Properties

Label 2352.2.q.bd.961.2
Level $2352$
Weight $2$
Character 2352.961
Analytic conductor $18.781$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2352.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.7808145554\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 147)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 961.2
Root \(0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 2352.961
Dual form 2352.2.q.bd.1537.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{3} +(-0.292893 + 0.507306i) q^{5} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{3} +(-0.292893 + 0.507306i) q^{5} +(-0.500000 + 0.866025i) q^{9} +(-1.00000 - 1.73205i) q^{11} +5.41421 q^{13} -0.585786 q^{15} +(-3.12132 - 5.40629i) q^{17} +(1.41421 - 2.44949i) q^{19} +(1.82843 - 3.16693i) q^{23} +(2.32843 + 4.03295i) q^{25} -1.00000 q^{27} -1.17157 q^{29} +(-3.41421 - 5.91359i) q^{31} +(1.00000 - 1.73205i) q^{33} +(2.00000 - 3.46410i) q^{37} +(2.70711 + 4.68885i) q^{39} -2.24264 q^{41} +5.65685 q^{43} +(-0.292893 - 0.507306i) q^{45} +(1.41421 - 2.44949i) q^{47} +(3.12132 - 5.40629i) q^{51} +(1.00000 + 1.73205i) q^{53} +1.17157 q^{55} +2.82843 q^{57} +(-3.41421 - 5.91359i) q^{59} +(-1.87868 + 3.25397i) q^{61} +(-1.58579 + 2.74666i) q^{65} +(2.82843 + 4.89898i) q^{67} +3.65685 q^{69} +13.3137 q^{71} +(2.94975 + 5.10911i) q^{73} +(-2.32843 + 4.03295i) q^{75} +(1.17157 - 2.02922i) q^{79} +(-0.500000 - 0.866025i) q^{81} +15.3137 q^{83} +3.65685 q^{85} +(-0.585786 - 1.01461i) q^{87} +(2.87868 - 4.98602i) q^{89} +(3.41421 - 5.91359i) q^{93} +(0.828427 + 1.43488i) q^{95} +5.41421 q^{97} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{3} - 4q^{5} - 2q^{9} + O(q^{10}) \) \( 4q + 2q^{3} - 4q^{5} - 2q^{9} - 4q^{11} + 16q^{13} - 8q^{15} - 4q^{17} - 4q^{23} - 2q^{25} - 4q^{27} - 16q^{29} - 8q^{31} + 4q^{33} + 8q^{37} + 8q^{39} + 8q^{41} - 4q^{45} + 4q^{51} + 4q^{53} + 16q^{55} - 8q^{59} - 16q^{61} - 12q^{65} - 8q^{69} + 8q^{71} - 8q^{73} + 2q^{75} + 16q^{79} - 2q^{81} + 16q^{83} - 8q^{85} - 8q^{87} + 20q^{89} + 8q^{93} - 8q^{95} + 16q^{97} + 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1471\) \(1765\) \(2257\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) 0 0
\(5\) −0.292893 + 0.507306i −0.130986 + 0.226874i −0.924057 0.382255i \(-0.875148\pi\)
0.793071 + 0.609129i \(0.208481\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) −1.00000 1.73205i −0.301511 0.522233i 0.674967 0.737848i \(-0.264158\pi\)
−0.976478 + 0.215615i \(0.930824\pi\)
\(12\) 0 0
\(13\) 5.41421 1.50163 0.750816 0.660511i \(-0.229660\pi\)
0.750816 + 0.660511i \(0.229660\pi\)
\(14\) 0 0
\(15\) −0.585786 −0.151249
\(16\) 0 0
\(17\) −3.12132 5.40629i −0.757031 1.31122i −0.944358 0.328919i \(-0.893316\pi\)
0.187327 0.982298i \(-0.440018\pi\)
\(18\) 0 0
\(19\) 1.41421 2.44949i 0.324443 0.561951i −0.656957 0.753928i \(-0.728157\pi\)
0.981399 + 0.191977i \(0.0614899\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.82843 3.16693i 0.381253 0.660350i −0.609988 0.792410i \(-0.708826\pi\)
0.991242 + 0.132060i \(0.0421592\pi\)
\(24\) 0 0
\(25\) 2.32843 + 4.03295i 0.465685 + 0.806591i
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −1.17157 −0.217556 −0.108778 0.994066i \(-0.534694\pi\)
−0.108778 + 0.994066i \(0.534694\pi\)
\(30\) 0 0
\(31\) −3.41421 5.91359i −0.613211 1.06211i −0.990696 0.136097i \(-0.956544\pi\)
0.377485 0.926016i \(-0.376789\pi\)
\(32\) 0 0
\(33\) 1.00000 1.73205i 0.174078 0.301511i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 2.00000 3.46410i 0.328798 0.569495i −0.653476 0.756948i \(-0.726690\pi\)
0.982274 + 0.187453i \(0.0600231\pi\)
\(38\) 0 0
\(39\) 2.70711 + 4.68885i 0.433484 + 0.750816i
\(40\) 0 0
\(41\) −2.24264 −0.350242 −0.175121 0.984547i \(-0.556032\pi\)
−0.175121 + 0.984547i \(0.556032\pi\)
\(42\) 0 0
\(43\) 5.65685 0.862662 0.431331 0.902194i \(-0.358044\pi\)
0.431331 + 0.902194i \(0.358044\pi\)
\(44\) 0 0
\(45\) −0.292893 0.507306i −0.0436619 0.0756247i
\(46\) 0 0
