Properties

Label 805.2.c.a.484.2
Level $805$
Weight $2$
Character 805.484
Analytic conductor $6.428$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 805 = 5 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 805.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.42795736271\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
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 484.2
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 805.484
Dual form 805.2.c.a.484.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{3} +2.00000 q^{4} +(2.00000 - 1.00000i) q^{5} +1.00000i q^{7} +2.00000 q^{9} +O(q^{10})\) \(q+1.00000i q^{3} +2.00000 q^{4} +(2.00000 - 1.00000i) q^{5} +1.00000i q^{7} +2.00000 q^{9} -1.00000 q^{11} +2.00000i q^{12} +1.00000i q^{13} +(1.00000 + 2.00000i) q^{15} +4.00000 q^{16} -1.00000i q^{17} -2.00000 q^{19} +(4.00000 - 2.00000i) q^{20} -1.00000 q^{21} +1.00000i q^{23} +(3.00000 - 4.00000i) q^{25} +5.00000i q^{27} +2.00000i q^{28} -7.00000 q^{29} +4.00000 q^{31} -1.00000i q^{33} +(1.00000 + 2.00000i) q^{35} +4.00000 q^{36} -8.00000i q^{37} -1.00000 q^{39} -6.00000 q^{41} -8.00000i q^{43} -2.00000 q^{44} +(4.00000 - 2.00000i) q^{45} +7.00000i q^{47} +4.00000i q^{48} -1.00000 q^{49} +1.00000 q^{51} +2.00000i q^{52} +4.00000i q^{53} +(-2.00000 + 1.00000i) q^{55} -2.00000i q^{57} +4.00000 q^{59} +(2.00000 + 4.00000i) q^{60} -10.0000 q^{61} +2.00000i q^{63} +8.00000 q^{64} +(1.00000 + 2.00000i) q^{65} +14.0000i q^{67} -2.00000i q^{68} -1.00000 q^{69} +2.00000i q^{73} +(4.00000 + 3.00000i) q^{75} -4.00000 q^{76} -1.00000i q^{77} +15.0000 q^{79} +(8.00000 - 4.00000i) q^{80} +1.00000 q^{81} -8.00000i q^{83} -2.00000 q^{84} +(-1.00000 - 2.00000i) q^{85} -7.00000i q^{87} -6.00000 q^{89} -1.00000 q^{91} +2.00000i q^{92} +4.00000i q^{93} +(-4.00000 + 2.00000i) q^{95} +7.00000i q^{97} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 4 q^{4} + 4 q^{5} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 4 q^{4} + 4 q^{5} + 4 q^{9} - 2 q^{11} + 2 q^{15} + 8 q^{16} - 4 q^{19} + 8 q^{20} - 2 q^{21} + 6 q^{25} - 14 q^{29} + 8 q^{31} + 2 q^{35} + 8 q^{36} - 2 q^{39} - 12 q^{41} - 4 q^{44} + 8 q^{45} - 2 q^{49} + 2 q^{51} - 4 q^{55} + 8 q^{59} + 4 q^{60} - 20 q^{61} + 16 q^{64} + 2 q^{65} - 2 q^{69} + 8 q^{75} - 8 q^{76} + 30 q^{79} + 16 q^{80} + 2 q^{81} - 4 q^{84} - 2 q^{85} - 12 q^{89} - 2 q^{91} - 8 q^{95} - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/805\mathbb{Z}\right)^\times\).

\(n\) \(162\) \(281\) \(346\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(3\) 1.00000i 0.577350i 0.957427 + 0.288675i \(0.0932147\pi\)
−0.957427 + 0.288675i \(0.906785\pi\)
\(4\) 2.00000 1.00000
\(5\) 2.00000 1.00000i 0.894427 0.447214i
\(6\) 0 0
\(7\) 1.00000i 0.377964i
\(8\) 0 0
\(9\) 2.00000 0.666667
\(10\) 0 0
\(11\) −1.00000 −0.301511 −0.150756 0.988571i \(-0.548171\pi\)
−0.150756 + 0.988571i \(0.548171\pi\)
\(12\) 2.00000i 0.577350i
\(13\) 1.00000i 0.277350i 0.990338 + 0.138675i \(0.0442844\pi\)
−0.990338 + 0.138675i \(0.955716\pi\)
\(14\) 0 0
\(15\) 1.00000 + 2.00000i 0.258199 + 0.516398i
\(16\) 4.00000 1.00000
\(17\) 1.00000i 0.242536i −0.992620 0.121268i \(-0.961304\pi\)
0.992620 0.121268i \(-0.0386960\pi\)
\(18\) 0 0
\(19\) −2.00000 −0.458831 −0.229416 0.973329i \(-0.573682\pi\)
−0.229416 + 0.973329i \(0.573682\pi\)
\(20\) 4.00000 2.00000i 0.894427 0.447214i
\(21\) −1.00000 −0.218218
\(22\) 0 0
\(23\) 1.00000i 0.208514i
\(24\) 0 0
\(25\) 3.00000 4.00000i 0.600000 0.800000i
\(26\) 0 0
\(27\) 5.00000i 0.962250i
\(28\) 2.00000i 0.377964i
\(29\) −7.00000 −1.29987 −0.649934 0.759991i \(-0.725203\pi\)
−0.649934 + 0.759991i \(0.725203\pi\)
\(30\) 0 0
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 0 0
\(33\) 1.00000i 0.174078i
\(34\) 0 0
\(35\) 1.00000 + 2.00000i 0.169031 + 0.338062i
\(36\) 4.00000 0.666667
\(37\) 8.00000i 1.31519i −0.753371 0.657596i \(-0.771573\pi\)
0.753371 0.657596i \(-0.228427\pi\)
