Properties

Label 1287.2.b.c.298.3
Level $1287$
Weight $2$
Character 1287.298
Analytic conductor $10.277$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1287 = 3^{2} \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1287.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.2767467401\)
Analytic rank: \(0\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} + \cdots)\)
Defining polynomial: \(x^{14} + 23 x^{12} + 201 x^{10} + 835 x^{8} + 1695 x^{6} + 1565 x^{4} + 511 x^{2} + 49\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: no (minimal twist has level 429)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 298.3
Root \(-2.15754i\) of defining polynomial
Character \(\chi\) \(=\) 1287.298
Dual form 1287.2.b.c.298.12

$q$-expansion

\(f(q)\) \(=\) \(q-2.15754i q^{2} -2.65498 q^{4} +0.710210i q^{5} +2.30964i q^{7} +1.41315i q^{8} +O(q^{10})\) \(q-2.15754i q^{2} -2.65498 q^{4} +0.710210i q^{5} +2.30964i q^{7} +1.41315i q^{8} +1.53231 q^{10} -1.00000i q^{11} +(-1.40848 + 3.31906i) q^{13} +4.98315 q^{14} -2.26104 q^{16} -6.68027 q^{17} +0.242517i q^{19} -1.88559i q^{20} -2.15754 q^{22} +9.53531 q^{23} +4.49560 q^{25} +(7.16101 + 3.03885i) q^{26} -6.13206i q^{28} +2.95273 q^{29} +4.02017i q^{31} +7.70458i q^{32} +14.4130i q^{34} -1.64033 q^{35} +3.42304i q^{37} +0.523240 q^{38} -1.00363 q^{40} +9.46022i q^{41} +11.8791 q^{43} +2.65498i q^{44} -20.5728i q^{46} +12.9178i q^{47} +1.66555 q^{49} -9.69944i q^{50} +(3.73948 - 8.81205i) q^{52} -6.78954 q^{53} +0.710210 q^{55} -3.26386 q^{56} -6.37063i q^{58} -7.81320i q^{59} +0.910585 q^{61} +8.67368 q^{62} +12.1009 q^{64} +(-2.35723 - 1.00032i) q^{65} -9.32216i q^{67} +17.7360 q^{68} +3.53908i q^{70} +12.9704i q^{71} +8.51665i q^{73} +7.38534 q^{74} -0.643877i q^{76} +2.30964 q^{77} +1.82360 q^{79} -1.60581i q^{80} +20.4108 q^{82} +4.64671i q^{83} -4.74440i q^{85} -25.6297i q^{86} +1.41315 q^{88} -14.7714i q^{89} +(-7.66585 - 3.25308i) q^{91} -25.3161 q^{92} +27.8707 q^{94} -0.172238 q^{95} -1.86542i q^{97} -3.59349i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 18q^{4} + O(q^{10}) \) \( 14q - 18q^{4} - 16q^{14} + 34q^{16} - 4q^{17} + 6q^{22} + 8q^{23} - 26q^{25} + 6q^{26} + 24q^{29} + 8q^{35} + 32q^{38} - 20q^{40} + 32q^{43} - 46q^{49} + 4q^{52} - 20q^{53} + 12q^{55} + 32q^{56} - 20q^{61} - 72q^{62} - 58q^{64} - 12q^{65} + 20q^{68} + 12q^{77} + 12q^{79} + 20q^{82} - 30q^{88} + 16q^{91} + 24q^{92} + 64q^{94} + 36q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1287\mathbb{Z}\right)^\times\).

\(n\) \(496\) \(937\) \(1145\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.15754i 1.52561i −0.646628 0.762806i \(-0.723821\pi\)
0.646628 0.762806i \(-0.276179\pi\)
\(3\) 0 0
\(4\) −2.65498 −1.32749
\(5\) 0.710210i 0.317616i 0.987310 + 0.158808i \(0.0507650\pi\)
−0.987310 + 0.158808i \(0.949235\pi\)
\(6\) 0 0
\(7\) 2.30964i 0.872963i 0.899713 + 0.436482i \(0.143776\pi\)
−0.899713 + 0.436482i \(0.856224\pi\)
\(8\) 1.41315i 0.499622i
\(9\) 0 0
\(10\) 1.53231 0.484558
\(11\) 1.00000i 0.301511i
\(12\) 0 0
\(13\) −1.40848 + 3.31906i −0.390642 + 0.920543i
\(14\) 4.98315 1.33180
\(15\) 0 0
\(16\) −2.26104 −0.565261
\(17\) −6.68027 −1.62020 −0.810102 0.586289i \(-0.800588\pi\)
−0.810102 + 0.586289i \(0.800588\pi\)
\(18\) 0 0
\(19\) 0.242517i 0.0556372i 0.999613 + 0.0278186i \(0.00885607\pi\)
−0.999613 + 0.0278186i \(0.991144\pi\)
\(20\) 1.88559i 0.421631i
\(21\) 0 0
\(22\) −2.15754 −0.459989
\(23\) 9.53531 1.98825 0.994125 0.108242i \(-0.0345220\pi\)
0.994125 + 0.108242i \(0.0345220\pi\)
\(24\) 0 0
\(25\) 4.49560 0.899120
\(26\) 7.16101 + 3.03885i 1.40439 + 0.595968i
\(27\) 0 0
\(28\) 6.13206i 1.15885i
\(29\) 2.95273 0.548308 0.274154 0.961686i \(-0.411602\pi\)
0.274154 + 0.961686i \(0.411602\pi\)
