Properties

Label 120.2.m.a.59.4
Level $120$
Weight $2$
Character 120.59
Analytic conductor $0.958$
Analytic rank $0$
Dimension $4$
CM discriminant -15
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 120.m (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.958204824255\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{3}, \sqrt{-5})\)
Defining polynomial: \( x^{4} + x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 59.4
Root \(0.866025 + 1.11803i\) of defining polynomial
Character \(\chi\) \(=\) 120.59
Dual form 120.2.m.a.59.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 + 1.11803i) q^{2} -1.73205 q^{3} +(-0.500000 + 1.93649i) q^{4} +2.23607i q^{5} +(-1.50000 - 1.93649i) q^{6} +(-2.59808 + 1.11803i) q^{8} +3.00000 q^{9} +O(q^{10})\) \(q+(0.866025 + 1.11803i) q^{2} -1.73205 q^{3} +(-0.500000 + 1.93649i) q^{4} +2.23607i q^{5} +(-1.50000 - 1.93649i) q^{6} +(-2.59808 + 1.11803i) q^{8} +3.00000 q^{9} +(-2.50000 + 1.93649i) q^{10} +(0.866025 - 3.35410i) q^{12} -3.87298i q^{15} +(-3.50000 - 1.93649i) q^{16} +6.92820 q^{17} +(2.59808 + 3.35410i) q^{18} +4.00000 q^{19} +(-4.33013 - 1.11803i) q^{20} -8.94427i q^{23} +(4.50000 - 1.93649i) q^{24} -5.00000 q^{25} -5.19615 q^{27} +(4.33013 - 3.35410i) q^{30} +7.74597i q^{31} +(-0.866025 - 5.59017i) q^{32} +(6.00000 + 7.74597i) q^{34} +(-1.50000 + 5.80948i) q^{36} +(3.46410 + 4.47214i) q^{38} +(-2.50000 - 5.80948i) q^{40} +6.70820i q^{45} +(10.0000 - 7.74597i) q^{46} +8.94427i q^{47} +(6.06218 + 3.35410i) q^{48} -7.00000 q^{49} +(-4.33013 - 5.59017i) q^{50} -12.0000 q^{51} -4.47214i q^{53} +(-4.50000 - 5.80948i) q^{54} -6.92820 q^{57} +(7.50000 + 1.93649i) q^{60} -15.4919i q^{61} +(-8.66025 + 6.70820i) q^{62} +(5.50000 - 5.80948i) q^{64} +(-3.46410 + 13.4164i) q^{68} +15.4919i q^{69} +(-7.79423 + 3.35410i) q^{72} +8.66025 q^{75} +(-2.00000 + 7.74597i) q^{76} -7.74597i q^{79} +(4.33013 - 7.82624i) q^{80} +9.00000 q^{81} +3.46410 q^{83} +15.4919i q^{85} +(-7.50000 + 5.80948i) q^{90} +(17.3205 + 4.47214i) q^{92} -13.4164i q^{93} +(-10.0000 + 7.74597i) q^{94} +8.94427i q^{95} +(1.50000 + 9.68246i) q^{96} +(-6.06218 - 7.82624i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{4} - 6 q^{6} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{4} - 6 q^{6} + 12 q^{9} - 10 q^{10} - 14 q^{16} + 16 q^{19} + 18 q^{24} - 20 q^{25} + 24 q^{34} - 6 q^{36} - 10 q^{40} + 40 q^{46} - 28 q^{49} - 48 q^{51} - 18 q^{54} + 30 q^{60} + 22 q^{64} - 8 q^{76} + 36 q^{81} - 30 q^{90} - 40 q^{94} + 6 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/120\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(41\) \(61\) \(97\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 1.11803i 0.612372 + 0.790569i
\(3\) −1.73205 −1.00000
\(4\) −0.500000 + 1.93649i −0.250000 + 0.968246i
\(5\) 2.23607i 1.00000i
\(6\) −1.50000 1.93649i −0.612372 0.790569i
\(7\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) −2.59808 + 1.11803i −0.918559 + 0.395285i
\(9\) 3.00000 1.00000
\(10\) −2.50000 + 1.93649i −0.790569 + 0.612372i
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 0.866025 3.35410i 0.250000 0.968246i
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 0 0
\(15\) 3.87298i 1.00000i
\(16\) −3.50000 1.93649i −0.875000 0.484123i
\(17\) 6.92820 1.68034 0.840168 0.542326i \(-0.182456\pi\)
0.840168 + 0.542326i \(0.182456\pi\)
\(18\) 2.59808 + 3.35410i 0.612372 + 0.790569i
\(19\) 4.00000 0.917663 0.458831 0.888523i \(-0.348268\pi\)
