −28.0000 + 12.1244i −1.28473 + 0.556304i
\(476\) 0 0
\(477\) −13.5000 + 23.3827i −0.618123 + 1.07062i
\(478\) 0 0
\(479\) 10.3923i 0.474837i 0.971408 + 0.237418i \(0.0763012\pi\)
−0.971408 + 0.237418i \(0.923699\pi\)
\(480\) 0 0
\(481\) 12.0000 0.547153
\(482\) 0 0
\(483\) −4.50000 7.79423i −0.204757 0.354650i
\(484\) 0 0
\(485\) 48.0000 2.17957
\(486\) 0 0
\(487\) 3.46410i 0.156973i 0.996915 + 0.0784867i \(0.0250088\pi\)
−0.996915 + 0.0784867i \(0.974991\pi\)
\(488\) 0 0
\(489\) −15.0000 + 8.66025i −0.678323 + 0.391630i
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 15.5885i 0.702069i
\(494\) 0 0
\(495\) −18.0000 + 31.1769i −0.809040 + 1.40130i
\(496\) 0 0
\(497\) −12.0000 −0.538274
\(498\) 0 0
\(499\) −10.0000 −0.447661 −0.223831 0.974628i \(-0.571856\pi\)
−0.223831 + 0.974628i \(0.571856\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 25.9808i 1.15842i 0.815177 + 0.579212i \(0.196640\pi\)
−0.815177 + 0.579212i \(0.803360\pi\)
\(504\) 0 0
\(505\) 36.0000 1.60198
\(506\) 0 0
\(507\) 15.0000 8.66025i 0.666173 0.384615i
\(508\) 0 0
\(509\) 6.00000 0.265945 0.132973 0.991120i \(-0.457548\pi\)
0.132973 + 0.991120i \(0.457548\pi\)
\(510\) 0 0
\(511\) −11.0000 −0.486611
\(512\) 0 0
\(513\) −9.00000 20.7846i −0.397360 0.917663i
\(514\) 0 0
\(515\) 12.0000 0.528783
\(516\) 0 0
\(517\) 12.0000 0.527759
\(518\) 0 0
\(519\) 9.00000 5.19615i 0.395056 0.228086i
\(520\) 0 0
\(521\) −24.0000 −1.05146 −0.525730 0.850652i \(-0.676208\pi\)
−0.525730 + 0.850652i \(0.676208\pi\)
\(522\) 0 0
\(523\) 32.9090i 1.43901i 0.694488 + 0.719504i \(0.255631\pi\)
−0.694488 + 0.719504i \(0.744369\pi\)
\(524\) 0 0
\(525\) 10.5000 6.06218i 0.458258 0.264575i
\(526\) 0 0
\(527\) −18.0000 −0.784092
\(528\) 0 0
\(529\) −4.00000 −0.173913
\(530\) 0 0
\(531\) 4.50000 7.79423i 0.195283 0.338241i
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 10.3923i 0.449299i
\(536\) 0 0
\(537\) −18.0000 + 10.3923i −0.776757 + 0.448461i
\(538\) 0 0
\(539\) 20.7846i 0.895257i
\(540\) 0 0
\(541\) 38.0000 1.63375 0.816874 0.576816i \(-0.195705\pi\)
0.816874 + 0.576816i \(0.195705\pi\)
\(542\) 0 0
\(543\) −12.0000 20.7846i −0.514969 0.891953i
\(544\) 0 0
\(545\) 54.0000 2.31311
\(546\) 0 0
\(547\) 24.2487i 1.03680i −0.855138 0.518400i \(-0.826528\pi\)
0.855138 0.518400i \(-0.173472\pi\)
\(548\) 0 0
\(549\) −12.0000 + 20.7846i −0.512148 + 0.887066i
\(550\) 0 0
\(551\) 36.0000 15.5885i 1.53365 0.664091i
\(552\) 0 0
\(553\) 6.92820i 0.294617i
\(554\) 0 0
\(555\) −36.0000 + 20.7846i −1.52811 + 0.882258i
\(556\) 0 0
\(557\) 45.0333i 1.90812i 0.299611 + 0.954062i \(0.403143\pi\)
−0.299611 + 0.954062i \(0.596857\pi\)
\(558\) 0 0
\(559\) 3.46410i 0.146516i