\(38\) 0 0
\(39\) −1.00000 −0.160128
\(40\) 0 0
\(41\) −6.00000 −0.937043 −0.468521 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 0 0
\(43\) 8.00000i 1.21999i −0.792406 0.609994i \(-0.791172\pi\)
0.792406 0.609994i \(-0.208828\pi\)
\(44\) −2.00000 −0.301511
\(45\) 4.00000 2.00000i 0.596285 0.298142i
\(46\) 0 0
\(47\) 7.00000i 1.02105i 0.859861 + 0.510527i \(0.170550\pi\)
−0.859861 + 0.510527i \(0.829450\pi\)
\(48\) 4.00000i 0.577350i
\(49\) −1.00000 −0.142857
\(50\) 0 0
\(51\) 1.00000 0.140028
\(52\) 2.00000i 0.277350i
\(53\) 4.00000i 0.549442i 0.961524 + 0.274721i \(0.0885855\pi\)
−0.961524 + 0.274721i \(0.911414\pi\)
\(54\) 0 0
\(55\) −2.00000 + 1.00000i −0.269680 + 0.134840i
\(56\) 0 0
\(57\) 2.00000i 0.264906i
\(58\) 0 0
\(59\) 4.00000 0.520756 0.260378 0.965507i \(-0.416153\pi\)
0.260378 + 0.965507i \(0.416153\pi\)
\(60\) 2.00000 + 4.00000i 0.258199 + 0.516398i
\(61\) −10.0000 −1.28037 −0.640184 0.768221i \(-0.721142\pi\)
−0.640184 + 0.768221i \(0.721142\pi\)
\(62\) 0 0
\(63\) 2.00000i 0.251976i
\(64\) 8.00000 1.00000
\(65\) 1.00000 + 2.00000i 0.124035 + 0.248069i
\(66\) 0 0
\(67\) 14.0000i 1.71037i 0.518321 + 0.855186i \(0.326557\pi\)
−0.518321 + 0.855186i \(0.673443\pi\)
\(68\) 2.00000i 0.242536i
\(69\) −1.00000 −0.120386
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 2.00000i 0.234082i 0.993127 + 0.117041i \(0.0373409\pi\)
−0.993127 + 0.117041i \(0.962659\pi\)
\(74\) 0 0
\(75\) 4.00000 + 3.00000i 0.461880 + 0.346410i
\(76\) −4.00000 −0.458831
\(77\) 1.00000i 0.113961i
\(78\) 0 0
\(79\) 15.0000 1.68763 0.843816 0.536633i \(-0.180304\pi\)
0.843816 + 0.536633i \(0.180304\pi\)
\(80\) 8.00000 4.00000i 0.894427 0.447214i
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 8.00000i 0.878114i −0.898459 0.439057i \(-0.855313\pi\)
0.898459 0.439057i \(-0.144687\pi\)
\(84\) −2.00000 −0.218218
\(85\) −1.00000 2.00000i −0.108465 0.216930i
\(86\) 0 0
\(87\) 7.00000i 0.750479i
\(88\) 0 0
\(89\) −6.00000 −0.635999 −0.317999 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 2.00000i 0.208514i
\(93\) 4.00000i 0.414781i
\(94\) 0 0
\(95\) −4.00000 + 2.00000i −0.410391 + 0.205196i
\(96\) 0 0
\(97\) 7.00000i 0.710742i 0.934725 + 0.355371i \(0.115646\pi\)
−0.934725 + 0.355371i \(0.884354\pi\)
\(98\) 0 0
\(99\) −2.00000 −0.201008
\(100\) 6.00000 8.00000i 0.600000 0.800000i
\(101\) −4.00000 −0.398015 −0.199007 0.979998i \(-0.563772\pi\)
−0.199007 + 0.979998i \(0.563772\pi\)
\(102\) 0 0
\(103\) 7.00000i 0.689730i 0.938652 + 0.344865i \(0.112075\pi\)
−0.938652 + 0.344865i \(0.887925\pi\)
\(104\) 0 0
\(105\) −2.00000 + 1.00000i −0.195180 + 0.0975900i
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 10.0000i 0.962250i
\(109\) 5.00000 0.478913 0.239457 0.970907i \(-0.423031\pi\)
0.239457 + 0.970907i \(0.423031\pi\)
\(110\) 0 0
\(111\) 8.00000 0.759326
\(112\) 4.00000i 0.377964i
\(113\) 18.0000i 1.69330i −0.532152 0.846649i \(-0.678617\pi\)
0.532152 0.846649i \(-0.321383\pi\)
\(114\) 0 0
\(115\) 1.00000 + 2.00000i 0.0932505 + 0.186501i
\(116\) −14.0000 −1.29987
\(117\) 2.00000i 0.184900i
\(118\) 0 0
\(119\) 1.00000 0.0916698
\(120\) 0 0
\(121\) −10.0000 −0.909091
\(122\) 0 0
\(123\) 6.00000i 0.541002i
\(124\) 8.00000 0.718421
\(125\) 2.00000 11.0000i 0.178885 0.983870i
\(126\) 0 0
\(127\) 2.00000i 0.177471i −0.996055 0.0887357i \(-0.971717\pi\)
0.996055 0.0887357i \(-0.0282826\pi\)
\(128\) 0 0
\(129\) 8.00000 0.704361
\(130\) 0 0
\(131\) −20.0000 −1.74741 −0.873704 0.486458i \(-0.838289\pi\)
−0.873704 + 0.486458i \(0.838289\pi\)
\(132\) 2.00000i 0.174078i
\(133\) 2.00000i 0.173422i
\(134\) 0 0
\(135\) 5.00000 + 10.0000i 0.430331 + 0.860663i
\(136\) 0 0
\(137\) 10.0000i 0.854358i −0.904167 0.427179i \(-0.859507\pi\)
0.904167 0.427179i \(-0.140493\pi\)
\(138\) 0 0
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 2.00000 + 4.00000i 0.169031 + 0.338062i
\(141\) −7.00000 −0.589506
\(142\) 0 0