0.458831 + 0.888523i \(0.348268\pi\)
\(20\) −4.33013 1.11803i −0.968246 0.250000i
\(21\) 0 0
\(22\) 0 0
\(23\) 8.94427i 1.86501i −0.361158 0.932505i \(-0.617618\pi\)
0.361158 0.932505i \(-0.382382\pi\)
\(24\) 4.50000 1.93649i 0.918559 0.395285i
\(25\) −5.00000 −1.00000
\(26\) 0 0
\(27\) −5.19615 −1.00000
\(28\) 0 0
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 4.33013 3.35410i 0.790569 0.612372i
\(31\) 7.74597i 1.39122i 0.718421 + 0.695608i \(0.244865\pi\)
−0.718421 + 0.695608i \(0.755135\pi\)
\(32\) −0.866025 5.59017i −0.153093 0.988212i
\(33\) 0 0
\(34\) 6.00000 + 7.74597i 1.02899 + 1.32842i
\(35\) 0 0
\(36\) −1.50000 + 5.80948i −0.250000 + 0.968246i
\(37\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) 3.46410 + 4.47214i 0.561951 + 0.725476i
\(39\) 0 0
\(40\) −2.50000 5.80948i −0.395285 0.918559i
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 0 0
\(45\) 6.70820i 1.00000i
\(46\) 10.0000 7.74597i 1.47442 1.14208i
\(47\) 8.94427i 1.30466i 0.757937 + 0.652328i \(0.226208\pi\)
−0.757937 + 0.652328i \(0.773792\pi\)
\(48\) 6.06218 + 3.35410i 0.875000 + 0.484123i
\(49\) −7.00000 −1.00000
\(50\) −4.33013 5.59017i −0.612372 0.790569i
\(51\) −12.0000 −1.68034
\(52\) 0 0
\(53\) 4.47214i 0.614295i −0.951662 0.307148i \(-0.900625\pi\)
0.951662 0.307148i \(-0.0993745\pi\)
\(54\) −4.50000 5.80948i −0.612372 0.790569i
\(55\) 0 0
\(56\) 0 0
\(57\) −6.92820 −0.917663
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 7.50000 + 1.93649i 0.968246 + 0.250000i
\(61\) 15.4919i 1.98354i −0.128037 0.991769i \(-0.540868\pi\)
0.128037 0.991769i \(-0.459132\pi\)
\(62\) −8.66025 + 6.70820i −1.09985 + 0.851943i
\(63\) 0 0
\(64\) 5.50000 5.80948i 0.687500 0.726184i
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) −3.46410 + 13.4164i −0.420084 + 1.62698i
\(69\) 15.4919i 1.86501i
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) −7.79423 + 3.35410i −0.918559 + 0.395285i
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 0 0
\(75\) 8.66025 1.00000
\(76\) −2.00000 + 7.74597i −0.229416 + 0.888523i
\(77\) 0 0
\(78\) 0 0
\(79\) 7.74597i 0.871489i −0.900070 0.435745i \(-0.856485\pi\)
0.900070 0.435745i \(-0.143515\pi\)
\(80\) 4.33013 7.82624i 0.484123 0.875000i
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) 3.46410 0.380235 0.190117 0.981761i \(-0.439113\pi\)
0.190117 + 0.981761i \(0.439113\pi\)
\(84\) 0 0
\(85\) 15.4919i 1.68034i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) −7.50000 + 5.80948i −0.790569 + 0.612372i
\(91\) 0 0
\(92\) 17.3205 + 4.47214i 1.80579 + 0.466252i
\(93\) 13.4164i 1.39122i
\(94\) −10.0000 + 7.74597i −1.03142 + 0.798935i
\(95\) 8.94427i 0.917663i
\(96\) 1.50000 + 9.68246i 0.153093 + 0.988212i
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) −6.06218 7.82624i −0.612372 0.790569i
\(99\) 0 0
\(100\) 2.50000 9.68246i 0.250000 0.968246i
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) −10.3923 13.4164i −1.02899 1.32842i
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 5.00000 3.87298i 0.485643 0.376177i
\(107\) 10.3923 1.00466 0.502331 0.864675i \(-0.332476\pi\)
0.502331 + 0.864675i \(0.332476\pi\)
\(108\) 2.59808 10.0623i 0.250000 0.968246i
\(109\) 15.4919i 1.48386i −0.670478 0.741929i \(-0.733911\pi\)
0.670478 0.741929i \(-0.266089\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −20.7846 −1.95525 −0.977626 0.210352i \(-0.932539\pi\)
−0.977626 + 0.210352i \(0.932539\pi\)
