Properties

Label 912.2.f.a.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.a.113.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.50000 - 0.866025i) q^{3} -3.46410i q^{5} -1.00000 q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(-1.50000 - 0.866025i) q^{3} -3.46410i q^{5} -1.00000 q^{7} +(1.50000 + 2.59808i) q^{9} -3.46410i q^{11} -1.73205i q^{13} +(-3.00000 + 5.19615i) q^{15} -1.73205i q^{17} +(4.00000 - 1.73205i) q^{19} +(1.50000 + 0.866025i) q^{21} -5.19615i q^{23} -7.00000 q^{25} -5.19615i q^{27} -9.00000 q^{29} +10.3923i q^{31} +(-3.00000 + 5.19615i) q^{33} +3.46410i q^{35} +6.92820i q^{37} +(-1.50000 + 2.59808i) q^{39} -2.00000 q^{43} +(9.00000 - 5.19615i) q^{45} +3.46410i q^{47} -6.00000 q^{49} +(-1.50000 + 2.59808i) q^{51} +9.00000 q^{53} -12.0000 q^{55} +(-7.50000 - 0.866025i) q^{57} -3.00000 q^{59} -8.00000 q^{61} +(-1.50000 - 2.59808i) q^{63} -6.00000 q^{65} -8.66025i q^{67} +(-4.50000 + 7.79423i) q^{69} -12.0000 q^{71} +11.0000 q^{73} +(10.5000 + 6.06218i) q^{75} +3.46410i q^{77} -6.92820i q^{79} +(-4.50000 + 7.79423i) q^{81} +10.3923i q^{83} -6.00000 q^{85} +(13.5000 + 7.79423i) q^{87} -6.00000 q^{89} +1.73205i q^{91} +(9.00000 - 15.5885i) q^{93} +(-6.00000 - 13.8564i) q^{95} -13.8564i q^{97} +(9.00000 - 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 3 q^{3} - 2 q^{7} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 3 q^{3} - 2 q^{7} + 3 q^{9} - 6 q^{15} + 8 q^{19} + 3 q^{21} - 14 q^{25} - 18 q^{29} - 6 q^{33} - 3 q^{39} - 4 q^{43} + 18 q^{45} - 12 q^{49} - 3 q^{51} + 18 q^{53} - 24 q^{55} - 15 q^{57} - 6 q^{59} - 16 q^{61} - 3 q^{63} - 12 q^{65} - 9 q^{69} - 24 q^{71} + 22 q^{73} + 21 q^{75} - 9 q^{81} - 12 q^{85} + 27 q^{87} - 12 q^{89} + 18 q^{93} - 12 q^{95} + 18 q^{99}+O(q^{100}) \) 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 \(-0.717953\pi\)
0.632456 0.774597i \(-0.282047\pi\)
\(6\) 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 \(-0.825099\pi\)
0.852803 0.522233i \(-0.174901\pi\)
\(12\) 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 \(-0.932640\pi\)
0.977692 0.210042i \(-0.0673601\pi\)
\(18\) 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 \(-0.817767\pi\)
0.840548 0.541736i \(-0.182233\pi\)
\(24\) 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 \(-0.814897\pi\)
−0.835629 + 0.549294i \(0.814897\pi\)
\(30\) 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 \(0.0813007\pi\)
−0.967559 + 0.252646i \(0.918699\pi\)
\(48\) 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 \(-0.287894\pi\)
0.618123 + 0.786082i \(0.287894\pi\)
\(54\) 0 0
\(55\) −12.0000 −1.61808
\(56\) 0 0
\(57\) −7.50000 0.866025i −0.993399 0.114708i
\(58\) 0 0
\(59\) −3.00000 −0.390567 −0.195283 0.980747i \(-0.562563\pi\)
−0.195283 + 0.980747i \(0.562563\pi\)
\(60\) 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 \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) 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 \(0.193193\pi\)
−0.821401 + 0.570352i \(0.806807\pi\)
\(84\) 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 \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) 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 \(0.172965\pi\)
−0.855963 + 0.517036i \(0.827035\pi\)
\(102\) 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 \(-0.453678\pi\)
0.145010 + 0.989430i \(0.453678\pi\)
\(108\) 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 \(-0.309095\pi\)
0.564433 + 0.825479i \(0.309095\pi\)
\(114\) 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 \(0.0483556\pi\)
−0.988483 + 0.151330i \(0.951644\pi\)
\(132\) 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 \(-0.879376\pi\)
0.929053 0.369948i \(-0.120624\pi\)
\(138\) 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 \(-0.908408\pi\)
0.958886 0.283790i \(-0.0915919\pi\)
\(150\) 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
\(171\) 10.5000 + 7.79423i 0.802955 + 0.596040i
\(172\) 0 0
\(173\) −6.00000 −0.456172 −0.228086 0.973641i \(-0.573247\pi\)
−0.228086 + 0.973641i \(0.573247\pi\)
\(174\) 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 \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) 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 \(0.242081\pi\)
−0.724479 + 0.689297i \(0.757919\pi\)
\(192\) 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 \(-0.531743\pi\)
−0.0995585 + 0.995032i \(0.531743\pi\)
\(228\) 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 \(-0.927128\pi\)
0.973909 0.226941i \(-0.0728724\pi\)
\(234\) 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 \(-0.871738\pi\)
0.919910 0.392130i \(-0.128262\pi\)
\(240\) 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 \(-0.855933\pi\)
0.899314 0.437304i \(-0.144067\pi\)
\(252\) 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 \(-0.559920\pi\)
−0.187135 + 0.982334i \(0.559920\pi\)
\(258\) 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 \(-0.965939\pi\)
0.994280 0.106803i \(-0.0340614\pi\)
\(264\) 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 \(-0.684892\pi\)