\(560\) 0 0
\(561\) −9.00000 + 5.19615i −0.379980 + 0.219382i
\(562\) 0 0
\(563\) 24.0000 1.01148 0.505740 0.862686i \(-0.331220\pi\)
0.505740 + 0.862686i \(0.331220\pi\)
\(564\) 0 0
\(565\) 41.5692i 1.74883i
\(566\) 0 0
\(567\) 4.50000 + 7.79423i 0.188982 + 0.327327i
\(568\) 0 0
\(569\) 24.0000 1.00613 0.503066 0.864248i \(-0.332205\pi\)
0.503066 + 0.864248i \(0.332205\pi\)
\(570\) 0 0
\(571\) 16.0000 0.669579 0.334790 0.942293i \(-0.391335\pi\)
0.334790 + 0.942293i \(0.391335\pi\)
\(572\) 0 0
\(573\) −16.5000 28.5788i −0.689297 1.19390i
\(574\) 0 0
\(575\) 36.3731i 1.51686i
\(576\) 0 0
\(577\) 25.0000 1.04076 0.520382 0.853934i \(-0.325790\pi\)
0.520382 + 0.853934i \(0.325790\pi\)
\(578\) 0 0
\(579\) −3.00000 5.19615i −0.124676 0.215945i
\(580\) 0 0
\(581\) 10.3923i 0.431145i
\(582\) 0 0
\(583\) 31.1769i 1.29122i
\(584\) 0 0
\(585\) 9.00000 15.5885i 0.372104 0.644503i
\(586\) 0 0
\(587\) 13.8564i 0.571915i 0.958242 + 0.285958i \(0.0923116\pi\)
−0.958242 + 0.285958i \(0.907688\pi\)
\(588\) 0 0
\(589\) 18.0000 + 41.5692i 0.741677 + 1.71283i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 20.7846i 0.853522i −0.904365 0.426761i \(-0.859655\pi\)
0.904365 0.426761i \(-0.140345\pi\)
\(594\) 0 0
\(595\) 6.00000 0.245976
\(596\) 0 0
\(597\) −16.5000 + 9.52628i −0.675300 + 0.389885i
\(598\) 0 0
\(599\) −12.0000 −0.490307 −0.245153 0.969484i \(-0.578838\pi\)
−0.245153 + 0.969484i \(0.578838\pi\)
\(600\) 0 0
\(601\) 10.3923i 0.423911i 0.977279 + 0.211955i \(0.0679832\pi\)
−0.977279 + 0.211955i \(0.932017\pi\)
\(602\) 0 0
\(603\) −22.5000 12.9904i −0.916271 0.529009i
\(604\) 0 0
\(605\) 3.46410i 0.140836i
\(606\) 0 0
\(607\) 27.7128i 1.12483i −0.826856 0.562414i \(-0.809873\pi\)
0.826856 0.562414i \(-0.190127\pi\)
\(608\) 0 0
\(609\) −13.5000 + 7.79423i −0.547048 + 0.315838i
\(610\) 0 0
\(611\) −6.00000 −0.242734
\(612\) 0 0
\(613\) −2.00000 −0.0807792 −0.0403896 0.999184i \(-0.512860\pi\)
−0.0403896 + 0.999184i \(0.512860\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 48.4974i 1.95243i −0.216799 0.976216i \(-0.569561\pi\)
0.216799 0.976216i \(-0.430439\pi\)
\(618\) 0 0
\(619\) −4.00000 −0.160774 −0.0803868 0.996764i \(-0.525616\pi\)
−0.0803868 + 0.996764i \(0.525616\pi\)
\(620\) 0 0
\(621\) 27.0000 1.08347
\(622\) 0 0
\(623\) −6.00000 −0.240385
\(624\) 0 0
\(625\) −11.0000 −0.440000
\(626\) 0 0
\(627\) 21.0000 + 15.5885i 0.838659 + 0.622543i
\(628\) 0 0
\(629\) −12.0000 −0.478471
\(630\) 0 0
\(631\) −16.0000 −0.636950 −0.318475 0.947931i \(-0.603171\pi\)
−0.318475 + 0.947931i \(0.603171\pi\)
\(632\) 0 0
\(633\) −10.5000 18.1865i −0.417338 0.722850i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 10.3923i 0.411758i