\(30\) 0 0
\(31\) 4.02017i 0.722044i 0.932557 + 0.361022i \(0.117572\pi\)
−0.932557 + 0.361022i \(0.882428\pi\)
\(32\) 7.70458i 1.36199i
\(33\) 0 0
\(34\) 14.4130i 2.47180i
\(35\) −1.64033 −0.277267
\(36\) 0 0
\(37\) 3.42304i 0.562744i 0.959599 + 0.281372i \(0.0907895\pi\)
−0.959599 + 0.281372i \(0.909211\pi\)
\(38\) 0.523240 0.0848807
\(39\) 0 0
\(40\) −1.00363 −0.158688
\(41\) 9.46022i 1.47744i 0.674013 + 0.738719i \(0.264569\pi\)
−0.674013 + 0.738719i \(0.735431\pi\)
\(42\) 0 0
\(43\) 11.8791 1.81155 0.905776 0.423757i \(-0.139289\pi\)
0.905776 + 0.423757i \(0.139289\pi\)
\(44\) 2.65498i 0.400253i
\(45\) 0 0
\(46\) 20.5728i 3.03330i
\(47\) 12.9178i 1.88426i 0.335249 + 0.942130i \(0.391180\pi\)
−0.335249 + 0.942130i \(0.608820\pi\)
\(48\) 0 0
\(49\) 1.66555 0.237935
\(50\) 9.69944i 1.37171i
\(51\) 0 0
\(52\) 3.73948 8.81205i 0.518573 1.22201i
\(53\) −6.78954 −0.932615 −0.466307 0.884623i \(-0.654416\pi\)
−0.466307 + 0.884623i \(0.654416\pi\)
\(54\) 0 0
\(55\) 0.710210 0.0957647
\(56\) −3.26386 −0.436152
\(57\) 0 0
\(58\) 6.37063i 0.836504i
\(59\) 7.81320i 1.01719i −0.861005 0.508596i \(-0.830165\pi\)
0.861005 0.508596i \(-0.169835\pi\)
\(60\) 0 0
\(61\) 0.910585 0.116588 0.0582942 0.998299i \(-0.481434\pi\)
0.0582942 + 0.998299i \(0.481434\pi\)
\(62\) 8.67368 1.10156
\(63\) 0 0
\(64\) 12.1009 1.51261
\(65\) −2.35723 1.00032i −0.292379 0.124074i
\(66\) 0 0
\(67\) 9.32216i 1.13888i −0.822032 0.569442i \(-0.807159\pi\)
0.822032 0.569442i \(-0.192841\pi\)
\(68\) 17.7360 2.15080
\(69\) 0 0
\(70\) 3.53908i 0.423001i
\(71\) 12.9704i 1.53930i 0.638466 + 0.769650i \(0.279569\pi\)
−0.638466 + 0.769650i \(0.720431\pi\)
\(72\) 0 0
\(73\) 8.51665i 0.996798i 0.866948 + 0.498399i \(0.166079\pi\)
−0.866948 + 0.498399i \(0.833921\pi\)
\(74\) 7.38534 0.858529
\(75\) 0 0
\(76\) 0.643877i 0.0738578i
\(77\) 2.30964 0.263208
\(78\) 0 0
\(79\) 1.82360 0.205172 0.102586 0.994724i \(-0.467288\pi\)
0.102586 + 0.994724i \(0.467288\pi\)
\(80\) 1.60581i 0.179536i
\(81\) 0 0
\(82\) 20.4108 2.25400
\(83\) 4.64671i 0.510042i 0.966935 + 0.255021i \(0.0820824\pi\)
−0.966935 + 0.255021i \(0.917918\pi\)
\(84\) 0 0
\(85\) 4.74440i 0.514602i
\(86\) 25.6297i 2.76372i
\(87\) 0 0
\(88\) 1.41315 0.150642
\(89\) 14.7714i 1.56576i −0.622171 0.782881i \(-0.713749\pi\)
0.622171 0.782881i \(-0.286251\pi\)
\(90\) 0 0
\(91\) −7.66585 3.25308i −0.803600 0.341016i
\(92\) −25.3161 −2.63938
\(93\) 0 0
\(94\) 27.8707 2.87465
\(95\) −0.172238 −0.0176712
\(96\) 0 0
\(97\) 1.86542i 0.189405i −0.995506 0.0947025i \(-0.969810\pi\)
0.995506 0.0947025i \(-0.0301900\pi\)
\(98\) 3.59349i 0.362997i
\(99\) 0 0
\(100\) −11.9357 −1.19357
\(101\) −2.45086 −0.243870 −0.121935 0.992538i \(-0.538910\pi\)
−0.121935 + 0.992538i \(0.538910\pi\)
\(102\) 0 0
\(103\) −10.2811 −1.01302 −0.506512 0.862233i \(-0.669066\pi\)
−0.506512 + 0.862233i \(0.669066\pi\)
\(104\) −4.69032 1.99039i −0.459924 0.195173i
\(105\) 0 0
\(106\) 14.6487i 1.42281i
\(107\) −19.6690 −1.90148 −0.950739 0.309993i \(-0.899673\pi\)
−0.950739 + 0.309993i \(0.899673\pi\)
\(108\) 0 0
\(109\) 1.27506i 0.122128i −0.998134 0.0610642i \(-0.980551\pi\)
0.998134 0.0610642i \(-0.0194494\pi\)
\(110\) 1.53231i 0.146100i
\(111\) 0 0
\(112\) 5.22220i 0.493452i
\(113\) 0.638739 0.0600875 0.0300438 0.999549i \(-0.490435\pi\)
0.0300438 + 0.999549i \(0.490435\pi\)
\(114\) 0 0
\(115\) 6.77207i 0.631499i
\(116\) −7.83943 −0.727873
\(117\) 0 0
\(118\) −16.8573 −1.55184
\(119\) 15.4290i 1.41438i
\(120\) 0 0
\(121\) −1.00000 −0.0909091
\(122\) 1.96462i 0.177869i
\(123\) 0 0
\(124\) 10.6735i 0.958506i
\(125\) 6.74387i 0.603190i
\(126\) 0 0
\(127\) −10.3681 −0.920021 −0.460010 0.887914i \(-0.652154\pi\)
−0.460010 + 0.887914i \(0.652154\pi\)
\(128\) 10.6989i 0.945660i
\(129\) 0 0