\(143\) 1.00000i 0.0836242i
\(144\) 8.00000 0.666667
\(145\) −14.0000 + 7.00000i −1.16264 + 0.581318i
\(146\) 0 0
\(147\) 1.00000i 0.0824786i
\(148\) 16.0000i 1.31519i
\(149\) −14.0000 −1.14692 −0.573462 0.819232i \(-0.694400\pi\)
−0.573462 + 0.819232i \(0.694400\pi\)
\(150\) 0 0
\(151\) −1.00000 −0.0813788 −0.0406894 0.999172i \(-0.512955\pi\)
−0.0406894 + 0.999172i \(0.512955\pi\)
\(152\) 0 0
\(153\) 2.00000i 0.161690i
\(154\) 0 0
\(155\) 8.00000 4.00000i 0.642575 0.321288i
\(156\) −2.00000 −0.160128
\(157\) 18.0000i 1.43656i −0.695756 0.718278i \(-0.744931\pi\)
0.695756 0.718278i \(-0.255069\pi\)
\(158\) 0 0
\(159\) −4.00000 −0.317221
\(160\) 0 0
\(161\) −1.00000 −0.0788110
\(162\) 0 0
\(163\) 4.00000i 0.313304i −0.987654 0.156652i \(-0.949930\pi\)
0.987654 0.156652i \(-0.0500701\pi\)
\(164\) −12.0000 −0.937043
\(165\) −1.00000 2.00000i −0.0778499 0.155700i
\(166\) 0 0
\(167\) 3.00000i 0.232147i 0.993241 + 0.116073i \(0.0370308\pi\)
−0.993241 + 0.116073i \(0.962969\pi\)
\(168\) 0 0
\(169\) 12.0000 0.923077
\(170\) 0 0
\(171\) −4.00000 −0.305888
\(172\) 16.0000i 1.21999i
\(173\) 7.00000i 0.532200i 0.963945 + 0.266100i \(0.0857352\pi\)
−0.963945 + 0.266100i \(0.914265\pi\)
\(174\) 0 0
\(175\) 4.00000 + 3.00000i 0.302372 + 0.226779i
\(176\) −4.00000 −0.301511
\(177\) 4.00000i 0.300658i
\(178\) 0 0
\(179\) 4.00000 0.298974 0.149487 0.988764i \(-0.452238\pi\)
0.149487 + 0.988764i \(0.452238\pi\)
\(180\) 8.00000 4.00000i 0.596285 0.298142i
\(181\) −16.0000 −1.18927 −0.594635 0.803996i \(-0.702704\pi\)
−0.594635 + 0.803996i \(0.702704\pi\)
\(182\) 0 0
\(183\) 10.0000i 0.739221i
\(184\) 0 0
\(185\) −8.00000 16.0000i −0.588172 1.17634i
\(186\) 0 0
\(187\) 1.00000i 0.0731272i
\(188\) 14.0000i 1.02105i
\(189\) −5.00000 −0.363696
\(190\) 0 0
\(191\) −25.0000 −1.80894 −0.904468 0.426541i \(-0.859732\pi\)
−0.904468 + 0.426541i \(0.859732\pi\)
\(192\) 8.00000i 0.577350i
\(193\) 14.0000i 1.00774i −0.863779 0.503871i \(-0.831909\pi\)
0.863779 0.503871i \(-0.168091\pi\)
\(194\) 0 0
\(195\) −2.00000 + 1.00000i −0.143223 + 0.0716115i
\(196\) −2.00000 −0.142857
\(197\) 18.0000i 1.28245i −0.767354 0.641223i \(-0.778427\pi\)
0.767354 0.641223i \(-0.221573\pi\)
\(198\) 0 0
\(199\) −12.0000 −0.850657 −0.425329 0.905039i \(-0.639842\pi\)
−0.425329 + 0.905039i \(0.639842\pi\)
\(200\) 0 0
\(201\) −14.0000 −0.987484
\(202\) 0 0
\(203\) 7.00000i 0.491304i
\(204\) 2.00000 0.140028
\(205\) −12.0000 + 6.00000i −0.838116 + 0.419058i
\(206\) 0 0
\(207\) 2.00000i 0.139010i
\(208\) 4.00000i 0.277350i
\(209\) 2.00000 0.138343
\(210\) 0 0
\(211\) −5.00000 −0.344214 −0.172107 0.985078i \(-0.555058\pi\)
−0.172107 + 0.985078i \(0.555058\pi\)
\(212\) 8.00000i 0.549442i
\(213\) 0 0
\(214\) 0 0
\(215\) −8.00000 16.0000i −0.545595 1.09119i
\(216\) 0 0
\(217\) 4.00000i 0.271538i
\(218\) 0 0
\(219\) −2.00000 −0.135147
\(220\) −4.00000 + 2.00000i −0.269680 + 0.134840i
\(221\) 1.00000 0.0672673
\(222\) 0 0
\(223\) 25.0000i 1.67412i 0.547108 + 0.837062i \(0.315729\pi\)
−0.547108 + 0.837062i \(0.684271\pi\)
\(224\) 0 0
\(225\) 6.00000 8.00000i 0.400000 0.533333i
\(226\) 0 0
\(227\) 15.0000i 0.995585i −0.867296 0.497792i \(-0.834144\pi\)
0.867296 0.497792i \(-0.165856\pi\)
\(228\) 4.00000i 0.264906i
\(229\) 14.0000 0.925146 0.462573 0.886581i \(-0.346926\pi\)
0.462573 + 0.886581i \(0.346926\pi\)
\(230\) 0 0
\(231\) 1.00000 0.0657952
\(232\) 0 0
\(233\) 10.0000i 0.655122i 0.944830 + 0.327561i \(0.106227\pi\)
−0.944830 + 0.327561i \(0.893773\pi\)
\(234\) 0 0
\(235\) 7.00000 + 14.0000i 0.456630 + 0.913259i
\(236\) 8.00000 0.520756
\(237\) 15.0000i 0.974355i
\(238\) 0 0
\(239\) 9.00000 0.582162 0.291081 0.956698i \(-0.405985\pi\)
0.291081 + 0.956698i \(0.405985\pi\)
\(240\) 4.00000 + 8.00000i 0.258199 + 0.516398i
\(241\) 10.0000 0.644157 0.322078 0.946713i \(-0.395619\pi\)
0.322078 + 0.946713i \(0.395619\pi\)
\(242\) 0 0
\(243\) 16.0000i 1.02640i
\(244\) −20.0000 −1.28037