\(114\) −6.00000 7.74597i −0.561951 0.725476i
\(115\) 20.0000 1.86501
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 4.33013 + 10.0623i 0.395285 + 0.918559i
\(121\) 11.0000 1.00000
\(122\) 17.3205 13.4164i 1.56813 1.21466i
\(123\) 0 0
\(124\) −15.0000 3.87298i −1.34704 0.347804i
\(125\) 11.1803i 1.00000i
\(126\) 0 0
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 11.2583 + 1.11803i 0.995105 + 0.0988212i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 11.6190i 1.00000i
\(136\) −18.0000 + 7.74597i −1.54349 + 0.664211i
\(137\) −6.92820 −0.591916 −0.295958 0.955201i \(-0.595639\pi\)
−0.295958 + 0.955201i \(0.595639\pi\)
\(138\) −17.3205 + 13.4164i −1.47442 + 1.14208i
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 0 0
\(141\) 15.4919i 1.30466i
\(142\) 0 0
\(143\) 0 0
\(144\) −10.5000 5.80948i −0.875000 0.484123i
\(145\) 0 0
\(146\) 0 0
\(147\) 12.1244 1.00000
\(148\) 0 0
\(149\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(150\) 7.50000 + 9.68246i 0.612372 + 0.790569i
\(151\) 23.2379i 1.89107i 0.325515 + 0.945537i \(0.394462\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) −10.3923 + 4.47214i −0.842927 + 0.362738i
\(153\) 20.7846 1.68034
\(154\) 0 0
\(155\) −17.3205 −1.39122
\(156\) 0 0
\(157\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(158\) 8.66025 6.70820i 0.688973 0.533676i
\(159\) 7.74597i 0.614295i
\(160\) 12.5000 1.93649i 0.988212 0.153093i
\(161\) 0 0
\(162\) 7.79423 + 10.0623i 0.612372 + 0.790569i
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 3.00000 + 3.87298i 0.232845 + 0.300602i
\(167\) 8.94427i 0.692129i −0.938211 0.346064i \(-0.887518\pi\)
0.938211 0.346064i \(-0.112482\pi\)
\(168\) 0 0
\(169\) −13.0000 −1.00000
\(170\) −17.3205 + 13.4164i −1.32842 + 1.02899i
\(171\) 12.0000 0.917663
\(172\) 0 0
\(173\) 22.3607i 1.70005i 0.526742 + 0.850026i \(0.323414\pi\)
−0.526742 + 0.850026i \(0.676586\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) −12.9904 3.35410i −0.968246 0.250000i
\(181\) 15.4919i 1.15151i 0.817624 + 0.575753i \(0.195291\pi\)
−0.817624 + 0.575753i \(0.804709\pi\)
\(182\) 0 0
\(183\) 26.8328i 1.98354i
\(184\) 10.0000 + 23.2379i 0.737210 + 1.71312i
\(185\) 0 0
\(186\) 15.0000 11.6190i 1.09985 0.851943i
\(187\) 0 0
\(188\) −17.3205 4.47214i −1.26323 0.326164i
\(189\) 0 0
\(190\) −10.0000 + 7.74597i −0.725476 + 0.561951i
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) −9.52628 + 10.0623i −0.687500 + 0.726184i
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 3.50000 13.5554i 0.250000 0.968246i
\(197\) 4.47214i 0.318626i 0.987228 + 0.159313i \(0.0509280\pi\)
−0.987228 + 0.159313i \(0.949072\pi\)
\(198\) 0 0
\(199\) 23.2379i 1.64729i −0.567105 0.823646i \(-0.691937\pi\)
0.567105 0.823646i \(-0.308063\pi\)
\(200\) 12.9904 5.59017i 0.918559 0.395285i
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 6.00000 23.2379i 0.420084 1.62698i
\(205\) 0 0
\(206\) 0 0
\(207\) 26.8328i 1.86501i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −28.0000 −1.92760 −0.963800 0.266627i \(-0.914091\pi\)
−0.963800 + 0.266627i \(0.914091\pi\)
\(212\) 8.66025 + 2.23607i 0.594789 + 0.153574i
\(213\) 0 0
\(214\) 9.00000 + 11.6190i 0.615227 + 0.794255i
\(215\) 0 0
\(216\) 13.5000 5.80948i 0.918559 0.395285i
\(217\) 0 0
\(218\) 17.3205 13.4164i 1.17309 0.908674i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) 0 0
\(225\) −15.0000 −1.00000