\(130\) −2.15822 + 5.08582i −0.189289 + 0.446056i
\(131\) 5.68692 0.496868 0.248434 0.968649i \(-0.420084\pi\)
0.248434 + 0.968649i \(0.420084\pi\)
\(132\) 0 0
\(133\) −0.560127 −0.0485692
\(134\) −20.1129 −1.73749
\(135\) 0 0
\(136\) 9.44019i 0.809490i
\(137\) 4.86363i 0.415528i −0.978179 0.207764i \(-0.933381\pi\)
0.978179 0.207764i \(-0.0666186\pi\)
\(138\) 0 0
\(139\) −4.41515 −0.374488 −0.187244 0.982313i \(-0.559956\pi\)
−0.187244 + 0.982313i \(0.559956\pi\)
\(140\) 4.35505 0.368069
\(141\) 0 0
\(142\) 27.9841 2.34837
\(143\) 3.31906 + 1.40848i 0.277554 + 0.117783i
\(144\) 0 0
\(145\) 2.09706i 0.174151i
\(146\) 18.3750 1.52073
\(147\) 0 0
\(148\) 9.08810i 0.747037i
\(149\) 9.50356i 0.778562i 0.921119 + 0.389281i \(0.127276\pi\)
−0.921119 + 0.389281i \(0.872724\pi\)
\(150\) 0 0
\(151\) 15.2126i 1.23798i 0.785398 + 0.618991i \(0.212458\pi\)
−0.785398 + 0.618991i \(0.787542\pi\)
\(152\) −0.342711 −0.0277976
\(153\) 0 0
\(154\) 4.98315i 0.401554i
\(155\) −2.85516 −0.229332
\(156\) 0 0
\(157\) 20.1949 1.61173 0.805866 0.592098i \(-0.201700\pi\)
0.805866 + 0.592098i \(0.201700\pi\)
\(158\) 3.93450i 0.313012i
\(159\) 0 0
\(160\) −5.47187 −0.432589
\(161\) 22.0232i 1.73567i
\(162\) 0 0
\(163\) 16.4974i 1.29217i −0.763264 0.646087i \(-0.776404\pi\)
0.763264 0.646087i \(-0.223596\pi\)
\(164\) 25.1167i 1.96129i
\(165\) 0 0
\(166\) 10.0255 0.778126
\(167\) 5.50507i 0.425995i 0.977053 + 0.212998i \(0.0683226\pi\)
−0.977053 + 0.212998i \(0.931677\pi\)
\(168\) 0 0
\(169\) −9.03237 9.34967i −0.694798 0.719205i
\(170\) −10.2362 −0.785082
\(171\) 0 0
\(172\) −31.5389 −2.40482
\(173\) −12.7126 −0.966524 −0.483262 0.875476i \(-0.660548\pi\)
−0.483262 + 0.875476i \(0.660548\pi\)
\(174\) 0 0
\(175\) 10.3832i 0.784899i
\(176\) 2.26104i 0.170432i
\(177\) 0 0
\(178\) −31.8698 −2.38875
\(179\) 24.4279 1.82583 0.912913 0.408154i \(-0.133828\pi\)
0.912913 + 0.408154i \(0.133828\pi\)
\(180\) 0 0
\(181\) −0.931324 −0.0692248 −0.0346124 0.999401i \(-0.511020\pi\)
−0.0346124 + 0.999401i \(0.511020\pi\)
\(182\) −7.01866 + 16.5394i −0.520258 + 1.22598i
\(183\) 0 0
\(184\) 13.4748i 0.993374i
\(185\) −2.43108 −0.178736
\(186\) 0 0
\(187\) 6.68027i 0.488510i
\(188\) 34.2966i 2.50134i
\(189\) 0 0
\(190\) 0.371610i 0.0269594i
\(191\) −4.68209 −0.338784 −0.169392 0.985549i \(-0.554180\pi\)
−0.169392 + 0.985549i \(0.554180\pi\)
\(192\) 0 0
\(193\) 10.2671i 0.739039i −0.929223 0.369520i \(-0.879522\pi\)
0.929223 0.369520i \(-0.120478\pi\)
\(194\) −4.02473 −0.288959
\(195\) 0 0
\(196\) −4.42200 −0.315857
\(197\) 11.5842i 0.825341i 0.910880 + 0.412671i \(0.135404\pi\)
−0.910880 + 0.412671i \(0.864596\pi\)
\(198\) 0 0
\(199\) −17.2330 −1.22162 −0.610808 0.791779i \(-0.709155\pi\)
−0.610808 + 0.791779i \(0.709155\pi\)
\(200\) 6.35294i 0.449221i
\(201\) 0 0
\(202\) 5.28783i 0.372050i
\(203\) 6.81975i 0.478652i
\(204\) 0 0
\(205\) −6.71875 −0.469258
\(206\) 22.1818i 1.54548i
\(207\) 0 0
\(208\) 3.18463 7.50454i 0.220814 0.520346i
\(209\) 0.242517 0.0167752
\(210\) 0 0
\(211\) −10.6905 −0.735967 −0.367983 0.929832i \(-0.619952\pi\)
−0.367983 + 0.929832i \(0.619952\pi\)
\(212\) 18.0261 1.23804
\(213\) 0 0
\(214\) 42.4367i 2.90092i
\(215\) 8.43668i 0.575377i
\(216\) 0 0
\(217\) −9.28516 −0.630318
\(218\) −2.75099 −0.186320
\(219\) 0 0
\(220\) −1.88559 −0.127127
\(221\) 9.40902 22.1722i 0.632919 1.49147i
\(222\) 0 0
\(223\) 5.33992i 0.357587i 0.983887 + 0.178794i \(0.0572194\pi\)
−0.983887 + 0.178794i \(0.942781\pi\)
\(224\) −17.7948 −1.18897
\(225\) 0 0
\(226\) 1.37811i 0.0916702i
\(227\) 7.82431i 0.519318i −0.965700 0.259659i \(-0.916390\pi\)
0.965700 0.259659i \(-0.0836101\pi\)
\(228\) 0 0
\(229\) 10.6805i 0.705784i −0.935664 0.352892i \(-0.885198\pi\)
0.935664 0.352892i \(-0.114802\pi\)
\(230\) 14.6110 0.963422