\(245\) −2.00000 + 1.00000i −0.127775 + 0.0638877i
\(246\) 0 0
\(247\) 2.00000i 0.127257i
\(248\) 0 0
\(249\) 8.00000 0.506979
\(250\) 0 0
\(251\) −12.0000 −0.757433 −0.378717 0.925513i \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) 4.00000i 0.251976i
\(253\) 1.00000i 0.0628695i
\(254\) 0 0
\(255\) 2.00000 1.00000i 0.125245 0.0626224i
\(256\) 16.0000 1.00000
\(257\) 18.0000i 1.12281i 0.827541 + 0.561405i \(0.189739\pi\)
−0.827541 + 0.561405i \(0.810261\pi\)
\(258\) 0 0
\(259\) 8.00000 0.497096
\(260\) 2.00000 + 4.00000i 0.124035 + 0.248069i
\(261\) −14.0000 −0.866578
\(262\) 0 0
\(263\) 2.00000i 0.123325i 0.998097 + 0.0616626i \(0.0196403\pi\)
−0.998097 + 0.0616626i \(0.980360\pi\)
\(264\) 0 0
\(265\) 4.00000 + 8.00000i 0.245718 + 0.491436i
\(266\) 0 0
\(267\) 6.00000i 0.367194i
\(268\) 28.0000i 1.71037i
\(269\) 6.00000 0.365826 0.182913 0.983129i \(-0.441447\pi\)
0.182913 + 0.983129i \(0.441447\pi\)
\(270\) 0 0
\(271\) 10.0000 0.607457 0.303728 0.952759i \(-0.401768\pi\)
0.303728 + 0.952759i \(0.401768\pi\)
\(272\) 4.00000i 0.242536i
\(273\) 1.00000i 0.0605228i
\(274\) 0 0
\(275\) −3.00000 + 4.00000i −0.180907 + 0.241209i
\(276\) −2.00000 −0.120386
\(277\) 24.0000i 1.44202i −0.692925 0.721010i \(-0.743678\pi\)
0.692925 0.721010i \(-0.256322\pi\)
\(278\) 0 0
\(279\) 8.00000 0.478947
\(280\) 0 0
\(281\) 9.00000 0.536895 0.268447 0.963294i \(-0.413489\pi\)
0.268447 + 0.963294i \(0.413489\pi\)
\(282\) 0 0
\(283\) 17.0000i 1.01055i 0.862960 + 0.505273i \(0.168608\pi\)
−0.862960 + 0.505273i \(0.831392\pi\)
\(284\) 0 0
\(285\) −2.00000 4.00000i −0.118470 0.236940i
\(286\) 0 0
\(287\) 6.00000i 0.354169i
\(288\) 0 0
\(289\) 16.0000 0.941176
\(290\) 0 0
\(291\) −7.00000 −0.410347
\(292\) 4.00000i 0.234082i
\(293\) 27.0000i 1.57736i −0.614806 0.788678i \(-0.710766\pi\)
0.614806 0.788678i \(-0.289234\pi\)
\(294\) 0 0
\(295\) 8.00000 4.00000i 0.465778 0.232889i
\(296\) 0 0
\(297\) 5.00000i 0.290129i
\(298\) 0 0
\(299\) −1.00000 −0.0578315
\(300\) 8.00000 + 6.00000i 0.461880 + 0.346410i
\(301\) 8.00000 0.461112
\(302\) 0 0
\(303\) 4.00000i 0.229794i
\(304\) −8.00000 −0.458831
\(305\) −20.0000 + 10.0000i −1.14520 + 0.572598i
\(306\) 0 0
\(307\) 9.00000i 0.513657i 0.966457 + 0.256829i \(0.0826776\pi\)
−0.966457 + 0.256829i \(0.917322\pi\)
\(308\) 2.00000i 0.113961i
\(309\) −7.00000 −0.398216
\(310\) 0 0
\(311\) −18.0000 −1.02069 −0.510343 0.859971i \(-0.670482\pi\)
−0.510343 + 0.859971i \(0.670482\pi\)
\(312\) 0 0
\(313\) 9.00000i 0.508710i −0.967111 0.254355i \(-0.918137\pi\)
0.967111 0.254355i \(-0.0818632\pi\)
\(314\) 0 0
\(315\) 2.00000 + 4.00000i 0.112687 + 0.225374i
\(316\) 30.0000 1.68763
\(317\) 6.00000i 0.336994i 0.985702 + 0.168497i \(0.0538913\pi\)
−0.985702 + 0.168497i \(0.946109\pi\)
\(318\) 0 0
\(319\) 7.00000 0.391925
\(320\) 16.0000 8.00000i 0.894427 0.447214i
\(321\) 0 0
\(322\) 0 0
\(323\) 2.00000i 0.111283i
\(324\) 2.00000 0.111111
\(325\) 4.00000 + 3.00000i 0.221880 + 0.166410i
\(326\) 0 0
\(327\) 5.00000i 0.276501i
\(328\) 0 0
\(329\) −7.00000 −0.385922
\(330\) 0 0
\(331\) −4.00000 −0.219860 −0.109930 0.993939i \(-0.535063\pi\)
−0.109930 + 0.993939i \(0.535063\pi\)
\(332\) 16.0000i 0.878114i
\(333\) 16.0000i 0.876795i
\(334\) 0 0
\(335\) 14.0000 + 28.0000i 0.764902 + 1.52980i
\(336\) −4.00000 −0.218218
\(337\) 10.0000i 0.544735i 0.962193 + 0.272367i \(0.0878066\pi\)
−0.962193 + 0.272367i \(0.912193\pi\)
\(338\) 0 0
\(339\) 18.0000 0.977626
\(340\) −2.00000 4.00000i −0.108465 0.216930i
\(341\) −4.00000 −0.216612
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 0 0
\(345\) −2.00000 + 1.00000i −0.107676 + 0.0538382i
\(346\) 0 0
\(347\) 8.00000i 0.429463i −0.976673 0.214731i \(-0.931112\pi\)
0.976673 0.214731i \(-0.0688876\pi\)
\(348\) 14.0000i 0.750479i
\(349\) 10.0000 0.535288 0.267644 0.963518i \(-0.413755\pi\)
0.267644 + 0.963518i \(0.413755\pi\)
\(350\) 0 0
\(351\) −5.00000 −0.266880
\(352\) 0 0