−0.548740 + 0.835993i \(0.684892\pi\)
\(270\) 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 \(-0.383483\pi\)
0.357930 + 0.933748i \(0.383483\pi\)
\(282\) 0 0
\(283\) 10.0000 0.594438 0.297219 0.954809i \(-0.403941\pi\)
0.297219 + 0.954809i \(0.403941\pi\)
\(284\) 0 0
\(285\) −3.00000 + 25.9808i −0.177705 + 1.53897i
\(286\) 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 \(-0.289795\pi\)
0.613417 + 0.789760i \(0.289795\pi\)
\(294\) 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 \(-0.779596\pi\)
0.769704 0.638401i \(-0.220404\pi\)
\(312\) 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 \(-0.526849\pi\)
−0.0842484 + 0.996445i \(0.526849\pi\)
\(318\) 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 \(-0.732997\pi\)
0.668346 0.743851i \(-0.267003\pi\)
\(348\) 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 \(-0.756991\pi\)
0.722464 0.691408i \(-0.243009\pi\)
\(354\) 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 \(0.167689\pi\)
−0.864416 + 0.502778i \(0.832311\pi\)
\(360\) 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 \(-0.451012\pi\)
0.153293 + 0.988181i \(0.451012\pi\)
\(384\) 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 \(0.0279895\pi\)
−0.996136 + 0.0878185i \(0.972010\pi\)
\(390\) 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
\(399\) 7.50000 + 0.866025i 0.375470 + 0.0433555i
\(400\) 0 0
\(401\) −24.0000 −1.19850 −0.599251 0.800561i \(-0.704535\pi\)
−0.599251 + 0.800561i \(0.704535\pi\)
\(402\) 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 \(0.0816965\pi\)
−0.967244 + 0.253849i \(0.918303\pi\)
\(420\) 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 \(-0.406674\pi\)
0.289010 + 0.957326i \(0.406674\pi\)
\(432\) 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 \(-0.865019\pi\)
0.911427 0.411461i \(-0.134981\pi\)
\(444\) 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 \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) 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 \(0.104583\pi\)
−0.946509 + 0.322679i \(0.895417\pi\)
\(462\) 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 \(0.221562\pi\)
−0.767375 + 0.641198i \(0.778438\pi\)
\(468\) 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 \(-0.923699\pi\)
0.971408 0.237418i \(-0.0763012\pi\)
\(480\) 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 \(-0.803360\pi\)
0.815177 0.579212i \(-0.196640\pi\)
\(504\) 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 \(-0.542452\pi\)
−0.132973 + 0.991120i \(0.542452\pi\)
\(510\) 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 \(-0.323792\pi\)
0.525730 + 0.850652i \(0.323792\pi\)
\(522\) 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 \(-0.596857\pi\)
0.299611 0.954062i \(-0.403143\pi\)
\(558\) 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 \(-0.668780\pi\)
−0.505740 + 0.862686i \(0.668780\pi\)
\(564\) 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 \(-0.667795\pi\)
−0.503066 + 0.864248i \(0.667795\pi\)
\(570\) 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 \(-0.907688\pi\)
0.958242 0.285958i \(-0.0923116\pi\)
\(588\) 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 \(0.140345\pi\)
−0.904365 + 0.426761i \(0.859655\pi\)
\(594\) 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 \(-0.421162\pi\)
0.245153 + 0.969484i \(0.421162\pi\)
\(600\) 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 \(0.430439\pi\)
−0.216799 + 0.976216i \(0.569561\pi\)
\(618\) 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
\(627\) −3.00000 + 25.9808i −0.119808 + 1.03757i
\(628\) 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 \(-0.298155\pi\)
0.592464 + 0.805597i \(0.298155\pi\)
\(642\) 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 \(0.0108396\pi\)
−0.999420 + 0.0340470i \(0.989160\pi\)
\(648\) 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 \(0.110055\pi\)
−0.940822 + 0.338902i \(0.889945\pi\)
\(654\) 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 \(-0.722206\pi\)
−0.642749 + 0.766077i \(0.722206\pi\)
\(660\) 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 \(-0.406927\pi\)
0.288248 + 0.957556i \(0.406927\pi\)
\(678\) 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 \(-0.426264\pi\)
0.229584 + 0.973289i \(0.426264\pi\)
\(684\) 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 \(-0.948371\pi\)
0.986875 0.161486i \(-0.0516288\pi\)
\(720\) 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
\(741\) −1.50000 + 12.9904i −0.0551039 + 0.477214i
\(742\) 0 0
\(743\) 30.0000 1.10059 0.550297 0.834969i \(-0.314515\pi\)
0.550297 + 0.834969i \(0.314515\pi\)
\(744\) 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 \(0.0501716\pi\)
−0.987604 + 0.156967i \(0.949828\pi\)
\(762\) 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 \(-0.482818\pi\)
0.0539513 + 0.998544i \(0.482818\pi\)
\(774\) 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 \(-0.378696\pi\)
0.371929 + 0.928261i \(0.378696\pi\)
\(798\) 0