\(231\) 0 0
\(232\) 4.17263i 0.273947i
\(233\) 15.4509 1.01222 0.506112 0.862468i \(-0.331082\pi\)
0.506112 + 0.862468i \(0.331082\pi\)
\(234\) 0 0
\(235\) −9.17437 −0.598470
\(236\) 20.7439i 1.35031i
\(237\) 0 0
\(238\) −33.2888 −2.15779
\(239\) 16.9365i 1.09553i −0.836632 0.547765i \(-0.815479\pi\)
0.836632 0.547765i \(-0.184521\pi\)
\(240\) 0 0
\(241\) 0.0799646i 0.00515098i −0.999997 0.00257549i \(-0.999180\pi\)
0.999997 0.00257549i \(-0.000819804\pi\)
\(242\) 2.15754i 0.138692i
\(243\) 0 0
\(244\) −2.41758 −0.154770
\(245\) 1.18289i 0.0755720i
\(246\) 0 0
\(247\) −0.804929 0.341580i −0.0512164 0.0217342i
\(248\) −5.68108 −0.360749
\(249\) 0 0
\(250\) 14.5502 0.920234
\(251\) −7.57174 −0.477924 −0.238962 0.971029i \(-0.576807\pi\)
−0.238962 + 0.971029i \(0.576807\pi\)
\(252\) 0 0
\(253\) 9.53531i 0.599480i
\(254\) 22.3696i 1.40359i
\(255\) 0 0
\(256\) 1.11835 0.0698970
\(257\) 23.0242 1.43621 0.718105 0.695935i \(-0.245010\pi\)
0.718105 + 0.695935i \(0.245010\pi\)
\(258\) 0 0
\(259\) −7.90600 −0.491255
\(260\) 6.25840 + 2.65582i 0.388130 + 0.164707i
\(261\) 0 0
\(262\) 12.2698i 0.758028i
\(263\) 5.95047 0.366922 0.183461 0.983027i \(-0.441270\pi\)
0.183461 + 0.983027i \(0.441270\pi\)
\(264\) 0 0
\(265\) 4.82200i 0.296213i
\(266\) 1.20850i 0.0740977i
\(267\) 0 0
\(268\) 24.7502i 1.51186i
\(269\) 1.17571 0.0716841 0.0358420 0.999357i \(-0.488589\pi\)
0.0358420 + 0.999357i \(0.488589\pi\)
\(270\) 0 0
\(271\) 7.12706i 0.432938i −0.976290 0.216469i \(-0.930546\pi\)
0.976290 0.216469i \(-0.0694540\pi\)
\(272\) 15.1044 0.915837
\(273\) 0 0
\(274\) −10.4935 −0.633934
\(275\) 4.49560i 0.271095i
\(276\) 0 0
\(277\) 11.9736 0.719426 0.359713 0.933063i \(-0.382875\pi\)
0.359713 + 0.933063i \(0.382875\pi\)
\(278\) 9.52586i 0.571323i
\(279\) 0 0
\(280\) 2.31803i 0.138529i
\(281\) 18.7901i 1.12092i −0.828181 0.560461i \(-0.810624\pi\)
0.828181 0.560461i \(-0.189376\pi\)
\(282\) 0 0
\(283\) −10.5237 −0.625568 −0.312784 0.949824i \(-0.601262\pi\)
−0.312784 + 0.949824i \(0.601262\pi\)
\(284\) 34.4361i 2.04341i
\(285\) 0 0
\(286\) 3.03885 7.16101i 0.179691 0.423440i
\(287\) −21.8497 −1.28975
\(288\) 0 0
\(289\) 27.6260 1.62506
\(290\) 4.52448 0.265687
\(291\) 0 0
\(292\) 22.6115i 1.32324i
\(293\) 14.0111i 0.818540i 0.912413 + 0.409270i \(0.134217\pi\)
−0.912413 + 0.409270i \(0.865783\pi\)
\(294\) 0 0
\(295\) 5.54901 0.323076
\(296\) −4.83725 −0.281159
\(297\) 0 0
\(298\) 20.5043 1.18778
\(299\) −13.4303 + 31.6483i −0.776693 + 1.83027i
\(300\) 0 0
\(301\) 27.4366i 1.58142i
\(302\) 32.8217 1.88868
\(303\) 0 0
\(304\) 0.548341i 0.0314495i
\(305\) 0.646706i 0.0370303i
\(306\) 0 0
\(307\) 2.52126i 0.143896i 0.997408 + 0.0719481i \(0.0229216\pi\)
−0.997408 + 0.0719481i \(0.977078\pi\)
\(308\) −6.13206 −0.349406
\(309\) 0 0
\(310\) 6.16013i 0.349872i
\(311\) −22.9380 −1.30069 −0.650347 0.759638i \(-0.725376\pi\)
−0.650347 + 0.759638i \(0.725376\pi\)
\(312\) 0 0
\(313\) −21.6566 −1.22410 −0.612051 0.790818i \(-0.709655\pi\)
−0.612051 + 0.790818i \(0.709655\pi\)
\(314\) 43.5714i 2.45888i
\(315\) 0 0
\(316\) −4.84163 −0.272363
\(317\) 26.6050i 1.49429i 0.664664 + 0.747143i \(0.268575\pi\)
−0.664664 + 0.747143i \(0.731425\pi\)
\(318\) 0 0
\(319\) 2.95273i 0.165321i
\(320\) 8.59415i 0.480428i
\(321\) 0 0
\(322\) 47.5159 2.64796
\(323\) 1.62008i 0.0901435i
\(324\) 0 0
\(325\) −6.33196 + 14.9212i −0.351234 + 0.827679i
\(326\) −35.5937 −1.97135
\(327\) 0 0
\(328\) −13.3687 −0.738161
\(329\) −29.8356 −1.64489
\(330\) 0 0
\(331\) 24.7670i 1.36132i 0.732600 + 0.680659i \(0.238307\pi\)
−0.732600 + 0.680659i \(0.761693\pi\)
\(332\) 12.3369i 0.677076i
\(333\) 0 0
\(334\) 11.8774 0.649903
\(335\) 6.62069 0.361727
\(336\) 0 0
\(337\) 28.2890 1.54100 0.770499 0.637441i \(-0.220007\pi\)