\(353\) 9.00000i 0.479022i −0.970894 0.239511i \(-0.923013\pi\)
0.970894 0.239511i \(-0.0769871\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −12.0000 −0.635999
\(357\) 1.00000i 0.0529256i
\(358\) 0 0
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 0 0
\(361\) −15.0000 −0.789474
\(362\) 0 0
\(363\) 10.0000i 0.524864i
\(364\) −2.00000 −0.104828
\(365\) 2.00000 + 4.00000i 0.104685 + 0.209370i
\(366\) 0 0
\(367\) 23.0000i 1.20059i −0.799779 0.600295i \(-0.795050\pi\)
0.799779 0.600295i \(-0.204950\pi\)
\(368\) 4.00000i 0.208514i
\(369\) −12.0000 −0.624695
\(370\) 0 0
\(371\) −4.00000 −0.207670
\(372\) 8.00000i 0.414781i
\(373\) 14.0000i 0.724893i 0.932005 + 0.362446i \(0.118058\pi\)
−0.932005 + 0.362446i \(0.881942\pi\)
\(374\) 0 0
\(375\) 11.0000 + 2.00000i 0.568038 + 0.103280i
\(376\) 0 0
\(377\) 7.00000i 0.360518i
\(378\) 0 0
\(379\) 28.0000 1.43826 0.719132 0.694874i \(-0.244540\pi\)
0.719132 + 0.694874i \(0.244540\pi\)
\(380\) −8.00000 + 4.00000i −0.410391 + 0.205196i
\(381\) 2.00000 0.102463
\(382\) 0 0
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 0 0
\(385\) −1.00000 2.00000i −0.0509647 0.101929i
\(386\) 0 0
\(387\) 16.0000i 0.813326i
\(388\) 14.0000i 0.710742i
\(389\) 29.0000 1.47036 0.735179 0.677873i \(-0.237098\pi\)
0.735179 + 0.677873i \(0.237098\pi\)
\(390\) 0 0
\(391\) 1.00000 0.0505722
\(392\) 0 0
\(393\) 20.0000i 1.00887i
\(394\) 0 0
\(395\) 30.0000 15.0000i 1.50946 0.754732i
\(396\) −4.00000 −0.201008
\(397\) 33.0000i 1.65622i 0.560564 + 0.828111i \(0.310584\pi\)
−0.560564 + 0.828111i \(0.689416\pi\)
\(398\) 0 0
\(399\) 2.00000 0.100125
\(400\) 12.0000 16.0000i 0.600000 0.800000i
\(401\) −5.00000 −0.249688 −0.124844 0.992176i \(-0.539843\pi\)
−0.124844 + 0.992176i \(0.539843\pi\)
\(402\) 0 0
\(403\) 4.00000i 0.199254i
\(404\) −8.00000 −0.398015
\(405\) 2.00000 1.00000i 0.0993808 0.0496904i
\(406\) 0 0
\(407\) 8.00000i 0.396545i
\(408\) 0 0
\(409\) −4.00000 −0.197787 −0.0988936 0.995098i \(-0.531530\pi\)
−0.0988936 + 0.995098i \(0.531530\pi\)
\(410\) 0 0
\(411\) 10.0000 0.493264
\(412\) 14.0000i 0.689730i
\(413\) 4.00000i 0.196827i
\(414\) 0 0
\(415\) −8.00000 16.0000i −0.392705 0.785409i
\(416\) 0 0
\(417\) 4.00000i 0.195881i
\(418\) 0 0
\(419\) −12.0000 −0.586238 −0.293119 0.956076i \(-0.594693\pi\)
−0.293119 + 0.956076i \(0.594693\pi\)
\(420\) −4.00000 + 2.00000i −0.195180 + 0.0975900i
\(421\) −5.00000 −0.243685 −0.121843 0.992549i \(-0.538880\pi\)
−0.121843 + 0.992549i \(0.538880\pi\)
\(422\) 0 0
\(423\) 14.0000i 0.680703i
\(424\) 0 0
\(425\) −4.00000 3.00000i −0.194029 0.145521i
\(426\) 0 0
\(427\) 10.0000i 0.483934i
\(428\) 0 0
\(429\) 1.00000 0.0482805
\(430\) 0 0
\(431\) 11.0000 0.529851 0.264926 0.964269i \(-0.414653\pi\)
0.264926 + 0.964269i \(0.414653\pi\)
\(432\) 20.0000i 0.962250i
\(433\) 30.0000i 1.44171i 0.693087 + 0.720854i \(0.256250\pi\)
−0.693087 + 0.720854i \(0.743750\pi\)
\(434\) 0 0
\(435\) −7.00000 14.0000i −0.335624 0.671249i
\(436\) 10.0000 0.478913
\(437\) 2.00000i 0.0956730i
\(438\) 0 0
\(439\) 34.0000 1.62273 0.811366 0.584539i \(-0.198725\pi\)
0.811366 + 0.584539i \(0.198725\pi\)
\(440\) 0 0
\(441\) −2.00000 −0.0952381
\(442\) 0 0
\(443\) 40.0000i 1.90046i 0.311553 + 0.950229i \(0.399151\pi\)
−0.311553 + 0.950229i \(0.600849\pi\)
\(444\) 16.0000 0.759326
\(445\) −12.0000 + 6.00000i −0.568855 + 0.284427i
\(446\) 0 0
\(447\) 14.0000i 0.662177i
\(448\) 8.00000i 0.377964i
\(449\) −15.0000 −0.707894 −0.353947 0.935266i \(-0.615161\pi\)
−0.353947 + 0.935266i \(0.615161\pi\)
\(450\) 0 0
\(451\) 6.00000 0.282529
\(452\) 36.0000i 1.69330i
\(453\) 1.00000i 0.0469841i
\(454\) 0 0
\(455\) −2.00000 + 1.00000i −0.0937614 + 0.0468807i
\(456\) 0 0
\(457\) 2.00000i 0.0935561i −0.998905 0.0467780i \(-0.985105\pi\)
0.998905 0.0467780i \(-0.0148953\pi\)
\(458\) 0 0
\(459\) 5.00000 0.233380
\(460\) 2.00000 + 4.00000i 0.0932505 + 0.186501i
\(461\) 28.0000 1.30409 0.652045 0.758180i \(-0.273911\pi\)