\(226\) −18.0000 23.2379i −1.19734 1.54576i
\(227\) −24.2487 −1.60944 −0.804722 0.593652i \(-0.797686\pi\)
−0.804722 + 0.593652i \(0.797686\pi\)
\(228\) 3.46410 13.4164i 0.229416 0.888523i
\(229\) 15.4919i 1.02374i 0.859064 + 0.511868i \(0.171046\pi\)
−0.859064 + 0.511868i \(0.828954\pi\)
\(230\) 17.3205 + 22.3607i 1.14208 + 1.47442i
\(231\) 0 0
\(232\) 0 0
\(233\) 20.7846 1.36165 0.680823 0.732448i \(-0.261622\pi\)
0.680823 + 0.732448i \(0.261622\pi\)
\(234\) 0 0
\(235\) −20.0000 −1.30466
\(236\) 0 0
\(237\) 13.4164i 0.871489i
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) −7.50000 + 13.5554i −0.484123 + 0.875000i
\(241\) −2.00000 −0.128831 −0.0644157 0.997923i \(-0.520518\pi\)
−0.0644157 + 0.997923i \(0.520518\pi\)
\(242\) 9.52628 + 12.2984i 0.612372 + 0.790569i
\(243\) −15.5885 −1.00000
\(244\) 30.0000 + 7.74597i 1.92055 + 0.495885i
\(245\) 15.6525i 1.00000i
\(246\) 0 0
\(247\) 0 0
\(248\) −8.66025 20.1246i −0.549927 1.27791i
\(249\) −6.00000 −0.380235
\(250\) 12.5000 9.68246i 0.790569 0.612372i
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 26.8328i 1.68034i
\(256\) 8.50000 + 13.5554i 0.531250 + 0.847215i
\(257\) 6.92820 0.432169 0.216085 0.976375i \(-0.430671\pi\)
0.216085 + 0.976375i \(0.430671\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 8.94427i 0.551527i −0.961225 0.275764i \(-0.911069\pi\)
0.961225 0.275764i \(-0.0889307\pi\)
\(264\) 0 0
\(265\) 10.0000 0.614295
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) 12.9904 10.0623i 0.790569 0.612372i
\(271\) 7.74597i 0.470534i −0.971931 0.235267i \(-0.924404\pi\)
0.971931 0.235267i \(-0.0755965\pi\)
\(272\) −24.2487 13.4164i −1.47029 0.813489i
\(273\) 0 0
\(274\) −6.00000 7.74597i −0.362473 0.467951i
\(275\) 0 0
\(276\) −30.0000 7.74597i −1.80579 0.466252i
\(277\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(278\) −3.46410 4.47214i −0.207763 0.268221i
\(279\) 23.2379i 1.39122i
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 17.3205 13.4164i 1.03142 0.798935i
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) 0 0
\(285\) 15.4919i 0.917663i
\(286\) 0 0
\(287\) 0 0
\(288\) −2.59808 16.7705i −0.153093 0.988212i
\(289\) 31.0000 1.82353
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 31.3050i 1.82885i 0.404750 + 0.914427i \(0.367359\pi\)
−0.404750 + 0.914427i \(0.632641\pi\)
\(294\) 10.5000 + 13.5554i 0.612372 + 0.790569i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) −4.33013 + 16.7705i −0.250000 + 0.968246i
\(301\) 0 0
\(302\) −25.9808 + 20.1246i −1.49502 + 1.15804i
\(303\) 0 0
\(304\) −14.0000 7.74597i −0.802955 0.444262i
\(305\) 34.6410 1.98354
\(306\) 18.0000 + 23.2379i 1.02899 + 1.32842i
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −15.0000 19.3649i −0.851943 1.09985i
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 15.0000 + 3.87298i 0.843816 + 0.217872i
\(317\) 22.3607i 1.25590i −0.778253 0.627950i \(-0.783894\pi\)
0.778253 0.627950i \(-0.216106\pi\)
\(318\) −8.66025 + 6.70820i −0.485643 + 0.376177i
\(319\) 0 0
\(320\) 12.9904 + 12.2984i 0.726184 + 0.687500i
\(321\) −18.0000 −1.00466
\(322\) 0 0
\(323\) 27.7128 1.54198
\(324\) −4.50000 + 17.4284i −0.250000 + 0.968246i
\(325\) 0 0
\(326\) 0 0
\(327\) 26.8328i 1.48386i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 28.0000 1.53902 0.769510 0.638635i \(-0.220501\pi\)
0.769510 + 0.638635i \(0.220501\pi\)
\(332\) −1.73205 + 6.70820i −0.0950586 + 0.368161i
\(333\) 0 0