0.770499 + 0.637441i \(0.220007\pi\)
\(338\) −20.1723 + 19.4877i −1.09723 + 1.05999i
\(339\) 0 0
\(340\) 12.5963i 0.683129i
\(341\) 4.02017 0.217704
\(342\) 0 0
\(343\) 20.0143i 1.08067i
\(344\) 16.7869i 0.905091i
\(345\) 0 0
\(346\) 27.4280i 1.47454i
\(347\) 18.0814 0.970661 0.485331 0.874331i \(-0.338699\pi\)
0.485331 + 0.874331i \(0.338699\pi\)
\(348\) 0 0
\(349\) 21.0326i 1.12585i 0.826508 + 0.562924i \(0.190324\pi\)
−0.826508 + 0.562924i \(0.809676\pi\)
\(350\) 22.4022 1.19745
\(351\) 0 0
\(352\) 7.70458 0.410655
\(353\) 2.20127i 0.117162i 0.998283 + 0.0585810i \(0.0186576\pi\)
−0.998283 + 0.0585810i \(0.981342\pi\)
\(354\) 0 0
\(355\) −9.21169 −0.488906
\(356\) 39.2177i 2.07853i
\(357\) 0 0
\(358\) 52.7041i 2.78550i
\(359\) 7.76540i 0.409842i 0.978778 + 0.204921i \(0.0656938\pi\)
−0.978778 + 0.204921i \(0.934306\pi\)
\(360\) 0 0
\(361\) 18.9412 0.996905
\(362\) 2.00937i 0.105610i
\(363\) 0 0
\(364\) 20.3527 + 8.63687i 1.06677 + 0.452695i
\(365\) −6.04861 −0.316599
\(366\) 0 0
\(367\) −11.9604 −0.624326 −0.312163 0.950028i \(-0.601054\pi\)
−0.312163 + 0.950028i \(0.601054\pi\)
\(368\) −21.5597 −1.12388
\(369\) 0 0
\(370\) 5.24514i 0.272682i
\(371\) 15.6814i 0.814138i
\(372\) 0 0
\(373\) 14.1243 0.731330 0.365665 0.930747i \(-0.380842\pi\)
0.365665 + 0.930747i \(0.380842\pi\)
\(374\) 14.4130 0.745276
\(375\) 0 0
\(376\) −18.2548 −0.941418
\(377\) −4.15885 + 9.80029i −0.214192 + 0.504741i
\(378\) 0 0
\(379\) 3.34432i 0.171786i 0.996304 + 0.0858931i \(0.0273744\pi\)
−0.996304 + 0.0858931i \(0.972626\pi\)
\(380\) 0.457288 0.0234584
\(381\) 0 0
\(382\) 10.1018i 0.516853i
\(383\) 5.63621i 0.287997i −0.989578 0.143998i \(-0.954004\pi\)
0.989578 0.143998i \(-0.0459960\pi\)
\(384\) 0 0
\(385\) 1.64033i 0.0835991i
\(386\) −22.1516 −1.12749
\(387\) 0 0
\(388\) 4.95266i 0.251433i
\(389\) 14.3490 0.727523 0.363761 0.931492i \(-0.381492\pi\)
0.363761 + 0.931492i \(0.381492\pi\)
\(390\) 0 0
\(391\) −63.6984 −3.22137
\(392\) 2.35366i 0.118878i
\(393\) 0 0
\(394\) 24.9934 1.25915
\(395\) 1.29514i 0.0651657i
\(396\) 0 0
\(397\) 14.8769i 0.746648i −0.927701 0.373324i \(-0.878218\pi\)
0.927701 0.373324i \(-0.121782\pi\)
\(398\) 37.1809i 1.86371i
\(399\) 0 0
\(400\) −10.1647 −0.508237
\(401\) 19.6380i 0.980675i −0.871533 0.490337i \(-0.836874\pi\)
0.871533 0.490337i \(-0.163126\pi\)
\(402\) 0 0
\(403\) −13.3432 5.66233i −0.664672 0.282061i
\(404\) 6.50698 0.323734
\(405\) 0 0
\(406\) 14.7139 0.730237
\(407\) 3.42304 0.169674
\(408\) 0 0
\(409\) 23.1731i 1.14584i −0.819613 0.572918i \(-0.805811\pi\)
0.819613 0.572918i \(-0.194189\pi\)
\(410\) 14.4960i 0.715905i
\(411\) 0 0
\(412\) 27.2961 1.34478
\(413\) 18.0457 0.887971
\(414\) 0 0
\(415\) −3.30014 −0.161997
\(416\) −25.5720 10.8517i −1.25377 0.532050i
\(417\) 0 0
\(418\) 0.523240i 0.0255925i
\(419\) 3.70294 0.180900 0.0904502 0.995901i \(-0.471169\pi\)
0.0904502 + 0.995901i \(0.471169\pi\)
\(420\) 0 0
\(421\) 23.7239i 1.15623i −0.815955 0.578116i \(-0.803788\pi\)
0.815955 0.578116i \(-0.196212\pi\)
\(422\) 23.0653i 1.12280i
\(423\) 0 0
\(424\) 9.59460i 0.465955i
\(425\) −30.0318 −1.45676
\(426\) 0 0
\(427\) 2.10313i 0.101777i
\(428\) 52.2209 2.52419
\(429\) 0 0
\(430\) 18.2025 0.877802
\(431\) 31.0695i 1.49656i −0.663381 0.748282i \(-0.730879\pi\)
0.663381 0.748282i \(-0.269121\pi\)
\(432\) 0 0
\(433\) −23.0541 −1.10791 −0.553954 0.832547i \(-0.686882\pi\)
−0.553954 + 0.832547i \(0.686882\pi\)
\(434\) 20.0331i 0.961620i
\(435\) 0 0
\(436\) 3.38525i 0.162124i
\(437\) 2.31247i 0.110621i
\(438\) 0 0
\(439\) −2.39273 −0.114199 −0.0570994 0.998368i \(-0.518185\pi\)
−0.0570994 + 0.998368i \(0.518185\pi\)
\(440\) 1.00363i 0.0478462i
\(441\) 0 0
\(442\) −47.8375 20.3003i −2.27540 0.965589i
\(443\) 17.1624 0.815411 0.407705 0.913113i \(-0.366329\pi\)