0.652045 + 0.758180i \(0.273911\pi\)
\(462\) 0 0
\(463\) 30.0000i 1.39422i −0.716965 0.697109i \(-0.754469\pi\)
0.716965 0.697109i \(-0.245531\pi\)
\(464\) −28.0000 −1.29987
\(465\) 4.00000 + 8.00000i 0.185496 + 0.370991i
\(466\) 0 0
\(467\) 27.0000i 1.24941i 0.780860 + 0.624705i \(0.214781\pi\)
−0.780860 + 0.624705i \(0.785219\pi\)
\(468\) 4.00000i 0.184900i
\(469\) −14.0000 −0.646460
\(470\) 0 0
\(471\) 18.0000 0.829396
\(472\) 0 0
\(473\) 8.00000i 0.367840i
\(474\) 0 0
\(475\) −6.00000 + 8.00000i −0.275299 + 0.367065i
\(476\) 2.00000 0.0916698
\(477\) 8.00000i 0.366295i
\(478\) 0 0
\(479\) 10.0000 0.456912 0.228456 0.973554i \(-0.426632\pi\)
0.228456 + 0.973554i \(0.426632\pi\)
\(480\) 0 0
\(481\) 8.00000 0.364769
\(482\) 0 0
\(483\) 1.00000i 0.0455016i
\(484\) −20.0000 −0.909091
\(485\) 7.00000 + 14.0000i 0.317854 + 0.635707i
\(486\) 0 0
\(487\) 14.0000i 0.634401i 0.948359 + 0.317200i \(0.102743\pi\)
−0.948359 + 0.317200i \(0.897257\pi\)
\(488\) 0 0
\(489\) 4.00000 0.180886
\(490\) 0 0
\(491\) 15.0000 0.676941 0.338470 0.940977i \(-0.390091\pi\)
0.338470 + 0.940977i \(0.390091\pi\)
\(492\) 12.0000i 0.541002i
\(493\) 7.00000i 0.315264i
\(494\) 0 0
\(495\) −4.00000 + 2.00000i −0.179787 + 0.0898933i
\(496\) 16.0000 0.718421
\(497\) 0 0
\(498\) 0 0
\(499\) −25.0000 −1.11915 −0.559577 0.828778i \(-0.689036\pi\)
−0.559577 + 0.828778i \(0.689036\pi\)
\(500\) 4.00000 22.0000i 0.178885 0.983870i
\(501\) −3.00000 −0.134030
\(502\) 0 0
\(503\) 5.00000i 0.222939i 0.993768 + 0.111469i \(0.0355557\pi\)
−0.993768 + 0.111469i \(0.964444\pi\)
\(504\) 0 0
\(505\) −8.00000 + 4.00000i −0.355995 + 0.177998i
\(506\) 0 0
\(507\) 12.0000i 0.532939i
\(508\) 4.00000i 0.177471i
\(509\) 8.00000 0.354594 0.177297 0.984157i \(-0.443265\pi\)
0.177297 + 0.984157i \(0.443265\pi\)
\(510\) 0 0
\(511\) −2.00000 −0.0884748
\(512\) 0 0
\(513\) 10.0000i 0.441511i
\(514\) 0 0
\(515\) 7.00000 + 14.0000i 0.308457 + 0.616914i
\(516\) 16.0000 0.704361
\(517\) 7.00000i 0.307860i
\(518\) 0 0
\(519\) −7.00000 −0.307266
\(520\) 0 0
\(521\) 12.0000 0.525730 0.262865 0.964833i \(-0.415333\pi\)
0.262865 + 0.964833i \(0.415333\pi\)
\(522\) 0 0
\(523\) 24.0000i 1.04945i −0.851273 0.524723i \(-0.824169\pi\)
0.851273 0.524723i \(-0.175831\pi\)
\(524\) −40.0000 −1.74741
\(525\) −3.00000 + 4.00000i −0.130931 + 0.174574i
\(526\) 0 0
\(527\) 4.00000i 0.174243i
\(528\) 4.00000i 0.174078i
\(529\) −1.00000 −0.0434783
\(530\) 0 0
\(531\) 8.00000 0.347170
\(532\) 4.00000i 0.173422i
\(533\) 6.00000i 0.259889i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 4.00000i 0.172613i
\(538\) 0 0
\(539\) 1.00000 0.0430730
\(540\) 10.0000 + 20.0000i 0.430331 + 0.860663i
\(541\) 43.0000 1.84871 0.924357 0.381528i \(-0.124602\pi\)
0.924357 + 0.381528i \(0.124602\pi\)
\(542\) 0 0
\(543\) 16.0000i 0.686626i
\(544\) 0 0
\(545\) 10.0000 5.00000i 0.428353 0.214176i
\(546\) 0 0
\(547\) 38.0000i 1.62476i 0.583127 + 0.812381i \(0.301829\pi\)
−0.583127 + 0.812381i \(0.698171\pi\)
\(548\) 20.0000i 0.854358i
\(549\) −20.0000 −0.853579
\(550\) 0 0
\(551\) 14.0000 0.596420
\(552\) 0 0
\(553\) 15.0000i 0.637865i
\(554\) 0 0
\(555\) 16.0000 8.00000i 0.679162 0.339581i
\(556\) −8.00000 −0.339276
\(557\) 42.0000i 1.77960i 0.456354 + 0.889799i \(0.349155\pi\)
−0.456354 + 0.889799i \(0.650845\pi\)
\(558\) 0 0
\(559\) 8.00000 0.338364
\(560\) 4.00000 + 8.00000i 0.169031 + 0.338062i
\(561\) −1.00000 −0.0422200
\(562\) 0 0
\(563\) 4.00000i 0.168580i −0.996441 0.0842900i \(-0.973138\pi\)
0.996441 0.0842900i \(-0.0268622\pi\)
\(564\) −14.0000 −0.589506
\(565\) −18.0000 36.0000i −0.757266 1.51453i
\(566\) 0 0
\(567\) 1.00000i 0.0419961i
\(568\) 0 0
\(569\) 10.0000 0.419222 0.209611 0.977785i \(-0.432780\pi\)
0.209611 + 0.977785i \(0.432780\pi\)
\(570\) 0 0
\(571\) −36.0000 −1.50655 −0.753277 0.657704i \(-0.771528\pi\)
−0.753277 + 0.657704i \(0.771528\pi\)
\(572\) 2.00000i 0.0836242i
\(573\) 25.0000i 1.04439i