\(47\) 1.41421 2.44949i 0.206284 0.357295i −0.744257 0.667893i \(-0.767196\pi\)
0.950541 + 0.310599i \(0.100530\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 3.12132 5.40629i 0.437072 0.757031i
\(52\) 0 0
\(53\) 1.00000 + 1.73205i 0.137361 + 0.237915i 0.926497 0.376303i \(-0.122805\pi\)
−0.789136 + 0.614218i \(0.789471\pi\)
\(54\) 0 0
\(55\) 1.17157 0.157975
\(56\) 0 0
\(57\) 2.82843 0.374634
\(58\) 0 0
\(59\) −3.41421 5.91359i −0.444493 0.769884i 0.553524 0.832833i \(-0.313283\pi\)
−0.998017 + 0.0629492i \(0.979949\pi\)
\(60\) 0 0
\(61\) −1.87868 + 3.25397i −0.240540 + 0.416628i −0.960868 0.277006i \(-0.910658\pi\)
0.720328 + 0.693634i \(0.243991\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1.58579 + 2.74666i −0.196693 + 0.340682i
\(66\) 0 0
\(67\) 2.82843 + 4.89898i 0.345547 + 0.598506i 0.985453 0.169948i \(-0.0543599\pi\)
−0.639906 + 0.768453i \(0.721027\pi\)
\(68\) 0 0
\(69\) 3.65685 0.440234
\(70\) 0 0
\(71\) 13.3137 1.58005 0.790023 0.613077i \(-0.210068\pi\)
0.790023 + 0.613077i \(0.210068\pi\)
\(72\) 0 0
\(73\) 2.94975 + 5.10911i 0.345242 + 0.597976i 0.985398 0.170269i \(-0.0544636\pi\)
−0.640156 + 0.768245i \(0.721130\pi\)
\(74\) 0 0
\(75\) −2.32843 + 4.03295i −0.268864 + 0.465685i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 1.17157 2.02922i 0.131812 0.228306i −0.792563 0.609790i \(-0.791254\pi\)
0.924375 + 0.381485i \(0.124587\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 15.3137 1.68090 0.840449 0.541891i \(-0.182291\pi\)
0.840449 + 0.541891i \(0.182291\pi\)
\(84\) 0 0
\(85\) 3.65685 0.396642
\(86\) 0 0
\(87\) −0.585786 1.01461i −0.0628029 0.108778i
\(88\) 0 0
\(89\) 2.87868 4.98602i 0.305139 0.528517i −0.672153 0.740412i \(-0.734630\pi\)
0.977292 + 0.211895i \(0.0679636\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 3.41421 5.91359i 0.354037 0.613211i
\(94\) 0 0
\(95\) 0.828427 + 1.43488i 0.0849948 + 0.147215i
\(96\) 0 0
\(97\) 5.41421 0.549730 0.274865 0.961483i \(-0.411367\pi\)
0.274865 + 0.961483i \(0.411367\pi\)
\(98\) 0 0
\(99\) 2.00000 0.201008
\(100\) 0 0
\(101\) −8.53553 14.7840i −0.849317 1.47106i −0.881818 0.471589i \(-0.843681\pi\)
0.0325010 0.999472i \(-0.489653\pi\)
\(102\) 0 0
\(103\) −6.24264 + 10.8126i −0.615106 + 1.06539i 0.375260 + 0.926919i \(0.377553\pi\)
−0.990366 + 0.138475i \(0.955780\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −5.82843 + 10.0951i −0.563455 + 0.975933i 0.433736 + 0.901040i \(0.357195\pi\)
−0.997192 + 0.0748933i \(0.976138\pi\)
\(108\) 0 0
\(109\) −2.82843 4.89898i −0.270914 0.469237i 0.698182 0.715920i \(-0.253993\pi\)
−0.969096 + 0.246683i \(0.920659\pi\)
\(110\) 0 0
\(111\) 4.00000 0.379663
\(112\) 0 0
\(113\) 17.3137 1.62874 0.814368 0.580348i \(-0.197084\pi\)
0.814368 + 0.580348i \(0.197084\pi\)
\(114\) 0 0
\(115\) 1.07107 + 1.85514i 0.0998776 + 0.172993i
\(116\) 0 0
\(117\) −2.70711 + 4.68885i −0.250272 + 0.433484i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) 0 0
\(123\) −1.12132 1.94218i −0.101106 0.175121i
\(124\) 0 0
\(125\) −5.65685 −0.505964
\(126\) 0 0
\(127\) −9.65685 −0.856907 −0.428454 0.903564i \(-0.640941\pi\)
−0.428454 + 0.903564i \(0.640941\pi\)
\(128\) 0 0
\(129\) 2.82843 + 4.89898i 0.249029 + 0.431331i
\(130\) 0 0
\(131\) 3.65685 6.33386i 0.319501 0.553392i −0.660883 0.750489i \(-0.729818\pi\)
0.980384 + 0.197097i \(0.0631514\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0.292893 0.507306i 0.0252082 0.0436619i
\(136\) 0 0
\(137\) 7.07107 + 12.2474i 0.604122 + 1.04637i 0.992190 + 0.124739i \(0.0398094\pi\)
−0.388067 + 0.921631i \(0.626857\pi\)
\(138\) 0 0
\(139\) 6.34315 0.538019 0.269009 0.963138i \(-0.413304\pi\)
0.269009 + 0.963138i \(0.413304\pi\)
\(140\) 0 0
\(141\) 2.82843 0.238197
\(142\) 0 0
\(143\) −5.41421 9.37769i −0.452759 0.784202i
\(144\) 0 0
\(145\) 0.343146 0.594346i 0.0284967 0.0493577i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 2.65685 4.60181i 0.217658 0.376995i −0.736434 0.676510i \(-0.763492\pi\)
0.954092 + 0.299515i \(0.0968249\pi\)