\(638\) 0 0
\(639\) 18.0000 31.1769i 0.712069 1.23334i
\(640\) 0 0
\(641\) −30.0000 −1.18493 −0.592464 0.805597i \(-0.701845\pi\)
−0.592464 + 0.805597i \(0.701845\pi\)
\(642\) 0 0
\(643\) 28.0000 1.10421 0.552106 0.833774i \(-0.313824\pi\)
0.552106 + 0.833774i \(0.313824\pi\)
\(644\) 0 0
\(645\) −6.00000 10.3923i −0.236250 0.409197i
\(646\) 0 0
\(647\) 1.73205i 0.0680939i −0.999420 0.0340470i \(-0.989160\pi\)
0.999420 0.0340470i \(-0.0108396\pi\)
\(648\) 0 0
\(649\) 10.3923i 0.407934i
\(650\) 0 0
\(651\) −9.00000 15.5885i −0.352738 0.610960i
\(652\) 0 0
\(653\) 17.3205i 0.677804i −0.940822 0.338902i \(-0.889945\pi\)
0.940822 0.338902i \(-0.110055\pi\)
\(654\) 0 0
\(655\) 12.0000 0.468879
\(656\) 0 0
\(657\) 16.5000 28.5788i 0.643726 1.11497i
\(658\) 0 0
\(659\) 33.0000 1.28550 0.642749 0.766077i \(-0.277794\pi\)
0.642749 + 0.766077i \(0.277794\pi\)
\(660\) 0 0
\(661\) 22.5167i 0.875797i −0.899025 0.437898i \(-0.855723\pi\)
0.899025 0.437898i \(-0.144277\pi\)
\(662\) 0 0
\(663\) 4.50000 2.59808i 0.174766 0.100901i
\(664\) 0 0
\(665\) −6.00000 13.8564i −0.232670 0.537328i
\(666\) 0 0
\(667\) 46.7654i 1.81076i
\(668\) 0 0
\(669\) −9.00000 15.5885i −0.347960 0.602685i
\(670\) 0 0
\(671\) 27.7128i 1.06984i
\(672\) 0 0
\(673\) 48.4974i 1.86944i −0.355387 0.934719i \(-0.615651\pi\)
0.355387 0.934719i \(-0.384349\pi\)
\(674\) 0 0
\(675\) 36.3731i 1.40000i
\(676\) 0 0
\(677\) −15.0000 −0.576497 −0.288248 0.957556i \(-0.593073\pi\)
−0.288248 + 0.957556i \(0.593073\pi\)
\(678\) 0 0
\(679\) 13.8564i 0.531760i
\(680\) 0 0
\(681\) 4.50000 2.59808i 0.172440 0.0995585i
\(682\) 0 0
\(683\) −12.0000 −0.459167 −0.229584 0.973289i \(-0.573736\pi\)
−0.229584 + 0.973289i \(0.573736\pi\)
\(684\) 0 0
\(685\) −30.0000 −1.14624
\(686\) 0 0
\(687\) −12.0000 + 6.92820i −0.457829 + 0.264327i
\(688\) 0 0
\(689\) 15.5885i 0.593873i
\(690\) 0 0
\(691\) −20.0000 −0.760836 −0.380418 0.924815i \(-0.624220\pi\)
−0.380418 + 0.924815i \(0.624220\pi\)
\(692\) 0 0
\(693\) −9.00000 5.19615i −0.341882 0.197386i
\(694\) 0 0
\(695\) 48.4974i 1.83961i
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 6.00000 + 10.3923i 0.226941 + 0.393073i
\(700\) 0 0
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 12.0000 + 27.7128i 0.452589 + 1.04521i
\(704\) 0 0
\(705\) 18.0000 10.3923i 0.677919 0.391397i
\(706\) 0 0
\(707\) 10.3923i 0.390843i
\(708\) 0 0
\(709\) −4.00000 −0.150223 −0.0751116 0.997175i \(-0.523931\pi\)
−0.0751116 + 0.997175i \(0.523931\pi\)
\(710\) 0 0
\(711\) −18.0000 10.3923i −0.675053 0.389742i
\(712\) 0 0
\(713\) −54.0000 −2.02232
\(714\) 0 0
\(715\) 20.7846i 0.777300i
\(716\) 0 0
\(717\) 10.5000 + 18.1865i 0.392130 + 0.679189i
\(718\) 0 0