0.407705 + 0.913113i \(0.366329\pi\)
\(444\) 0 0
\(445\) 10.4908 0.497311
\(446\) 11.5211 0.545539
\(447\) 0 0
\(448\) 27.9487i 1.32045i
\(449\) 29.0646i 1.37164i −0.727769 0.685822i \(-0.759443\pi\)
0.727769 0.685822i \(-0.240557\pi\)
\(450\) 0 0
\(451\) 9.46022 0.445465
\(452\) −1.69584 −0.0797656
\(453\) 0 0
\(454\) −16.8813 −0.792277
\(455\) 2.31037 5.44437i 0.108312 0.255236i
\(456\) 0 0
\(457\) 31.9111i 1.49274i 0.665532 + 0.746369i \(0.268205\pi\)
−0.665532 + 0.746369i \(0.731795\pi\)
\(458\) −23.0435 −1.07675
\(459\) 0 0
\(460\) 17.9797i 0.838308i
\(461\) 0.706685i 0.0329136i −0.999865 0.0164568i \(-0.994761\pi\)
0.999865 0.0164568i \(-0.00523860\pi\)
\(462\) 0 0
\(463\) 25.7813i 1.19816i 0.800690 + 0.599079i \(0.204467\pi\)
−0.800690 + 0.599079i \(0.795533\pi\)
\(464\) −6.67624 −0.309937
\(465\) 0 0
\(466\) 33.3360i 1.54426i
\(467\) 37.3541 1.72854 0.864270 0.503028i \(-0.167781\pi\)
0.864270 + 0.503028i \(0.167781\pi\)
\(468\) 0 0
\(469\) 21.5309 0.994203
\(470\) 19.7941i 0.913033i
\(471\) 0 0
\(472\) 11.0412 0.508212
\(473\) 11.8791i 0.546203i
\(474\) 0 0
\(475\) 1.09026i 0.0500245i
\(476\) 40.9638i 1.87757i
\(477\) 0 0
\(478\) −36.5411 −1.67135
\(479\) 1.74064i 0.0795318i −0.999209 0.0397659i \(-0.987339\pi\)
0.999209 0.0397659i \(-0.0126612\pi\)
\(480\) 0 0
\(481\) −11.3613 4.82128i −0.518030 0.219831i
\(482\) −0.172527 −0.00785839
\(483\) 0 0
\(484\) 2.65498 0.120681
\(485\) 1.32484 0.0601580
\(486\) 0 0
\(487\) 5.69783i 0.258193i −0.991632 0.129097i \(-0.958792\pi\)
0.991632 0.129097i \(-0.0412078\pi\)
\(488\) 1.28679i 0.0582502i
\(489\) 0 0
\(490\) 2.55213 0.115293
\(491\) −27.7388 −1.25183 −0.625917 0.779890i \(-0.715275\pi\)
−0.625917 + 0.779890i \(0.715275\pi\)
\(492\) 0 0
\(493\) −19.7250 −0.888370
\(494\) −0.736972 + 1.73667i −0.0331580 + 0.0781363i
\(495\) 0 0
\(496\) 9.08977i 0.408143i
\(497\) −29.9569 −1.34375
\(498\) 0 0
\(499\) 8.27073i 0.370249i −0.982715 0.185124i \(-0.940731\pi\)
0.982715 0.185124i \(-0.0592688\pi\)
\(500\) 17.9048i 0.800729i
\(501\) 0 0
\(502\) 16.3363i 0.729126i
\(503\) 12.7099 0.566706 0.283353 0.959016i \(-0.408553\pi\)
0.283353 + 0.959016i \(0.408553\pi\)
\(504\) 0 0
\(505\) 1.74062i 0.0774568i
\(506\) −20.5728 −0.914573
\(507\) 0 0
\(508\) 27.5271 1.22132
\(509\) 5.55978i 0.246433i 0.992380 + 0.123216i \(0.0393210\pi\)
−0.992380 + 0.123216i \(0.960679\pi\)
\(510\) 0 0
\(511\) −19.6704 −0.870168
\(512\) 23.8107i 1.05230i
\(513\) 0 0
\(514\) 49.6756i 2.19110i
\(515\) 7.30172i 0.321752i
\(516\) 0 0
\(517\) 12.9178 0.568126
\(518\) 17.0575i 0.749464i
\(519\) 0 0
\(520\) 1.41359 3.33111i 0.0619901 0.146079i
\(521\) 4.41425 0.193392 0.0966958 0.995314i \(-0.469173\pi\)
0.0966958 + 0.995314i \(0.469173\pi\)
\(522\) 0 0
\(523\) 15.5162 0.678474 0.339237 0.940701i \(-0.389831\pi\)
0.339237 + 0.940701i \(0.389831\pi\)
\(524\) −15.0986 −0.659587
\(525\) 0 0
\(526\) 12.8384i 0.559780i
\(527\) 26.8558i 1.16986i
\(528\) 0 0
\(529\) 67.9221 2.95314
\(530\) −10.4037 −0.451906
\(531\) 0 0
\(532\) 1.48713 0.0644751
\(533\) −31.3991 13.3245i −1.36005 0.577150i
\(534\) 0 0
\(535\) 13.9691i 0.603939i
\(536\) 13.1736 0.569011
\(537\) 0 0
\(538\) 2.53663i 0.109362i
\(539\) 1.66555i 0.0717402i
\(540\) 0 0
\(541\) 27.9827i 1.20307i −0.798846 0.601536i \(-0.794556\pi\)
0.798846 0.601536i \(-0.205444\pi\)
\(542\) −15.3769 −0.660495
\(543\) 0 0
\(544\) 51.4687i 2.20670i
\(545\) 0.905559 0.0387899
\(546\) 0 0
\(547\) −24.1470 −1.03245 −0.516226 0.856453i \(-0.672663\pi\)
−0.516226 + 0.856453i \(0.672663\pi\)
\(548\) 12.9128i 0.551609i
\(549\) 0 0
\(550\) −9.69944 −0.413586
\(551\) 0.716086i 0.0305063i
\(552\) 0 0
\(553\) 4.21188i 0.179107i
\(554\) 25.8336i 1.09756i
\(555\) 0 0
\(556\) 11.7221 0.497129