\(150\) 0 0
\(151\) 6.00000 + 10.3923i 0.488273 + 0.845714i 0.999909 0.0134886i \(-0.00429367\pi\)
−0.511636 + 0.859202i \(0.670960\pi\)
\(152\) 0 0
\(153\) 6.24264 0.504688
\(154\) 0 0
\(155\) 4.00000 0.321288
\(156\) 0 0
\(157\) −10.1213 17.5306i −0.807769 1.39910i −0.914406 0.404799i \(-0.867341\pi\)
0.106636 0.994298i \(-0.465992\pi\)
\(158\) 0 0
\(159\) −1.00000 + 1.73205i −0.0793052 + 0.137361i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 5.65685 9.79796i 0.443079 0.767435i −0.554837 0.831959i \(-0.687219\pi\)
0.997916 + 0.0645236i \(0.0205528\pi\)
\(164\) 0 0
\(165\) 0.585786 + 1.01461i 0.0456034 + 0.0789874i
\(166\) 0 0
\(167\) −19.7990 −1.53209 −0.766046 0.642786i \(-0.777779\pi\)
−0.766046 + 0.642786i \(0.777779\pi\)
\(168\) 0 0
\(169\) 16.3137 1.25490
\(170\) 0 0
\(171\) 1.41421 + 2.44949i 0.108148 + 0.187317i
\(172\) 0 0
\(173\) −3.46447 + 6.00063i −0.263398 + 0.456220i −0.967143 0.254234i \(-0.918177\pi\)
0.703744 + 0.710453i \(0.251510\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 3.41421 5.91359i 0.256628 0.444493i
\(178\) 0 0
\(179\) −4.17157 7.22538i −0.311798 0.540050i 0.666954 0.745099i \(-0.267598\pi\)
−0.978752 + 0.205049i \(0.934265\pi\)
\(180\) 0 0
\(181\) −5.41421 −0.402435 −0.201218 0.979547i \(-0.564490\pi\)
−0.201218 + 0.979547i \(0.564490\pi\)
\(182\) 0 0
\(183\) −3.75736 −0.277752
\(184\) 0 0
\(185\) 1.17157 + 2.02922i 0.0861358 + 0.149191i
\(186\) 0 0
\(187\) −6.24264 + 10.8126i −0.456507 + 0.790693i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −9.00000 + 15.5885i −0.651217 + 1.12794i 0.331611 + 0.943416i \(0.392408\pi\)
−0.982828 + 0.184525i \(0.940925\pi\)
\(192\) 0 0
\(193\) 8.65685 + 14.9941i 0.623134 + 1.07930i 0.988899 + 0.148592i \(0.0474742\pi\)
−0.365765 + 0.930707i \(0.619192\pi\)
\(194\) 0 0
\(195\) −3.17157 −0.227121
\(196\) 0 0
\(197\) 2.00000 0.142494 0.0712470 0.997459i \(-0.477302\pi\)
0.0712470 + 0.997459i \(0.477302\pi\)
\(198\) 0 0
\(199\) 5.17157 + 8.95743i 0.366603 + 0.634975i 0.989032 0.147701i \(-0.0471874\pi\)
−0.622429 + 0.782676i \(0.713854\pi\)
\(200\) 0 0
\(201\) −2.82843 + 4.89898i −0.199502 + 0.345547i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0.656854 1.13770i 0.0458767 0.0794608i
\(206\) 0 0
\(207\) 1.82843 + 3.16693i 0.127084 + 0.220117i
\(208\) 0 0
\(209\) −5.65685 −0.391293
\(210\) 0 0
\(211\) 20.9706 1.44367 0.721837 0.692064i \(-0.243298\pi\)
0.721837 + 0.692064i \(0.243298\pi\)
\(212\) 0 0
\(213\) 6.65685 + 11.5300i 0.456120 + 0.790023i
\(214\) 0 0
\(215\) −1.65685 + 2.86976i −0.112997 + 0.195716i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −2.94975 + 5.10911i −0.199325 + 0.345242i
\(220\) 0 0
\(221\) −16.8995 29.2708i −1.13678 1.96897i
\(222\) 0 0
\(223\) 8.97056 0.600713 0.300357 0.953827i \(-0.402894\pi\)
0.300357 + 0.953827i \(0.402894\pi\)
\(224\) 0 0
\(225\) −4.65685 −0.310457
\(226\) 0 0
\(227\) −7.89949 13.6823i −0.524308 0.908128i −0.999599 0.0282996i \(-0.990991\pi\)
0.475292 0.879828i \(-0.342343\pi\)
\(228\) 0 0
\(229\) −4.12132 + 7.13834i −0.272345 + 0.471715i −0.969462 0.245243i \(-0.921132\pi\)
0.697117 + 0.716957i \(0.254466\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −11.0711 + 19.1757i −0.725290 + 1.25624i 0.233565 + 0.972341i \(0.424961\pi\)
−0.958855 + 0.283898i \(0.908372\pi\)
\(234\) 0 0
\(235\) 0.828427 + 1.43488i 0.0540406 + 0.0936011i
\(236\) 0 0
\(237\) 2.34315 0.152204
\(238\) 0 0
\(239\) 4.34315 0.280935 0.140467 0.990085i \(-0.455139\pi\)
0.140467 + 0.990085i \(0.455139\pi\)
\(240\) 0 0
\(241\) 3.87868 + 6.71807i 0.249848 + 0.432749i 0.963483 0.267768i \(-0.0862861\pi\)
−0.713636 + 0.700517i \(0.752953\pi\)
\(242\) 0 0
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 7.65685 13.2621i 0.487194 0.843845i
\(248\) 0 0
\(249\) 7.65685 + 13.2621i 0.485233 + 0.840449i
\(250\) 0 0
\(251\) −4.48528 −0.283108 −0.141554 0.989931i \(-0.545210\pi\)
−0.141554 + 0.989931i \(0.545210\pi\)
\(252\) 0 0
\(253\) −7.31371 −0.459809