\(334\) 10.0000 7.74597i 0.547176 0.423840i
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) −11.2583 14.5344i −0.612372 0.790569i
\(339\) 36.0000 1.95525
\(340\) −30.0000 7.74597i −1.62698 0.420084i
\(341\) 0 0
\(342\) 10.3923 + 13.4164i 0.561951 + 0.725476i
\(343\) 0 0
\(344\) 0 0
\(345\) −34.6410 −1.86501
\(346\) −25.0000 + 19.3649i −1.34401 + 1.04106i
\(347\) −10.3923 −0.557888 −0.278944 0.960307i \(-0.589984\pi\)
−0.278944 + 0.960307i \(0.589984\pi\)
\(348\) 0 0
\(349\) 15.4919i 0.829264i −0.909989 0.414632i \(-0.863910\pi\)
0.909989 0.414632i \(-0.136090\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −20.7846 −1.10625 −0.553127 0.833097i \(-0.686565\pi\)
−0.553127 + 0.833097i \(0.686565\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) −7.50000 17.4284i −0.395285 0.918559i
\(361\) −3.00000 −0.157895
\(362\) −17.3205 + 13.4164i −0.910346 + 0.705151i
\(363\) −19.0526 −1.00000
\(364\) 0 0
\(365\) 0 0
\(366\) −30.0000 + 23.2379i −1.56813 + 1.21466i
\(367\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(368\) −17.3205 + 31.3050i −0.902894 + 1.63188i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 25.9808 + 6.70820i 1.34704 + 0.347804i
\(373\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(374\) 0 0
\(375\) 19.3649i 1.00000i
\(376\) −10.0000 23.2379i −0.515711 1.19840i
\(377\) 0 0
\(378\) 0 0
\(379\) −4.00000 −0.205466 −0.102733 0.994709i \(-0.532759\pi\)
−0.102733 + 0.994709i \(0.532759\pi\)
\(380\) −17.3205 4.47214i −0.888523 0.229416i
\(381\) 0 0
\(382\) 0 0
\(383\) 8.94427i 0.457031i 0.973540 + 0.228515i \(0.0733872\pi\)
−0.973540 + 0.228515i \(0.926613\pi\)
\(384\) −19.5000 1.93649i −0.995105 0.0988212i
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(390\) 0 0
\(391\) 61.9677i 3.13384i
\(392\) 18.1865 7.82624i 0.918559 0.395285i
\(393\) 0 0
\(394\) −5.00000 + 3.87298i −0.251896 + 0.195118i
\(395\) 17.3205 0.871489
\(396\) 0 0
\(397\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(398\) 25.9808 20.1246i 1.30230 1.00876i
\(399\) 0 0
\(400\) 17.5000 + 9.68246i 0.875000 + 0.484123i
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 20.1246i 1.00000i
\(406\) 0 0
\(407\) 0 0
\(408\) 31.1769 13.4164i 1.54349 0.664211i
\(409\) 26.0000 1.28562 0.642809 0.766027i \(-0.277769\pi\)
0.642809 + 0.766027i \(0.277769\pi\)
\(410\) 0 0
\(411\) 12.0000 0.591916
\(412\) 0 0
\(413\) 0 0
\(414\) 30.0000 23.2379i 1.47442 1.14208i
\(415\) 7.74597i 0.380235i
\(416\) 0 0
\(417\) 6.92820 0.339276
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) 15.4919i 0.755031i 0.926003 + 0.377515i \(0.123221\pi\)
−0.926003 + 0.377515i \(0.876779\pi\)
\(422\) −24.2487 31.3050i −1.18041 1.52390i
\(423\) 26.8328i 1.30466i
\(424\) 5.00000 + 11.6190i 0.242821 + 0.564266i
\(425\) −34.6410 −1.68034
\(426\) 0 0
\(427\) 0 0
\(428\) −5.19615 + 20.1246i −0.251166 + 0.972760i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 18.1865 + 10.0623i 0.875000 + 0.484123i
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 30.0000 + 7.74597i 1.43674 + 0.370965i
\(437\) 35.7771i 1.71145i
\(438\) 0 0
\(439\) 38.7298i 1.84847i 0.381819 + 0.924237i \(0.375298\pi\)
−0.381819 + 0.924237i \(0.624702\pi\)
\(440\) 0 0
\(441\) −21.0000 −1.00000
\(442\) 0 0
\(443\) 38.1051 1.81043 0.905214 0.424955i \(-0.139710\pi\)
0.905214 + 0.424955i \(0.139710\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) −12.9904 16.7705i −0.612372 0.790569i
\(451\) 0 0
