Properties

Label 2352.2.q.bd.1537.2
Level $2352$
Weight $2$
Character 2352.1537
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 1537.2
Root \(0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 2352.1537
Dual form 2352.2.q.bd.961.2

$q$-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 \(\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1471\) \(1765\) \(2257\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 0.793071 0.609129i \(-0.208481\pi\)
−0.924057 + 0.382255i \(0.875148\pi\)
\(6\) 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 −0.976478 0.215615i \(-0.930824\pi\)
0.674967 + 0.737848i \(0.264158\pi\)
\(12\) 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 0.187327 + 0.982298i \(0.440018\pi\)
−0.944358 + 0.328919i \(0.893316\pi\)
\(18\) 0 0
\(19\) 1.41421 + 2.44949i 0.324443 + 0.561951i 0.981399 0.191977i \(-0.0614899\pi\)
−0.656957 + 0.753928i \(0.728157\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.82843 + 3.16693i 0.381253 + 0.660350i 0.991242 0.132060i \(-0.0421592\pi\)
−0.609988 + 0.792410i \(0.708826\pi\)
\(24\) 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 0.377485 + 0.926016i \(0.376789\pi\)
−0.990696 + 0.136097i \(0.956544\pi\)
\(32\) 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 0.982274 0.187453i \(-0.0600231\pi\)
−0.653476 + 0.756948i \(0.726690\pi\)
\(38\) 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 0.950541 0.310599i \(-0.100530\pi\)
−0.744257 + 0.667893i \(0.767196\pi\)
\(48\) 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 −0.789136 0.614218i \(-0.789471\pi\)
0.926497 + 0.376303i \(0.122805\pi\)
\(54\) 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 −0.998017 0.0629492i \(-0.979949\pi\)
0.553524 + 0.832833i \(0.313283\pi\)
\(60\) 0 0
\(61\) −1.87868 3.25397i −0.240540 0.416628i 0.720328 0.693634i \(-0.243991\pi\)
−0.960868 + 0.277006i \(0.910658\pi\)
\(62\) 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 −0.639906 0.768453i \(-0.721027\pi\)
0.985453 + 0.169948i \(0.0543599\pi\)
\(68\) 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 −0.640156 0.768245i \(-0.721130\pi\)
0.985398 + 0.170269i \(0.0544636\pi\)
\(74\) 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 0.924375 0.381485i \(-0.124587\pi\)
−0.792563 + 0.609790i \(0.791254\pi\)
\(80\) 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 0.977292 0.211895i \(-0.0679636\pi\)
−0.672153 + 0.740412i \(0.734630\pi\)
\(90\) 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 0.0325010 + 0.999472i \(0.489653\pi\)
−0.881818 + 0.471589i \(0.843681\pi\)
\(102\) 0 0
\(103\) −6.24264 10.8126i −0.615106 1.06539i −0.990366 0.138475i \(-0.955780\pi\)
0.375260 0.926919i \(-0.377553\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −5.82843 10.0951i −0.563455 0.975933i −0.997192 0.0748933i \(-0.976138\pi\)
0.433736 0.901040i \(-0.357195\pi\)
\(108\) 0 0
\(109\) −2.82843 + 4.89898i −0.270914 + 0.469237i −0.969096 0.246683i \(-0.920659\pi\)
0.698182 + 0.715920i \(0.253993\pi\)
\(110\) 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 0.980384 0.197097i \(-0.0631514\pi\)
−0.660883 + 0.750489i \(0.729818\pi\)
\(132\) 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 −0.388067 0.921631i \(-0.626857\pi\)
0.992190 0.124739i \(-0.0398094\pi\)
\(138\) 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 0.954092 0.299515i \(-0.0968249\pi\)
−0.736434 + 0.676510i \(0.763492\pi\)
\(150\) 0 0
\(151\) 6.00000 10.3923i 0.488273 0.845714i −0.511636 0.859202i \(-0.670960\pi\)
0.999909 + 0.0134886i \(0.00429367\pi\)
\(152\) 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 0.106636 + 0.994298i \(0.465992\pi\)
−0.914406 + 0.404799i \(0.867341\pi\)
\(158\) 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 0.997916 0.0645236i \(-0.0205528\pi\)
−0.554837 + 0.831959i \(0.687219\pi\)
\(164\) 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 0.703744 0.710453i \(-0.251510\pi\)
−0.967143 + 0.254234i \(0.918177\pi\)
\(174\) 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 −0.978752 0.205049i \(-0.934265\pi\)
0.666954 + 0.745099i \(0.267598\pi\)
\(180\) 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 −0.982828 0.184525i \(-0.940925\pi\)
0.331611 0.943416i \(-0.392408\pi\)
\(192\) 0 0
\(193\) 8.65685 14.9941i 0.623134 1.07930i −0.365765 0.930707i \(-0.619192\pi\)