\(254\) 0 0
\(255\) 1.82843 + 3.16693i 0.114501 + 0.198321i
\(256\) 0 0
\(257\) 9.60660 16.6391i 0.599243 1.03792i −0.393690 0.919243i \(-0.628802\pi\)
0.992933 0.118677i \(-0.0378651\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0.585786 1.01461i 0.0362593 0.0628029i
\(262\) 0 0
\(263\) −8.65685 14.9941i −0.533805 0.924577i −0.999220 0.0394843i \(-0.987428\pi\)
0.465416 0.885092i \(-0.345905\pi\)
\(264\) 0 0
\(265\) −1.17157 −0.0719691
\(266\) 0 0
\(267\) 5.75736 0.352345
\(268\) 0 0
\(269\) −5.36396 9.29065i −0.327046 0.566461i 0.654878 0.755735i \(-0.272720\pi\)
−0.981924 + 0.189274i \(0.939387\pi\)
\(270\) 0 0
\(271\) 9.07107 15.7116i 0.551028 0.954409i −0.447173 0.894448i \(-0.647569\pi\)
0.998201 0.0599610i \(-0.0190976\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 4.65685 8.06591i 0.280819 0.486393i
\(276\) 0 0
\(277\) −6.65685 11.5300i −0.399972 0.692771i 0.593750 0.804649i \(-0.297647\pi\)
−0.993722 + 0.111878i \(0.964313\pi\)
\(278\) 0 0
\(279\) 6.82843 0.408807
\(280\) 0 0
\(281\) −16.4853 −0.983429 −0.491715 0.870756i \(-0.663630\pi\)
−0.491715 + 0.870756i \(0.663630\pi\)
\(282\) 0 0
\(283\) 4.24264 + 7.34847i 0.252199 + 0.436821i 0.964131 0.265427i \(-0.0855130\pi\)
−0.711932 + 0.702248i \(0.752180\pi\)
\(284\) 0 0
\(285\) −0.828427 + 1.43488i −0.0490718 + 0.0849948i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −10.9853 + 19.0271i −0.646193 + 1.11924i
\(290\) 0 0
\(291\) 2.70711 + 4.68885i 0.158693 + 0.274865i
\(292\) 0 0
\(293\) 19.4142 1.13419 0.567095 0.823652i \(-0.308067\pi\)
0.567095 + 0.823652i \(0.308067\pi\)
\(294\) 0 0
\(295\) 4.00000 0.232889
\(296\) 0 0
\(297\) 1.00000 + 1.73205i 0.0580259 + 0.100504i
\(298\) 0 0
\(299\) 9.89949 17.1464i 0.572503 0.991604i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 8.53553 14.7840i 0.490354 0.849317i
\(304\) 0 0
\(305\) −1.10051 1.90613i −0.0630147 0.109145i
\(306\) 0 0
\(307\) −1.85786 −0.106034 −0.0530170 0.998594i \(-0.516884\pi\)
−0.0530170 + 0.998594i \(0.516884\pi\)
\(308\) 0 0
\(309\) −12.4853 −0.710263
\(310\) 0 0
\(311\) −11.0711 19.1757i −0.627783 1.08735i −0.987996 0.154481i \(-0.950629\pi\)
0.360213 0.932870i \(-0.382704\pi\)
\(312\) 0 0
\(313\) 8.94975 15.5014i 0.505870 0.876192i −0.494107 0.869401i \(-0.664505\pi\)
0.999977 0.00679098i \(-0.00216165\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −5.00000 + 8.66025i −0.280828 + 0.486408i −0.971589 0.236675i \(-0.923942\pi\)
0.690761 + 0.723083i \(0.257276\pi\)
\(318\) 0 0
\(319\) 1.17157 + 2.02922i 0.0655955 + 0.113615i
\(320\) 0 0
\(321\) −11.6569 −0.650622
\(322\) 0 0
\(323\) −17.6569 −0.982454
\(324\) 0 0
\(325\) 12.6066 + 21.8353i 0.699288 + 1.21120i
\(326\) 0 0
\(327\) 2.82843 4.89898i 0.156412 0.270914i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −2.00000 + 3.46410i −0.109930 + 0.190404i −0.915742 0.401768i \(-0.868396\pi\)
0.805812 + 0.592172i \(0.201729\pi\)
\(332\) 0 0
\(333\) 2.00000 + 3.46410i 0.109599 + 0.189832i
\(334\) 0 0
\(335\) −3.31371 −0.181047
\(336\) 0 0
\(337\) −18.3431 −0.999215 −0.499607 0.866252i \(-0.666522\pi\)
−0.499607 + 0.866252i \(0.666522\pi\)
\(338\) 0 0
\(339\) 8.65685 + 14.9941i 0.470176 + 0.814368i
\(340\) 0 0
\(341\) −6.82843 + 11.8272i −0.369780 + 0.640478i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −1.07107 + 1.85514i −0.0576644 + 0.0998776i
\(346\) 0 0
\(347\) 5.34315 + 9.25460i 0.286835 + 0.496813i 0.973053 0.230584i \(-0.0740635\pi\)
−0.686217 + 0.727396i \(0.740730\pi\)
\(348\) 0 0
\(349\) 9.89949 0.529908 0.264954 0.964261i \(-0.414643\pi\)
0.264954 + 0.964261i \(0.414643\pi\)
\(350\) 0 0
\(351\) −5.41421 −0.288989
\(352\) 0 0
\(353\) −5.36396 9.29065i −0.285495 0.494492i 0.687234 0.726436i \(-0.258825\pi\)
−0.972729 + 0.231944i \(0.925491\pi\)
\(354\) 0 0
\(355\) −3.89949 + 6.75412i −0.206964 + 0.358472i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −5.82843 + 10.0951i −0.307613 + 0.532801i −0.977840 0.209355i \(-0.932863\pi\)
0.670227 + 0.742156i \(0.266197\pi\)