\(557\) 19.1326i 0.810675i −0.914167 0.405337i \(-0.867154\pi\)
0.914167 0.405337i \(-0.132846\pi\)
\(558\) 0 0
\(559\) −16.7315 + 39.4276i −0.707668 + 1.66761i
\(560\) 3.70886 0.156728
\(561\) 0 0
\(562\) −40.5404 −1.71009
\(563\) −3.91199 −0.164871 −0.0824353 0.996596i \(-0.526270\pi\)
−0.0824353 + 0.996596i \(0.526270\pi\)
\(564\) 0 0
\(565\) 0.453639i 0.0190847i
\(566\) 22.7053i 0.954373i
\(567\) 0 0
\(568\) −18.3290 −0.769069
\(569\) −15.8002 −0.662377 −0.331189 0.943565i \(-0.607450\pi\)
−0.331189 + 0.943565i \(0.607450\pi\)
\(570\) 0 0
\(571\) −20.2458 −0.847262 −0.423631 0.905835i \(-0.639245\pi\)
−0.423631 + 0.905835i \(0.639245\pi\)
\(572\) −8.81205 3.73948i −0.368450 0.156356i
\(573\) 0 0
\(574\) 47.1417i 1.96766i
\(575\) 42.8669 1.78768
\(576\) 0 0
\(577\) 7.07073i 0.294358i 0.989110 + 0.147179i \(0.0470194\pi\)
−0.989110 + 0.147179i \(0.952981\pi\)
\(578\) 59.6042i 2.47921i
\(579\) 0 0
\(580\) 5.56764i 0.231184i
\(581\) −10.7322 −0.445248
\(582\) 0 0
\(583\) 6.78954i 0.281194i
\(584\) −12.0353 −0.498023
\(585\) 0 0
\(586\) 30.2296 1.24877
\(587\) 27.1767i 1.12170i 0.827917 + 0.560851i \(0.189526\pi\)
−0.827917 + 0.560851i \(0.810474\pi\)
\(588\) 0 0
\(589\) −0.974959 −0.0401725
\(590\) 11.9722i 0.492889i
\(591\) 0 0
\(592\) 7.73963i 0.318097i
\(593\) 20.0431i 0.823070i −0.911394 0.411535i \(-0.864993\pi\)
0.911394 0.411535i \(-0.135007\pi\)
\(594\) 0 0
\(595\) 10.9579 0.449228
\(596\) 25.2318i 1.03353i
\(597\) 0 0
\(598\) 68.2825 + 28.9764i 2.79228 + 1.18493i
\(599\) 24.5855 1.00454 0.502268 0.864712i \(-0.332499\pi\)
0.502268 + 0.864712i \(0.332499\pi\)
\(600\) 0 0
\(601\) −34.1098 −1.39137 −0.695683 0.718349i \(-0.744898\pi\)
−0.695683 + 0.718349i \(0.744898\pi\)
\(602\) 59.1955 2.41263
\(603\) 0 0
\(604\) 40.3891i 1.64341i
\(605\) 0.710210i 0.0288741i
\(606\) 0 0
\(607\) 20.9453 0.850143 0.425071 0.905160i \(-0.360249\pi\)
0.425071 + 0.905160i \(0.360249\pi\)
\(608\) −1.86849 −0.0757773
\(609\) 0 0
\(610\) 1.39530 0.0564938
\(611\) −42.8751 18.1945i −1.73454 0.736071i
\(612\) 0 0
\(613\) 22.2792i 0.899848i 0.893067 + 0.449924i \(0.148549\pi\)
−0.893067 + 0.449924i \(0.851451\pi\)
\(614\) 5.43973 0.219530
\(615\) 0 0
\(616\) 3.26386i 0.131505i
\(617\) 27.4366i 1.10456i 0.833660 + 0.552279i \(0.186242\pi\)
−0.833660 + 0.552279i \(0.813758\pi\)
\(618\) 0 0
\(619\) 47.9288i 1.92642i −0.268747 0.963211i \(-0.586610\pi\)
0.268747 0.963211i \(-0.413390\pi\)
\(620\) 7.58040 0.304436
\(621\) 0 0
\(622\) 49.4896i 1.98435i
\(623\) 34.1166 1.36685
\(624\) 0 0
\(625\) 17.6884 0.707538
\(626\) 46.7250i 1.86751i
\(627\) 0 0
\(628\) −53.6171 −2.13956
\(629\) 22.8668i 0.911760i
\(630\) 0 0
\(631\) 23.8277i 0.948567i 0.880372 + 0.474284i \(0.157293\pi\)
−0.880372 + 0.474284i \(0.842707\pi\)
\(632\) 2.57702i 0.102508i
\(633\) 0 0
\(634\) 57.4013 2.27970
\(635\) 7.36353i 0.292213i
\(636\) 0 0
\(637\) −2.34589 + 5.52806i −0.0929475 + 0.219030i
\(638\) −6.37063 −0.252216
\(639\) 0 0
\(640\) 7.59848 0.300356
\(641\) −8.30355 −0.327970 −0.163985 0.986463i \(-0.552435\pi\)
−0.163985 + 0.986463i \(0.552435\pi\)
\(642\) 0 0
\(643\) 29.9185i 1.17987i −0.807451 0.589934i \(-0.799154\pi\)
0.807451 0.589934i \(-0.200846\pi\)
\(644\) 58.4710i 2.30408i
\(645\) 0 0
\(646\) −3.49538 −0.137524
\(647\) 5.87308 0.230895 0.115447 0.993314i \(-0.463170\pi\)
0.115447 + 0.993314i \(0.463170\pi\)
\(648\) 0 0
\(649\) −7.81320 −0.306695
\(650\) 32.1931 + 13.6615i 1.26272 + 0.535847i
\(651\) 0 0
\(652\) 43.8002i 1.71535i
\(653\) 5.43262 0.212595 0.106297 0.994334i \(-0.466100\pi\)
0.106297 + 0.994334i \(0.466100\pi\)
\(654\) 0 0
\(655\) 4.03891i 0.157813i
\(656\) 21.3900i 0.835138i
\(657\) 0 0
\(658\) 64.3715i 2.50946i
\(659\) −26.5954 −1.03601 −0.518004 0.855378i \(-0.673325\pi\)
−0.518004 + 0.855378i \(0.673325\pi\)