\(452\) 10.3923 40.2492i 0.488813 1.89316i
\(453\) 40.2492i 1.89107i
\(454\) −21.0000 27.1109i −0.985579 1.27238i
\(455\) 0 0
\(456\) 18.0000 7.74597i 0.842927 0.362738i
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) −17.3205 + 13.4164i −0.809334 + 0.626908i
\(459\) −36.0000 −1.68034
\(460\) −10.0000 + 38.7298i −0.466252 + 1.80579i
\(461\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(464\) 0 0
\(465\) 30.0000 1.39122
\(466\) 18.0000 + 23.2379i 0.833834 + 1.07647i
\(467\) 24.2487 1.12210 0.561048 0.827783i \(-0.310398\pi\)
0.561048 + 0.827783i \(0.310398\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −17.3205 22.3607i −0.798935 1.03142i
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) −15.0000 + 11.6190i −0.688973 + 0.533676i
\(475\) −20.0000 −0.917663
\(476\) 0 0
\(477\) 13.4164i 0.614295i
\(478\) 0 0
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) −21.6506 + 3.35410i −0.988212 + 0.153093i
\(481\) 0 0
\(482\) −1.73205 2.23607i −0.0788928 0.101850i
\(483\) 0 0
\(484\) −5.50000 + 21.3014i −0.250000 + 0.968246i
\(485\) 0 0
\(486\) −13.5000 17.4284i −0.612372 0.790569i
\(487\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(488\) 17.3205 + 40.2492i 0.784063 + 1.82200i
\(489\) 0 0
\(490\) 17.5000 13.5554i 0.790569 0.612372i
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 15.0000 27.1109i 0.673520 1.21731i
\(497\) 0 0
\(498\) −5.19615 6.70820i −0.232845 0.300602i
\(499\) −44.0000 −1.96971 −0.984855 0.173379i \(-0.944532\pi\)
−0.984855 + 0.173379i \(0.944532\pi\)
\(500\) 21.6506 + 5.59017i 0.968246 + 0.250000i
\(501\) 15.4919i 0.692129i
\(502\) 0 0
\(503\) 44.7214i 1.99403i −0.0772283 0.997013i \(-0.524607\pi\)
0.0772283 0.997013i \(-0.475393\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 22.5167 1.00000
\(508\) 0 0
\(509\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(510\) 30.0000 23.2379i 1.32842 1.02899i
\(511\) 0 0
\(512\) −7.79423 + 21.2426i −0.344459 + 0.938801i
\(513\) −20.7846 −0.917663
\(514\) 6.00000 + 7.74597i 0.264649 + 0.341660i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 38.7298i 1.70005i
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 10.0000 7.74597i 0.436021 0.337740i
\(527\) 53.6656i 2.33771i
\(528\) 0 0
\(529\) −57.0000 −2.47826
\(530\) 8.66025 + 11.1803i 0.376177 + 0.485643i
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 23.2379i 1.00466i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 22.5000 + 5.80948i 0.968246 + 0.250000i
\(541\) 46.4758i 1.99815i 0.0429934 + 0.999075i \(0.486311\pi\)
−0.0429934 + 0.999075i \(0.513689\pi\)
\(542\) 8.66025 6.70820i 0.371990 0.288142i
\(543\) 26.8328i 1.15151i
\(544\) −6.00000 38.7298i −0.257248 1.66053i
\(545\) 34.6410 1.48386
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 3.46410 13.4164i 0.147979 0.573121i
\(549\) 46.4758i 1.98354i
\(550\) 0 0
\(551\) 0 0
\(552\) −17.3205 40.2492i −0.737210 1.71312i
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 2.00000 7.74597i 0.0848189 0.328502i
\(557\) 22.3607i 0.947452i 0.880672 + 0.473726i \(0.157091\pi\)
−0.880672 + 0.473726i \(0.842909\pi\)
\(558\) −25.9808 + 20.1246i −1.09985 + 0.851943i
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −31.1769 −1.31395 −0.656975 0.753912i \(-0.728164\pi\)
−0.656975 + 0.753912i \(0.728164\pi\)
\(564\) 30.0000 + 7.74597i 1.26323 + 0.326164i
\(565\) 46.4758i 1.95525i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 17.3205 13.4164i 0.725476 0.561951i