\(360\) 0 0
\(361\) 5.50000 + 9.52628i 0.289474 + 0.501383i
\(362\) 0 0
\(363\) 7.00000 0.367405
\(364\) 0 0
\(365\) −3.45584 −0.180887
\(366\) 0 0
\(367\) 9.65685 + 16.7262i 0.504084 + 0.873099i 0.999989 + 0.00472187i \(0.00150302\pi\)
−0.495905 + 0.868377i \(0.665164\pi\)
\(368\) 0 0
\(369\) 1.12132 1.94218i 0.0583736 0.101106i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 16.6569 28.8505i 0.862459 1.49382i −0.00708885 0.999975i \(-0.502256\pi\)
0.869548 0.493848i \(-0.164410\pi\)
\(374\) 0 0
\(375\) −2.82843 4.89898i −0.146059 0.252982i
\(376\) 0 0
\(377\) −6.34315 −0.326689
\(378\) 0 0
\(379\) −31.3137 −1.60848 −0.804239 0.594307i \(-0.797427\pi\)
−0.804239 + 0.594307i \(0.797427\pi\)
\(380\) 0 0
\(381\) −4.82843 8.36308i −0.247368 0.428454i
\(382\) 0 0
\(383\) −14.8284 + 25.6836i −0.757697 + 1.31237i 0.186325 + 0.982488i \(0.440342\pi\)
−0.944022 + 0.329882i \(0.892991\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −2.82843 + 4.89898i −0.143777 + 0.249029i
\(388\) 0 0
\(389\) −5.07107 8.78335i −0.257113 0.445333i 0.708354 0.705857i \(-0.249438\pi\)
−0.965467 + 0.260524i \(0.916105\pi\)
\(390\) 0 0
\(391\) −22.8284 −1.15448
\(392\) 0 0
\(393\) 7.31371 0.368928
\(394\) 0 0
\(395\) 0.686292 + 1.18869i 0.0345311 + 0.0598096i
\(396\) 0 0
\(397\) −17.1924 + 29.7781i −0.862861 + 1.49452i 0.00629405 + 0.999980i \(0.497997\pi\)
−0.869155 + 0.494539i \(0.835337\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −11.0711 + 19.1757i −0.552863 + 0.957586i 0.445204 + 0.895429i \(0.353131\pi\)
−0.998066 + 0.0621570i \(0.980202\pi\)
\(402\) 0 0
\(403\) −18.4853 32.0174i −0.920817 1.59490i
\(404\) 0 0
\(405\) 0.585786 0.0291080
\(406\) 0 0
\(407\) −8.00000 −0.396545
\(408\) 0 0
\(409\) 9.29289 + 16.0958i 0.459504 + 0.795884i 0.998935 0.0461457i \(-0.0146939\pi\)
−0.539431 + 0.842030i \(0.681361\pi\)
\(410\) 0 0
\(411\) −7.07107 + 12.2474i −0.348790 + 0.604122i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −4.48528 + 7.76874i −0.220174 + 0.381352i
\(416\) 0 0
\(417\) 3.17157 + 5.49333i 0.155313 + 0.269009i
\(418\) 0 0
\(419\) −38.8284 −1.89689 −0.948446 0.316938i \(-0.897345\pi\)
−0.948446 + 0.316938i \(0.897345\pi\)
\(420\) 0 0
\(421\) −28.6274 −1.39521 −0.697607 0.716480i \(-0.745752\pi\)
−0.697607 + 0.716480i \(0.745752\pi\)
\(422\) 0 0
\(423\) 1.41421 + 2.44949i 0.0687614 + 0.119098i
\(424\) 0 0
\(425\) 14.5355 25.1763i 0.705077 1.22123i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 5.41421 9.37769i 0.261401 0.452759i
\(430\) 0 0
\(431\) 3.48528 + 6.03668i 0.167880 + 0.290777i 0.937674 0.347515i \(-0.112975\pi\)
−0.769794 + 0.638292i \(0.779641\pi\)
\(432\) 0 0
\(433\) −11.7574 −0.565023 −0.282511 0.959264i \(-0.591167\pi\)
−0.282511 + 0.959264i \(0.591167\pi\)
\(434\) 0 0
\(435\) 0.686292 0.0329052
\(436\) 0 0
\(437\) −5.17157 8.95743i −0.247390 0.428492i
\(438\) 0 0
\(439\) 17.6569 30.5826i 0.842716 1.45963i −0.0448746 0.998993i \(-0.514289\pi\)
0.887590 0.460634i \(-0.152378\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 0.514719 0.891519i 0.0244550 0.0423573i −0.853539 0.521029i \(-0.825548\pi\)
0.877994 + 0.478672i \(0.158882\pi\)
\(444\) 0 0
\(445\) 1.68629 + 2.92074i 0.0799379 + 0.138456i
\(446\) 0 0
\(447\) 5.31371 0.251330
\(448\) 0 0
\(449\) 17.3137 0.817084 0.408542 0.912739i \(-0.366037\pi\)
0.408542 + 0.912739i \(0.366037\pi\)
\(450\) 0 0
\(451\) 2.24264 + 3.88437i 0.105602 + 0.182908i
\(452\) 0 0
\(453\) −6.00000 + 10.3923i −0.281905 + 0.488273i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 9.00000 15.5885i 0.421002 0.729197i −0.575036 0.818128i \(-0.695012\pi\)
0.996038 + 0.0889312i \(0.0283451\pi\)
\(458\) 0 0
\(459\) 3.12132 + 5.40629i 0.145691 + 0.252344i
\(460\) 0 0
\(461\) −19.4142 −0.904210 −0.452105 0.891965i \(-0.649327\pi\)
−0.452105 + 0.891965i \(0.649327\pi\)
\(462\) 0 0
\(463\) −18.6274 −0.865689 −0.432845 0.901468i \(-0.642490\pi\)
−0.432845 + 0.901468i \(0.642490\pi\)
\(464\) 0 0