\(719\) 8.66025i 0.322973i 0.986875 + 0.161486i \(0.0516288\pi\)
−0.986875 + 0.161486i \(0.948371\pi\)
\(720\) 0 0
\(721\) 3.46410i 0.129010i
\(722\) 0 0
\(723\) 12.0000 + 20.7846i 0.446285 + 0.772988i
\(724\) 0 0
\(725\) −63.0000 −2.33976
\(726\) 0 0
\(727\) 7.00000 0.259616 0.129808 0.991539i \(-0.458564\pi\)
0.129808 + 0.991539i \(0.458564\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 3.46410i 0.128124i
\(732\) 0 0
\(733\) −22.0000 −0.812589 −0.406294 0.913742i \(-0.633179\pi\)
−0.406294 + 0.913742i \(0.633179\pi\)
\(734\) 0 0
\(735\) −18.0000 31.1769i −0.663940 1.14998i
\(736\) 0 0
\(737\) 30.0000 1.10506
\(738\) 0 0
\(739\) −40.0000 −1.47142 −0.735712 0.677295i \(-0.763152\pi\)
−0.735712 + 0.677295i \(0.763152\pi\)
\(740\) 0 0
\(741\) −10.5000 7.79423i −0.385727 0.286328i
\(742\) 0 0
\(743\) −30.0000 −1.10059 −0.550297 0.834969i \(-0.685485\pi\)
−0.550297 + 0.834969i \(0.685485\pi\)
\(744\) 0 0
\(745\) −24.0000 −0.879292
\(746\) 0 0
\(747\) −27.0000 15.5885i −0.987878 0.570352i
\(748\) 0 0
\(749\) 3.00000 0.109618
\(750\) 0 0
\(751\) 6.92820i 0.252814i −0.991978 0.126407i \(-0.959656\pi\)
0.991978 0.126407i \(-0.0403445\pi\)
\(752\) 0 0
\(753\) 12.0000 + 20.7846i 0.437304 + 0.757433i
\(754\) 0 0
\(755\) −12.0000 −0.436725
\(756\) 0 0
\(757\) 16.0000 0.581530 0.290765 0.956795i \(-0.406090\pi\)
0.290765 + 0.956795i \(0.406090\pi\)
\(758\) 0 0
\(759\) −27.0000 + 15.5885i −0.980038 + 0.565825i
\(760\) 0 0
\(761\) 8.66025i 0.313934i −0.987604 0.156967i \(-0.949828\pi\)
0.987604 0.156967i \(-0.0501716\pi\)
\(762\) 0 0
\(763\) 15.5885i 0.564340i
\(764\) 0 0
\(765\) −9.00000 + 15.5885i −0.325396 + 0.563602i
\(766\) 0 0
\(767\) 5.19615i 0.187622i
\(768\) 0 0
\(769\) 49.0000 1.76699 0.883493 0.468445i \(-0.155186\pi\)
0.883493 + 0.468445i \(0.155186\pi\)
\(770\) 0 0
\(771\) 9.00000 5.19615i 0.324127 0.187135i
\(772\) 0 0
\(773\) −3.00000 −0.107903 −0.0539513 0.998544i \(-0.517182\pi\)
−0.0539513 + 0.998544i \(0.517182\pi\)
\(774\) 0 0
\(775\) 72.7461i 2.61312i
\(776\) 0 0
\(777\) −6.00000 10.3923i −0.215249 0.372822i
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 41.5692i 1.48746i
\(782\) 0 0
\(783\) 46.7654i 1.67126i
\(784\) 0 0
\(785\) 13.8564i 0.494556i
\(786\) 0 0
\(787\) 22.5167i 0.802632i 0.915940 + 0.401316i \(0.131447\pi\)
−0.915940 + 0.401316i \(0.868553\pi\)
\(788\) 0 0
\(789\) 3.00000 + 5.19615i 0.106803 + 0.184988i
\(790\) 0 0
\(791\) 12.0000 0.426671
\(792\) 0 0
\(793\) 13.8564i 0.492055i
\(794\) 0 0
\(795\) −27.0000 46.7654i −0.957591 1.65860i
\(796\) 0 0
\(797\) −21.0000 −0.743858 −0.371929 0.928261i \(-0.621304\pi\)
−0.371929 + 0.928261i \(0.621304\pi\)
\(798\) 0 0
\(799\) 6.00000 0.212265