\(571\) 28.0000 1.17176 0.585882 0.810397i \(-0.300748\pi\)
0.585882 + 0.810397i \(0.300748\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 44.7214i 1.86501i
\(576\) 16.5000 17.4284i 0.687500 0.726184i
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) 26.8468 + 34.6591i 1.11668 + 1.44163i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) −35.0000 + 27.1109i −1.44584 + 1.11994i
\(587\) −45.0333 −1.85872 −0.929362 0.369170i \(-0.879642\pi\)
−0.929362 + 0.369170i \(0.879642\pi\)
\(588\) −6.06218 + 23.4787i −0.250000 + 0.968246i
\(589\) 30.9839i 1.27667i
\(590\) 0 0
\(591\) 7.74597i 0.318626i
\(592\) 0 0
\(593\) −48.4974 −1.99155 −0.995775 0.0918243i \(-0.970730\pi\)
−0.995775 + 0.0918243i \(0.970730\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 40.2492i 1.64729i
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) −22.5000 + 9.68246i −0.918559 + 0.395285i
\(601\) −38.0000 −1.55005 −0.775026 0.631929i \(-0.782263\pi\)
−0.775026 + 0.631929i \(0.782263\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −45.0000 11.6190i −1.83102 0.472768i
\(605\) 24.5967i 1.00000i
\(606\) 0 0
\(607\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(608\) −3.46410 22.3607i −0.140488 0.906845i
\(609\) 0 0
\(610\) 30.0000 + 38.7298i 1.21466 + 1.56813i
\(611\) 0 0
\(612\) −10.3923 + 40.2492i −0.420084 + 1.62698i
\(613\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −6.92820 −0.278919 −0.139459 0.990228i \(-0.544536\pi\)
−0.139459 + 0.990228i \(0.544536\pi\)
\(618\) 0 0
\(619\) 44.0000 1.76851 0.884255 0.467005i \(-0.154667\pi\)
0.884255 + 0.467005i \(0.154667\pi\)
\(620\) 8.66025 33.5410i 0.347804 1.34704i
\(621\) 46.4758i 1.86501i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 25.0000 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 38.7298i 1.54181i 0.636950 + 0.770905i \(0.280196\pi\)
−0.636950 + 0.770905i \(0.719804\pi\)
\(632\) 8.66025 + 20.1246i 0.344486 + 0.800514i
\(633\) 48.4974 1.92760
\(634\) 25.0000 19.3649i 0.992877 0.769079i
\(635\) 0 0
\(636\) −15.0000 3.87298i −0.594789 0.153574i
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) −2.50000 + 25.1744i −0.0988212 + 0.995105i
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) −15.5885 20.1246i −0.615227 0.794255i
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 24.0000 + 30.9839i 0.944267 + 1.21904i
\(647\) 44.7214i 1.75818i −0.476658 0.879089i \(-0.658152\pi\)
0.476658 0.879089i \(-0.341848\pi\)
\(648\) −23.3827 + 10.0623i −0.918559 + 0.395285i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 49.1935i 1.92509i −0.271122 0.962545i \(-0.587395\pi\)
0.271122 0.962545i \(-0.412605\pi\)
\(654\) −30.0000 + 23.2379i −1.17309 + 0.908674i
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 46.4758i 1.80770i −0.427850 0.903850i \(-0.640729\pi\)
0.427850 0.903850i \(-0.359271\pi\)
\(662\) 24.2487 + 31.3050i 0.942453 + 1.21670i
\(663\) 0 0
\(664\) −9.00000 + 3.87298i −0.349268 + 0.150301i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 17.3205 + 4.47214i 0.670151 + 0.173032i
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) 25.9808 1.00000
\(676\) 6.50000 25.1744i 0.250000 0.968246i
\(677\) 31.3050i 1.20315i 0.798817 + 0.601574i \(0.205459\pi\)
−0.798817 + 0.601574i \(0.794541\pi\)
\(678\) 31.1769 + 40.2492i 1.19734 + 1.54576i
\(679\) 0 0
\(680\) −17.3205 40.2492i −0.664211 1.54349i
\(681\) 42.0000 1.60944