\(465\) 2.00000 + 3.46410i 0.0927478 + 0.160644i
\(466\) 0 0
\(467\) 19.8995 34.4669i 0.920839 1.59494i 0.122718 0.992442i \(-0.460839\pi\)
0.798120 0.602498i \(-0.205828\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 10.1213 17.5306i 0.466366 0.807769i
\(472\) 0 0
\(473\) −5.65685 9.79796i −0.260102 0.450511i
\(474\) 0 0
\(475\) 13.1716 0.604353
\(476\) 0 0
\(477\) −2.00000 −0.0915737
\(478\) 0 0
\(479\) 15.0711 + 26.1039i 0.688615 + 1.19272i 0.972286 + 0.233794i \(0.0751142\pi\)
−0.283671 + 0.958922i \(0.591553\pi\)
\(480\) 0 0
\(481\) 10.8284 18.7554i 0.493734 0.855172i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1.58579 + 2.74666i −0.0720069 + 0.124720i
\(486\) 0 0
\(487\) −9.31371 16.1318i −0.422044 0.731002i 0.574095 0.818789i \(-0.305354\pi\)
−0.996139 + 0.0877864i \(0.972021\pi\)
\(488\) 0 0
\(489\) 11.3137 0.511624
\(490\) 0 0
\(491\) −38.9706 −1.75872 −0.879358 0.476160i \(-0.842028\pi\)
−0.879358 + 0.476160i \(0.842028\pi\)
\(492\) 0 0
\(493\) 3.65685 + 6.33386i 0.164696 + 0.285263i
\(494\) 0 0
\(495\) −0.585786 + 1.01461i −0.0263291 + 0.0456034i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −9.65685 + 16.7262i −0.432300 + 0.748766i −0.997071 0.0764820i \(-0.975631\pi\)
0.564771 + 0.825248i \(0.308965\pi\)
\(500\) 0 0
\(501\) −9.89949 17.1464i −0.442277 0.766046i
\(502\) 0 0
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 10.0000 0.444994
\(506\) 0 0
\(507\) 8.15685 + 14.1281i 0.362259 + 0.627450i
\(508\) 0 0
\(509\) 12.7782 22.1324i 0.566383 0.981003i −0.430537 0.902573i \(-0.641676\pi\)
0.996920 0.0784305i \(-0.0249909\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −1.41421 + 2.44949i −0.0624391 + 0.108148i
\(514\) 0 0
\(515\) −3.65685 6.33386i −0.161140 0.279103i
\(516\) 0 0
\(517\) −5.65685 −0.248788
\(518\) 0 0
\(519\) −6.92893 −0.304146
\(520\) 0 0
\(521\) 16.2929 + 28.2201i 0.713805 + 1.23635i 0.963419 + 0.268000i \(0.0863629\pi\)
−0.249614 + 0.968345i \(0.580304\pi\)
\(522\) 0 0
\(523\) −7.17157 + 12.4215i −0.313591 + 0.543156i −0.979137 0.203201i \(-0.934865\pi\)
0.665546 + 0.746357i \(0.268199\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −21.3137 + 36.9164i −0.928440 + 1.60810i
\(528\) 0 0
\(529\) 4.81371 + 8.33759i 0.209292 + 0.362504i
\(530\) 0 0
\(531\) 6.82843 0.296328
\(532\) 0 0
\(533\) −12.1421 −0.525934
\(534\) 0 0
\(535\) −3.41421 5.91359i −0.147609 0.255667i
\(536\) 0 0
\(537\) 4.17157 7.22538i 0.180017 0.311798i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 2.65685 4.60181i 0.114227 0.197847i −0.803243 0.595651i \(-0.796894\pi\)
0.917471 + 0.397804i \(0.130228\pi\)
\(542\) 0 0
\(543\) −2.70711 4.68885i −0.116173 0.201218i
\(544\) 0 0
\(545\) 3.31371 0.141944
\(546\) 0 0
\(547\) 3.02944 0.129529 0.0647647 0.997901i \(-0.479370\pi\)
0.0647647 + 0.997901i \(0.479370\pi\)
\(548\) 0 0
\(549\) −1.87868 3.25397i −0.0801801 0.138876i
\(550\) 0 0
\(551\) −1.65685 + 2.86976i −0.0705844 + 0.122256i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −1.17157 + 2.02922i −0.0497305 + 0.0861358i
\(556\) 0 0
\(557\) −13.0000 22.5167i −0.550828 0.954062i −0.998215 0.0597213i \(-0.980979\pi\)
0.447387 0.894340i \(-0.352355\pi\)
\(558\) 0 0
\(559\) 30.6274 1.29540
\(560\) 0 0
\(561\) −12.4853 −0.527129
\(562\) 0 0
\(563\) −3.41421 5.91359i −0.143892 0.249228i 0.785067 0.619411i \(-0.212628\pi\)
−0.928959 + 0.370183i \(0.879295\pi\)
\(564\) 0 0
\(565\) −5.07107 + 8.78335i −0.213341 + 0.369518i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −0.242641 + 0.420266i −0.0101720 + 0.0176185i −0.871067 0.491165i \(-0.836571\pi\)
0.860895 + 0.508783i \(0.169905\pi\)
\(570\) 0 0
\(571\) 16.8284 + 29.1477i 0.704248 + 1.21979i 0.966962 + 0.254919i \(0.0820489\pi\)
−0.262715 + 0.964874i \(0.584618\pi\)
\(572\) 0 0
\(573\) −18.0000 −0.751961
\(574\) 0 0
\(575\) 17.0294 0.710177
\(576\) 0 0
\(577\) 7.05025 + 12.2114i 0.293506 + 0.508367i 0.974636 0.223795i \(-0.0718446\pi\)
−0.681130 + 0.732162i \(0.738511\pi\)
\(578\) 0 0