\(574\) 0 0
\(575\) 4.00000 + 3.00000i 0.166812 + 0.125109i
\(576\) 16.0000 0.666667
\(577\) 3.00000i 0.124892i 0.998048 + 0.0624458i \(0.0198901\pi\)
−0.998048 + 0.0624458i \(0.980110\pi\)
\(578\) 0 0
\(579\) 14.0000 0.581820
\(580\) −28.0000 + 14.0000i −1.16264 + 0.581318i
\(581\) 8.00000 0.331896
\(582\) 0 0
\(583\) 4.00000i 0.165663i
\(584\) 0 0
\(585\) 2.00000 + 4.00000i 0.0826898 + 0.165380i
\(586\) 0 0
\(587\) 28.0000i 1.15568i 0.816149 + 0.577842i \(0.196105\pi\)
−0.816149 + 0.577842i \(0.803895\pi\)
\(588\) 2.00000i 0.0824786i
\(589\) −8.00000 −0.329634
\(590\) 0 0
\(591\) 18.0000 0.740421
\(592\) 32.0000i 1.31519i
\(593\) 37.0000i 1.51941i 0.650269 + 0.759704i \(0.274656\pi\)
−0.650269 + 0.759704i \(0.725344\pi\)
\(594\) 0 0
\(595\) 2.00000 1.00000i 0.0819920 0.0409960i
\(596\) −28.0000 −1.14692
\(597\) 12.0000i 0.491127i
\(598\) 0 0
\(599\) −25.0000 −1.02147 −0.510736 0.859738i \(-0.670627\pi\)
−0.510736 + 0.859738i \(0.670627\pi\)
\(600\) 0 0
\(601\) 10.0000 0.407909 0.203954 0.978980i \(-0.434621\pi\)
0.203954 + 0.978980i \(0.434621\pi\)
\(602\) 0 0
\(603\) 28.0000i 1.14025i
\(604\) −2.00000 −0.0813788
\(605\) −20.0000 + 10.0000i −0.813116 + 0.406558i
\(606\) 0 0
\(607\) 25.0000i 1.01472i 0.861735 + 0.507359i \(0.169378\pi\)
−0.861735 + 0.507359i \(0.830622\pi\)
\(608\) 0 0
\(609\) 7.00000 0.283654
\(610\) 0 0
\(611\) −7.00000 −0.283190
\(612\) 4.00000i 0.161690i
\(613\) 46.0000i 1.85792i 0.370177 + 0.928961i \(0.379297\pi\)
−0.370177 + 0.928961i \(0.620703\pi\)
\(614\) 0 0
\(615\) −6.00000 12.0000i −0.241943 0.483887i
\(616\) 0 0
\(617\) 28.0000i 1.12724i −0.826035 0.563619i \(-0.809409\pi\)
0.826035 0.563619i \(-0.190591\pi\)
\(618\) 0 0
\(619\) −22.0000 −0.884255 −0.442127 0.896952i \(-0.645776\pi\)
−0.442127 + 0.896952i \(0.645776\pi\)
\(620\) 16.0000 8.00000i 0.642575 0.321288i
\(621\) −5.00000 −0.200643
\(622\) 0 0
\(623\) 6.00000i 0.240385i
\(624\) −4.00000 −0.160128
\(625\) −7.00000 24.0000i −0.280000 0.960000i
\(626\) 0 0
\(627\) 2.00000i 0.0798723i
\(628\) 36.0000i 1.43656i
\(629\) −8.00000 −0.318981
\(630\) 0 0
\(631\) 7.00000 0.278666 0.139333 0.990246i \(-0.455504\pi\)
0.139333 + 0.990246i \(0.455504\pi\)
\(632\) 0 0
\(633\) 5.00000i 0.198732i
\(634\) 0 0
\(635\) −2.00000 4.00000i −0.0793676 0.158735i
\(636\) −8.00000 −0.317221
\(637\) 1.00000i 0.0396214i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −18.0000 −0.710957 −0.355479 0.934684i \(-0.615682\pi\)
−0.355479 + 0.934684i \(0.615682\pi\)
\(642\) 0 0
\(643\) 49.0000i 1.93237i −0.257847 0.966186i \(-0.583013\pi\)
0.257847 0.966186i \(-0.416987\pi\)
\(644\) −2.00000 −0.0788110
\(645\) 16.0000 8.00000i 0.629999 0.315000i
\(646\) 0 0
\(647\) 48.0000i 1.88707i −0.331266 0.943537i \(-0.607476\pi\)
0.331266 0.943537i \(-0.392524\pi\)
\(648\) 0 0
\(649\) −4.00000 −0.157014
\(650\) 0 0
\(651\) −4.00000 −0.156772
\(652\) 8.00000i 0.313304i
\(653\) 6.00000i 0.234798i 0.993085 + 0.117399i \(0.0374557\pi\)
−0.993085 + 0.117399i \(0.962544\pi\)
\(654\) 0 0
\(655\) −40.0000 + 20.0000i −1.56293 + 0.781465i
\(656\) −24.0000 −0.937043
\(657\) 4.00000i 0.156055i
\(658\) 0 0
\(659\) 41.0000 1.59713 0.798567 0.601906i \(-0.205592\pi\)
0.798567 + 0.601906i \(0.205592\pi\)
\(660\) −2.00000 4.00000i −0.0778499 0.155700i
\(661\) 20.0000 0.777910 0.388955 0.921257i \(-0.372836\pi\)
0.388955 + 0.921257i \(0.372836\pi\)
\(662\) 0 0
\(663\) 1.00000i 0.0388368i
\(664\) 0 0
\(665\) −2.00000 4.00000i −0.0775567 0.155113i
\(666\) 0 0
\(667\) 7.00000i 0.271041i
\(668\) 6.00000i 0.232147i
\(669\) −25.0000 −0.966556
\(670\) 0 0
\(671\) 10.0000 0.386046
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) 20.0000 + 15.0000i 0.769800 + 0.577350i
\(676\) 24.0000 0.923077
\(677\) 21.0000i 0.807096i 0.914959 + 0.403548i \(0.132223\pi\)
−0.914959 + 0.403548i \(0.867777\pi\)
\(678\) 0 0
\(679\) −7.00000 −0.268635
\(680\) 0 0
\(681\) 15.0000 0.574801
\(682\) 0 0