0.988899 0.148592i \(-0.0474742\pi\)
\(194\) 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 −0.622429 0.782676i \(-0.713854\pi\)
0.989032 + 0.147701i \(0.0471874\pi\)
\(200\) 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 0.475292 + 0.879828i \(0.342343\pi\)
−0.999599 + 0.0282996i \(0.990991\pi\)
\(228\) 0 0
\(229\) −4.12132 7.13834i −0.272345 0.471715i 0.697117 0.716957i \(-0.254466\pi\)
−0.969462 + 0.245243i \(0.921132\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −11.0711 19.1757i −0.725290 1.25624i −0.958855 0.283898i \(-0.908372\pi\)
0.233565 0.972341i \(-0.424961\pi\)
\(234\) 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 −0.713636 0.700517i \(-0.752953\pi\)
0.963483 + 0.267768i \(0.0862861\pi\)
\(242\) 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 0.992933 + 0.118677i \(0.0378651\pi\)
−0.393690 + 0.919243i \(0.628802\pi\)
\(258\) 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 0.465416 + 0.885092i \(0.345905\pi\)
−0.999220 + 0.0394843i \(0.987428\pi\)
\(264\) 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 −0.981924 0.189274i \(-0.939387\pi\)
0.654878 + 0.755735i \(0.272720\pi\)
\(270\) 0 0
\(271\) 9.07107 + 15.7116i 0.551028 + 0.954409i 0.998201 + 0.0599610i \(0.0190976\pi\)
−0.447173 + 0.894448i \(0.647569\pi\)
\(272\) 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 −0.993722 0.111878i \(-0.964313\pi\)
0.593750 + 0.804649i \(0.297647\pi\)
\(278\) 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 −0.711932 0.702248i \(-0.752180\pi\)
0.964131 + 0.265427i \(0.0855130\pi\)
\(284\) 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 0.360213 + 0.932870i \(0.382704\pi\)
−0.987996 + 0.154481i \(0.950629\pi\)
\(312\) 0 0
\(313\) 8.94975 + 15.5014i 0.505870 + 0.876192i 0.999977 + 0.00679098i \(0.00216165\pi\)
−0.494107 + 0.869401i \(0.664505\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −5.00000 8.66025i −0.280828 0.486408i 0.690761 0.723083i \(-0.257276\pi\)
−0.971589 + 0.236675i \(0.923942\pi\)
\(318\) 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 0.805812 0.592172i \(-0.201729\pi\)
−0.915742 + 0.401768i \(0.868396\pi\)
\(332\) 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 −0.686217 0.727396i \(-0.740730\pi\)
0.973053 + 0.230584i \(0.0740635\pi\)
\(348\) 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 −0.972729 0.231944i \(-0.925491\pi\)
0.687234 + 0.726436i \(0.258825\pi\)
\(354\) 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 0.670227 0.742156i \(-0.266197\pi\)
−0.977840 + 0.209355i \(0.932863\pi\)
\(360\) 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 −0.495905 0.868377i \(-0.665164\pi\)
0.999989 0.00472187i \(-0.00150302\pi\)
\(368\) 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 0.869548 + 0.493848i \(0.164410\pi\)
−0.00708885 + 0.999975i \(0.502256\pi\)
\(374\) 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 −0.944022 0.329882i \(-0.892991\pi\)
0.186325 0.982488i \(-0.440342\pi\)
\(384\) 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 −0.965467 0.260524i \(-0.916105\pi\)
0.708354 + 0.705857i \(0.249438\pi\)
\(390\) 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 −0.869155 0.494539i \(-0.835337\pi\)
0.00629405 0.999980i \(-0.497997\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −11.0711 19.1757i −0.552863 0.957586i −0.998066 0.0621570i \(-0.980202\pi\)
0.445204 0.895429i \(-0.353131\pi\)
\(402\) 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 −0.539431 0.842030i \(-0.681361\pi\)
0.998935 + 0.0461457i \(0.0146939\pi\)
\(410\) 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 −0.769794 0.638292i \(-0.779641\pi\)
0.937674 + 0.347515i \(0.112975\pi\)
\(432\) 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 0.887590 + 0.460634i \(0.152378\pi\)
−0.0448746 + 0.998993i \(0.514289\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 0.514719 + 0.891519i 0.0244550 + 0.0423573i 0.877994 0.478672i \(-0.158882\pi\)
−0.853539 + 0.521029i \(0.825548\pi\)
\(444\) 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 0.996038 0.0889312i \(-0.0283451\pi\)
−0.575036 + 0.818128i \(0.695012\pi\)
\(458\) 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 0.798120 + 0.602498i \(0.205828\pi\)
0.122718 + 0.992442i \(0.460839\pi\)
\(468\) 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 −0.283671 0.958922i \(-0.591553\pi\)