\(682\) 0 0
\(683\) −38.1051 −1.45805 −0.729026 0.684486i \(-0.760027\pi\)
−0.729026 + 0.684486i \(0.760027\pi\)
\(684\) −6.00000 + 23.2379i −0.229416 + 0.888523i
\(685\) 15.4919i 0.591916i
\(686\) 0 0
\(687\) 26.8328i 1.02374i
\(688\) 0 0
\(689\) 0 0
\(690\) −30.0000 38.7298i −1.14208 1.47442i
\(691\) 52.0000 1.97817 0.989087 0.147335i \(-0.0470696\pi\)
0.989087 + 0.147335i \(0.0470696\pi\)
\(692\) −43.3013 11.1803i −1.64607 0.425013i
\(693\) 0 0
\(694\) −9.00000 11.6190i −0.341635 0.441049i
\(695\) 8.94427i 0.339276i
\(696\) 0 0
\(697\) 0 0
\(698\) 17.3205 13.4164i 0.655591 0.507819i
\(699\) −36.0000 −1.36165
\(700\) 0 0
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 34.6410 1.30466
\(706\) −18.0000 23.2379i −0.677439 0.874570i
\(707\) 0 0
\(708\) 0 0
\(709\) 46.4758i 1.74544i −0.488225 0.872718i \(-0.662356\pi\)
0.488225 0.872718i \(-0.337644\pi\)
\(710\) 0 0
\(711\) 23.2379i 0.871489i
\(712\) 0 0
\(713\) 69.2820 2.59463
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 12.9904 23.4787i 0.484123 0.875000i
\(721\) 0 0
\(722\) −2.59808 3.35410i −0.0966904 0.124827i
\(723\) 3.46410 0.128831
\(724\) −30.0000 7.74597i −1.11494 0.287877i
\(725\) 0 0
\(726\) −16.5000 21.3014i −0.612372 0.790569i
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 0 0
\(729\) 27.0000 1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) −51.9615 13.4164i −1.92055 0.495885i
\(733\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(734\) 0 0
\(735\) 27.1109i 1.00000i
\(736\) −50.0000 + 7.74597i −1.84302 + 0.285520i
\(737\) 0 0
\(738\) 0 0
\(739\) 4.00000 0.147142 0.0735712 0.997290i \(-0.476560\pi\)
0.0735712 + 0.997290i \(0.476560\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 44.7214i 1.64067i −0.571885 0.820334i \(-0.693788\pi\)
0.571885 0.820334i \(-0.306212\pi\)
\(744\) 15.0000 + 34.8569i 0.549927 + 1.27791i
\(745\) 0 0
\(746\) 0 0
\(747\) 10.3923 0.380235
\(748\) 0 0
\(749\) 0 0
\(750\) −21.6506 + 16.7705i −0.790569 + 0.612372i
\(751\) 54.2218i 1.97858i −0.145962 0.989290i \(-0.546628\pi\)
0.145962 0.989290i \(-0.453372\pi\)
\(752\) 17.3205 31.3050i 0.631614 1.14157i
\(753\) 0 0
\(754\) 0 0
\(755\) −51.9615 −1.89107
\(756\) 0 0
\(757\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(758\) −3.46410 4.47214i −0.125822 0.162435i
\(759\) 0 0
\(760\) −10.0000 23.2379i −0.362738 0.842927i
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 46.4758i 1.68034i
\(766\) −10.0000 + 7.74597i −0.361315 + 0.279873i
\(767\) 0 0
\(768\) −14.7224 23.4787i −0.531250 0.847215i
\(769\) 46.0000 1.65880 0.829401 0.558653i \(-0.188682\pi\)
0.829401 + 0.558653i \(0.188682\pi\)
\(770\) 0 0
\(771\) −12.0000 −0.432169
\(772\) 0 0
\(773\) 4.47214i 0.160852i 0.996761 + 0.0804258i \(0.0256280\pi\)
−0.996761 + 0.0804258i \(0.974372\pi\)
\(774\) 0 0
\(775\) 38.7298i 1.39122i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 69.2820 53.6656i 2.47752 1.91908i
\(783\) 0 0
\(784\) 24.5000 + 13.5554i 0.875000 + 0.484123i
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) −8.66025 2.23607i −0.308509 0.0796566i
\(789\) 15.4919i 0.551527i
\(790\) 15.0000 + 19.3649i 0.533676 + 0.688973i
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) −17.3205 −0.614295
\(796\) 45.0000 + 11.6190i 1.59498 + 0.411823i
\(797\) 49.1935i 1.74252i 0.490819 + 0.871262i \(0.336698\pi\)
−0.490819 + 0.871262i \(0.663302\pi\)
\(798\) 0 0
\(799\) 61.9677i 2.19226i
\(800\) 4.33013