\(683\) 12.0000i 0.459167i 0.973289 + 0.229584i \(0.0737364\pi\)
−0.973289 + 0.229584i \(0.926264\pi\)
\(684\) −8.00000 −0.305888
\(685\) −10.0000 20.0000i −0.382080 0.764161i
\(686\) 0 0
\(687\) 14.0000i 0.534133i
\(688\) 32.0000i 1.21999i
\(689\) −4.00000 −0.152388
\(690\) 0 0
\(691\) 18.0000 0.684752 0.342376 0.939563i \(-0.388768\pi\)
0.342376 + 0.939563i \(0.388768\pi\)
\(692\) 14.0000i 0.532200i
\(693\) 2.00000i 0.0759737i
\(694\) 0 0
\(695\) −8.00000 + 4.00000i −0.303457 + 0.151729i
\(696\) 0 0
\(697\) 6.00000i 0.227266i
\(698\) 0 0
\(699\) −10.0000 −0.378235
\(700\) 8.00000 + 6.00000i 0.302372 + 0.226779i
\(701\) −15.0000 −0.566542 −0.283271 0.959040i \(-0.591420\pi\)
−0.283271 + 0.959040i \(0.591420\pi\)
\(702\) 0 0
\(703\) 16.0000i 0.603451i
\(704\) −8.00000 −0.301511
\(705\) −14.0000 + 7.00000i −0.527271 + 0.263635i
\(706\) 0 0
\(707\) 4.00000i 0.150435i
\(708\) 8.00000i 0.300658i
\(709\) 19.0000 0.713560 0.356780 0.934188i \(-0.383875\pi\)
0.356780 + 0.934188i \(0.383875\pi\)
\(710\) 0 0
\(711\) 30.0000 1.12509
\(712\) 0 0
\(713\) 4.00000i 0.149801i
\(714\) 0 0
\(715\) −1.00000 2.00000i −0.0373979 0.0747958i
\(716\) 8.00000 0.298974
\(717\) 9.00000i 0.336111i
\(718\) 0 0
\(719\) −30.0000 −1.11881 −0.559406 0.828894i \(-0.688971\pi\)
−0.559406 + 0.828894i \(0.688971\pi\)
\(720\) 16.0000 8.00000i 0.596285 0.298142i
\(721\) −7.00000 −0.260694
\(722\) 0 0
\(723\) 10.0000i 0.371904i
\(724\) −32.0000 −1.18927
\(725\) −21.0000 + 28.0000i −0.779920 + 1.03989i
\(726\) 0 0
\(727\) 8.00000i 0.296704i 0.988935 + 0.148352i \(0.0473968\pi\)
−0.988935 + 0.148352i \(0.952603\pi\)
\(728\) 0 0
\(729\) −13.0000 −0.481481
\(730\) 0 0
\(731\) −8.00000 −0.295891
\(732\) 20.0000i 0.739221i
\(733\) 3.00000i 0.110808i 0.998464 + 0.0554038i \(0.0176446\pi\)
−0.998464 + 0.0554038i \(0.982355\pi\)
\(734\) 0 0
\(735\) −1.00000 2.00000i −0.0368856 0.0737711i
\(736\) 0 0
\(737\) 14.0000i 0.515697i
\(738\) 0 0
\(739\) 43.0000 1.58178 0.790890 0.611958i \(-0.209618\pi\)
0.790890 + 0.611958i \(0.209618\pi\)
\(740\) −16.0000 32.0000i −0.588172 1.17634i
\(741\) 2.00000 0.0734718
\(742\) 0 0
\(743\) 24.0000i 0.880475i −0.897881 0.440237i \(-0.854894\pi\)
0.897881 0.440237i \(-0.145106\pi\)
\(744\) 0 0
\(745\) −28.0000 + 14.0000i −1.02584 + 0.512920i
\(746\) 0 0
\(747\) 16.0000i 0.585409i
\(748\) 2.00000i 0.0731272i
\(749\) 0 0
\(750\) 0 0
\(751\) −7.00000 −0.255434 −0.127717 0.991811i \(-0.540765\pi\)
−0.127717 + 0.991811i \(0.540765\pi\)
\(752\) 28.0000i 1.02105i
\(753\) 12.0000i 0.437304i
\(754\) 0 0
\(755\) −2.00000 + 1.00000i −0.0727875 + 0.0363937i
\(756\) −10.0000 −0.363696
\(757\) 8.00000i 0.290765i 0.989376 + 0.145382i \(0.0464413\pi\)
−0.989376 + 0.145382i \(0.953559\pi\)
\(758\) 0 0
\(759\) 1.00000 0.0362977
\(760\) 0 0
\(761\) −28.0000 −1.01500 −0.507500 0.861652i \(-0.669430\pi\)
−0.507500 + 0.861652i \(0.669430\pi\)
\(762\) 0 0
\(763\) 5.00000i 0.181012i
\(764\) −50.0000 −1.80894
\(765\) −2.00000 4.00000i −0.0723102 0.144620i
\(766\) 0 0
\(767\) 4.00000i 0.144432i
\(768\) 16.0000i 0.577350i
\(769\) 2.00000 0.0721218 0.0360609 0.999350i \(-0.488519\pi\)
0.0360609 + 0.999350i \(0.488519\pi\)
\(770\) 0 0
\(771\) −18.0000 −0.648254
\(772\) 28.0000i 1.00774i
\(773\) 49.0000i 1.76241i −0.472737 0.881204i \(-0.656734\pi\)
0.472737 0.881204i \(-0.343266\pi\)
\(774\) 0 0
\(775\) 12.0000 16.0000i 0.431053 0.574737i
\(776\) 0 0
\(777\) 8.00000i 0.286998i
\(778\) 0 0
\(779\) 12.0000 0.429945
\(780\) −4.00000 + 2.00000i −0.143223 + 0.0716115i
\(781\) 0 0
\(782\) 0 0
\(783\) 35.0000i 1.25080i
\(784\) −4.00000 −0.142857
\(785\) −18.0000 36.0000i −0.642448 1.28490i
\(786\) 0 0
\(787\) 35.0000i 1.24762i −0.781578 0.623808i \(-0.785585\pi\)
0.781578 0.623808i \(-0.214415\pi\)
\(788\) 36.0000i 1.28245i
\(789\) −2.00000 −0.0712019
\(790\) 0 0
\(791\) 18.0000 0.640006
\(792\) 0 0
\(793\) 10.0000i 0.355110i
\(794\) 0 0
\(795\) −8.00000 + 4.00000i −0.283731 +