0.972286 0.233794i \(-0.0751142\pi\)
\(480\) 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 −0.996139 0.0877864i \(-0.972021\pi\)
0.574095 + 0.818789i \(0.305354\pi\)
\(488\) 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 0.564771 0.825248i \(-0.308965\pi\)
−0.997071 + 0.0764820i \(0.975631\pi\)
\(500\) 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 0.996920 + 0.0784305i \(0.0249909\pi\)
−0.430537 + 0.902573i \(0.641676\pi\)
\(510\) 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 −0.249614 0.968345i \(-0.580304\pi\)
0.963419 0.268000i \(-0.0863629\pi\)
\(522\) 0 0
\(523\) −7.17157 12.4215i −0.313591 0.543156i 0.665546 0.746357i \(-0.268199\pi\)
−0.979137 + 0.203201i \(0.934865\pi\)
\(524\) 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 0.917471 0.397804i \(-0.130228\pi\)
−0.803243 + 0.595651i \(0.796894\pi\)
\(542\) 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 0.447387 + 0.894340i \(0.352355\pi\)
−0.998215 + 0.0597213i \(0.980979\pi\)
\(558\) 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 −0.928959 0.370183i \(-0.879295\pi\)
0.785067 + 0.619411i \(0.212628\pi\)
\(564\) 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 0.860895 0.508783i \(-0.169905\pi\)
−0.871067 + 0.491165i \(0.836571\pi\)
\(570\) 0 0
\(571\) 16.8284 29.1477i 0.704248 1.21979i −0.262715 0.964874i \(-0.584618\pi\)
0.966962 0.254919i \(-0.0820489\pi\)
\(572\) 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 −0.681130 0.732162i \(-0.738511\pi\)
0.974636 + 0.223795i \(0.0718446\pi\)
\(578\) 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 0.997100 0.0761034i \(-0.0242479\pi\)
−0.564457 + 0.825462i \(0.690915\pi\)
\(594\) 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 −0.885732 0.464198i \(-0.846343\pi\)
0.844873 + 0.534967i \(0.179676\pi\)
\(600\) 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 −0.992538 0.121934i \(-0.961090\pi\)
0.390671 0.920530i \(-0.372243\pi\)
\(608\) 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 0.446565 + 0.894751i \(0.352647\pi\)
−0.998160 + 0.0606394i \(0.980686\pi\)
\(614\) 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 −0.911640 0.410990i \(-0.865183\pi\)
0.811748 + 0.584008i \(0.198516\pi\)
\(620\) 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 −0.810431 0.585835i \(-0.800767\pi\)
0.912563 + 0.408936i \(0.134100\pi\)
\(642\) 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 −0.579380 0.815057i \(-0.696705\pi\)
0.995551 + 0.0942294i \(0.0300387\pi\)
\(648\) 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 0.609490 0.792794i \(-0.291374\pi\)
−0.991325 + 0.131436i \(0.958041\pi\)
\(654\) 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 −0.930100 0.367306i \(-0.880280\pi\)
0.783146 + 0.621838i \(0.213614\pi\)
\(662\) 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 −0.998321 0.0579196i \(-0.981553\pi\)
0.449001 0.893531i \(-0.351780\pi\)
\(678\) 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 −0.934732 0.355354i \(-0.884360\pi\)
0.775111 + 0.631825i \(0.217694\pi\)
\(684\) 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 0.554495 0.832187i \(-0.312911\pi\)
−0.997943 + 0.0641132i \(0.979578\pi\)
\(692\) 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 0.610295 0.792174i \(-0.291051\pi\)
−0.991191 + 0.132443i \(0.957718\pi\)
\(710\) 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 0.516105 0.856525i \(-0.327381\pi\)
−0.999825 + 0.0186972i \(0.994048\pi\)
\(720\) 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 0.941576 0.336800i \(-0.109345\pi\)
−0.762465 + 0.647029i \(0.776011\pi\)
\(734\) 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 −0.497621 0.867395i \(-0.665793\pi\)
0.999996 0.00274517i \(-0.000873816\pi\)
\(740\) 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 0.886609 0.462519i \(-0.153054\pi\)
−0.843858 + 0.536567i \(0.819721\pi\)
\(752\) 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 −0.887090 0.461597i \(-0.847277\pi\)
0.0437901 0.999041i \(-0.486057\pi\)
\(762\) 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 −0.992135 0.125174i \(-0.960051\pi\)
0.604471 + 0.796627i \(0.293385\pi\)
\(774\) 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 −0.0438344 0.999039i \(-0.513957\pi\)
0.887110 0.461558i \(-0.152709\pi\)
\(788\) 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