\(579\) −8.65685 + 14.9941i −0.359767 + 0.623134i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 2.00000 3.46410i 0.0828315 0.143468i
\(584\) 0 0
\(585\) −1.58579 2.74666i −0.0655642 0.113561i
\(586\) 0 0
\(587\) 17.1716 0.708747 0.354373 0.935104i \(-0.384694\pi\)
0.354373 + 0.935104i \(0.384694\pi\)
\(588\) 0 0
\(589\) −19.3137 −0.795807
\(590\) 0 0
\(591\) 1.00000 + 1.73205i 0.0411345 + 0.0712470i
\(592\) 0 0
\(593\) 10.5355 18.2481i 0.432643 0.749359i −0.564457 0.825462i \(-0.690915\pi\)
0.997100 + 0.0761034i \(0.0242479\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −5.17157 + 8.95743i −0.211658 + 0.366603i
\(598\) 0 0
\(599\) −1.00000 1.73205i −0.0408589 0.0707697i 0.844873 0.534967i \(-0.179676\pi\)
−0.885732 + 0.464198i \(0.846343\pi\)
\(600\) 0 0
\(601\) −0.928932 −0.0378919 −0.0189460 0.999821i \(-0.506031\pi\)
−0.0189460 + 0.999821i \(0.506031\pi\)
\(602\) 0 0
\(603\) −5.65685 −0.230365
\(604\) 0 0
\(605\) 2.05025 + 3.55114i 0.0833546 + 0.144374i
\(606\) 0 0
\(607\) −14.8284 + 25.6836i −0.601867 + 1.04246i 0.390671 + 0.920530i \(0.372243\pi\)
−0.992538 + 0.121934i \(0.961090\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 7.65685 13.2621i 0.309763 0.536526i
\(612\) 0 0
\(613\) −13.6569 23.6544i −0.551595 0.955391i −0.998160 0.0606394i \(-0.980686\pi\)
0.446565 0.894751i \(-0.352647\pi\)
\(614\) 0 0
\(615\) 1.31371 0.0529738
\(616\) 0 0
\(617\) −7.51472 −0.302531 −0.151266 0.988493i \(-0.548335\pi\)
−0.151266 + 0.988493i \(0.548335\pi\)
\(618\) 0 0
\(619\) −2.48528 4.30463i −0.0998919 0.173018i 0.811748 0.584008i \(-0.198516\pi\)
−0.911640 + 0.410990i \(0.865183\pi\)
\(620\) 0 0
\(621\) −1.82843 + 3.16693i −0.0733723 + 0.127084i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −9.98528 + 17.2950i −0.399411 + 0.691801i
\(626\) 0 0
\(627\) −2.82843 4.89898i −0.112956 0.195646i
\(628\) 0 0
\(629\) −24.9706 −0.995642
\(630\) 0 0
\(631\) −0.686292 −0.0273208 −0.0136604 0.999907i \(-0.504348\pi\)
−0.0136604 + 0.999907i \(0.504348\pi\)
\(632\) 0 0
\(633\) 10.4853 + 18.1610i 0.416753 + 0.721837i
\(634\) 0 0
\(635\) 2.82843 4.89898i 0.112243 0.194410i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −6.65685 + 11.5300i −0.263341 + 0.456120i
\(640\) 0 0
\(641\) 2.58579 + 4.47871i 0.102132 + 0.176899i 0.912563 0.408936i \(-0.134100\pi\)
−0.810431 + 0.585835i \(0.800767\pi\)
\(642\) 0 0
\(643\) −50.4264 −1.98862 −0.994312 0.106510i \(-0.966033\pi\)
−0.994312 + 0.106510i \(0.966033\pi\)
\(644\) 0 0
\(645\) −3.31371 −0.130477
\(646\) 0 0
\(647\) 10.5858 + 18.3351i 0.416170 + 0.720828i 0.995551 0.0942294i \(-0.0300387\pi\)
−0.579380 + 0.815057i \(0.696705\pi\)
\(648\) 0 0
\(649\) −6.82843 + 11.8272i −0.268039 + 0.464258i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −9.75736 + 16.9002i −0.381835 + 0.661358i −0.991325 0.131436i \(-0.958041\pi\)
0.609490 + 0.792794i \(0.291374\pi\)
\(654\) 0 0
\(655\) 2.14214 + 3.71029i 0.0837002 + 0.144973i
\(656\) 0 0
\(657\) −5.89949 −0.230161
\(658\) 0 0
\(659\) 13.3137 0.518628 0.259314 0.965793i \(-0.416503\pi\)
0.259314 + 0.965793i \(0.416503\pi\)
\(660\) 0 0
\(661\) −3.77817 6.54399i −0.146954 0.254532i 0.783146 0.621838i \(-0.213614\pi\)
−0.930100 + 0.367306i \(0.880280\pi\)
\(662\) 0 0
\(663\) 16.8995 29.2708i 0.656322 1.13678i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −2.14214 + 3.71029i −0.0829438 + 0.143663i
\(668\) 0 0
\(669\) 4.48528 + 7.76874i 0.173411 + 0.300357i
\(670\) 0 0
\(671\) 7.51472 0.290102
\(672\) 0 0
\(673\) 0.686292 0.0264546 0.0132273 0.999913i \(-0.495789\pi\)
0.0132273 + 0.999913i \(0.495789\pi\)
\(674\) 0 0
\(675\) −2.32843 4.03295i −0.0896212 0.155228i
\(676\) 0 0
\(677\) −14.2929 + 24.7560i −0.549321 + 0.951451i 0.449001 + 0.893531i \(0.351780\pi\)
−0.998321 + 0.0579196i \(0.981553\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 7.89949 13.6823i 0.302709 0.524308i
\(682\) 0 0
\(683\) −4.17157 7.22538i −0.159621 0.276471i 0.775111 0.631825i \(-0.217694\pi\)
−0.934732 + 0.355354i \(0.884360\pi\)
\(684\) 0 0
\(685\) −8.28427 −0.316526
\(686\) 0 0
\(687\) −8.24264 −0.314476
\(688\) 0 0
\(689\) 5.41421 + 9.37769i 0.206265 + 0.357262i
\(690\) 0 0
\(691\) −11.6569 + 20.1903i −0.443448 + 0.768074i −0.997943 0.0641132i \(-0.979578\pi\)
0.554495 + 0.832187i \(0.312911\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −1.85786 + 3.21792i −0.0704728 + 0.122062i
\(696\) 0 0
\(697\) 7.00000 + 12.1244i 0.265144 + 0.459243i
\(698\) 0 0
\(699\) −22.1421 −0.837492
\(700\) 0 0
\(701\) −22.8284 −0.862218 −0.431109 0.902300i \(-0.641878\pi\)
−0.431109 + 0.902300i \(0.641878\pi\)
\(702\) 0 0
\(703\) −5.65685 9.79796i −0.213352 0.369537i
\(704\) 0 0
\(705\) −0.828427 + 1.43488i −0.0312004 + 0.0540406i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −10.1421 + 17.5667i −0.380896 + 0.659731i −0.991191 0.132443i \(-0.957718\pi\)
0.610295 + 0.792174i \(0.291051\pi\)
\(710\) 0 0
\(711\) 1.17157 + 2.02922i 0.0439374 + 0.0761018i
\(712\) 0 0
\(713\) −24.9706 −0.935155
\(714\) 0 0
\(715\) 6.34315 0.237220
\(716\) 0 0
\(717\) 2.17157 + 3.76127i 0.0810989 + 0.140467i
\(718\) 0 0
\(719\) −12.9706 + 22.4657i −0.483720 + 0.837828i −0.999825 0.0186972i \(-0.994048\pi\)
0.516105 + 0.856525i \(0.327381\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −3.87868 + 6.71807i −0.144250 + 0.249848i
\(724\) 0 0
\(725\) −2.72792 4.72490i −0.101312 0.175478i
\(726\) 0 0
\(727\) 4.48528 0.166350 0.0831749 0.996535i \(-0.473494\pi\)
0.0831749 + 0.996535i \(0.473494\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −17.6569 30.5826i −0.653062 1.13114i
\(732\) 0 0
\(733\) 4.84924 8.39913i 0.179111 0.310229i −0.762465 0.647029i \(-0.776011\pi\)
0.941576 + 0.336800i \(0.109345\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 5.65685 9.79796i 0.208373 0.360912i
\(738\) 0 0
\(739\) 13.6569 + 23.6544i 0.502376 + 0.870140i 0.999996 + 0.00274517i \(0.000873816\pi\)
−0.497621 + 0.867395i \(0.665793\pi\)
\(740\) 0 0
\(741\) 15.3137 0.562563
\(742\) 0 0
\(743\) 17.0294 0.624749 0.312375 0.949959i \(-0.398876\pi\)
0.312375 + 0.949959i \(0.398876\pi\)
\(744\) 0 0
\(745\) 1.55635 + 2.69568i 0.0570202 + 0.0987619i
\(746\) 0 0
\(747\) −7.65685 + 13.2621i −0.280150 + 0.485233i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 1.17157 2.02922i 0.0427513 0.0740474i −0.843858 0.536567i \(-0.819721\pi\)
0.886609 + 0.462519i \(0.153054\pi\)
\(752\) 0 0
\(753\) −2.24264 3.88437i −0.0817264 0.141554i
\(754\) 0 0
\(755\) −7.02944 −0.255827
\(756\) 0 0
\(757\) 37.6569 1.36866 0.684331 0.729172i \(-0.260094\pi\)
0.684331 + 0.729172i \(0.260094\pi\)
\(758\) 0 0
\(759\) −3.65685 6.33386i −0.132735 0.229904i
\(760\) 0 0
\(761\) −23.2635 + 40.2935i −0.843300 + 1.46064i 0.0437901 + 0.999041i \(0.486057\pi\)
−0.887090 + 0.461597i \(0.847277\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −1.82843 + 3.16693i −0.0661069 + 0.114501i
\(766\) 0 0
\(767\) −18.4853 32.0174i −0.667465 1.15608i
\(768\) 0 0
\(769\) −29.6985 −1.07095 −0.535477 0.844550i \(-0.679868\pi\)
−0.535477 + 0.844550i \(0.679868\pi\)
\(770\) 0 0
\(771\) 19.2132 0.691947
\(772\) 0 0
\(773\) −10.7782 18.6683i −0.387664 0.671454i 0.604471 0.796627i \(-0.293385\pi\)
−0.992135 + 0.125174i \(0.960051\pi\)
\(774\) 0 0
\(775\) 15.8995 27.5387i 0.571127 0.989220i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −3.17157 + 5.49333i −0.113633 + 0.196819i
\(780\) 0 0
\(781\) −13.3137 23.0600i −0.476402 0.825152i
\(782\) 0 0
\(783\) 1.17157 0.0418686
\(784\) 0 0
\(785\) 11.8579 0.423225
\(786\) 0 0
\(787\) 23.6569 + 40.9749i 0.843276 + 1.46060i 0.887110 + 0.461558i \(0.152709\pi\)
−0.0438344 + 0.999039i \(0.513957\pi\)
\(788\) 0 0
\(789\) 8.65685 14.9941i 0.308192 0.533805i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −10.1716 + 17.6177i −0.361203 + 0.625622i
\(794\) 0 0
\(795\) −0.585786 1.01461i −0.0207757 0.0359846i
\(796\) 0 0
\(797\) 28.3848 1.00544 0.502720 0.864449i \(-0.332333\pi\)
0.502720 + 0.864449i \(0.332333\pi\)
\(798\) 0 0
\(799\) −17.6569 −0.624655