\(660\) 0 0
\(661\) 27.7763i 1.08037i −0.841545 0.540187i \(-0.818354\pi\)
0.841545 0.540187i \(-0.181646\pi\)
\(662\) 53.4359 2.07684
\(663\) 0 0
\(664\) −6.56647 −0.254828
\(665\) 0.397808i 0.0154263i
\(666\) 0 0
\(667\) 28.1552 1.09017
\(668\) 14.6158i 0.565504i
\(669\) 0 0
\(670\) 14.2844i 0.551855i
\(671\) 0.910585i 0.0351527i
\(672\) 0 0
\(673\) −3.00054 −0.115663 −0.0578313 0.998326i \(-0.518419\pi\)
−0.0578313 + 0.998326i \(0.518419\pi\)
\(674\) 61.0346i 2.35096i
\(675\) 0 0
\(676\) 23.9808 + 24.8232i 0.922337 + 0.954737i
\(677\) 25.1724 0.967452 0.483726 0.875219i \(-0.339283\pi\)
0.483726 + 0.875219i \(0.339283\pi\)
\(678\) 0 0
\(679\) 4.30846 0.165344
\(680\) 6.70452 0.257107
\(681\) 0 0
\(682\) 8.67368i 0.332132i
\(683\) 39.1652i 1.49861i −0.662223 0.749307i \(-0.730387\pi\)
0.662223 0.749307i \(-0.269613\pi\)
\(684\) 0 0
\(685\) 3.45420 0.131978
\(686\) 43.1817 1.64869
\(687\) 0 0
\(688\) −26.8592 −1.02400
\(689\) 9.56293 22.5349i 0.364318 0.858512i
\(690\) 0 0
\(691\) 33.3472i 1.26859i −0.773092 0.634294i \(-0.781291\pi\)
0.773092 0.634294i \(-0.218709\pi\)
\(692\) 33.7518 1.28305
\(693\) 0 0
\(694\) 39.0114i 1.48085i
\(695\) 3.13568i 0.118943i
\(696\) 0 0
\(697\) 63.1969i 2.39375i
\(698\) 45.3787 1.71761
\(699\) 0 0
\(700\) 27.5673i 1.04195i
\(701\) 8.45704 0.319418 0.159709 0.987164i \(-0.448944\pi\)
0.159709 + 0.987164i \(0.448944\pi\)
\(702\) 0 0
\(703\) −0.830144 −0.0313095
\(704\) 12.1009i 0.456068i
\(705\) 0 0
\(706\) 4.74934 0.178744
\(707\) 5.66061i 0.212889i
\(708\) 0 0
\(709\) 7.03783i 0.264311i −0.991229 0.132156i \(-0.957810\pi\)
0.991229 0.132156i \(-0.0421899\pi\)
\(710\) 19.8746i 0.745880i
\(711\) 0 0
\(712\) 20.8741 0.782290
\(713\) 38.3336i 1.43560i
\(714\) 0 0
\(715\) −1.00032 + 2.35723i −0.0374097 + 0.0881555i
\(716\) −64.8555 −2.42377
\(717\) 0 0
\(718\) 16.7542 0.625260
\(719\) −5.52947 −0.206215 −0.103107 0.994670i \(-0.532879\pi\)
−0.103107 + 0.994670i \(0.532879\pi\)
\(720\) 0 0
\(721\) 23.7456i 0.884333i
\(722\) 40.8664i 1.52089i
\(723\) 0 0
\(724\) 2.47265 0.0918952
\(725\) 13.2743 0.492995
\(726\) 0 0
\(727\) 38.7533 1.43728 0.718640 0.695383i \(-0.244765\pi\)
0.718640 + 0.695383i \(0.244765\pi\)
\(728\) 4.59708 10.8330i 0.170379 0.401496i
\(729\) 0 0
\(730\) 13.0501i 0.483006i
\(731\) −79.3558 −2.93508
\(732\) 0 0
\(733\) 9.60595i 0.354804i −0.984138 0.177402i \(-0.943231\pi\)
0.984138 0.177402i \(-0.0567693\pi\)
\(734\) 25.8050i 0.952480i
\(735\) 0 0
\(736\) 73.4655i 2.70798i
\(737\) −9.32216 −0.343386
\(738\) 0 0
\(739\) 21.6659i 0.796995i 0.917169 + 0.398497i \(0.130468\pi\)
−0.917169 + 0.398497i \(0.869532\pi\)
\(740\) 6.45446 0.237271
\(741\) 0 0
\(742\) −33.8333 −1.24206
\(743\) 12.3149i 0.451790i 0.974152 + 0.225895i \(0.0725305\pi\)
−0.974152 + 0.225895i \(0.927469\pi\)
\(744\) 0 0
\(745\) −6.74952 −0.247283
\(746\) 30.4738i 1.11572i
\(747\) 0 0
\(748\) 17.7360i 0.648492i
\(749\) 45.4285i 1.65992i
\(750\) 0 0
\(751\) −2.50813 −0.0915231 −0.0457616 0.998952i \(-0.514571\pi\)
−0.0457616 + 0.998952i \(0.514571\pi\)
\(752\) 29.2078i 1.06510i
\(753\) 0 0
\(754\) 21.1445 + 8.97290i 0.770038 + 0.326774i
\(755\) −10.8041 −0.393202
\(756\) 0 0
\(757\) 2.89889 0.105362 0.0526809 0.998611i \(-0.483223\pi\)
0.0526809 + 0.998611i \(0.483223\pi\)
\(758\) 7.21551 0.262079
\(759\) 0 0
\(760\) 0.243397i 0.00882894i
\(761\) 33.6764i 1.22077i 0.792105 + 0.610384i \(0.208985\pi\)
−0.792105 + 0.610384i \(0.791015\pi\)
\(762\) 0 0
\(763\) 2.94493 0.106614
\(764\) 12.4309 0.449733
\(765\) 0 0
\(766\) −12.1604 −0.439371
\(767\) 25.9325 + 11.0047i 0.936369 + 0.397358i
\(768\) 0 0
\(769\) 25.1224i 0.905935i −0.891527 0.452968i \(-0.850365\pi\)
0.891527 0.452968i \(-0.149635\pi\)
\(770\) 3.53908 0.127540
\(771\) 0 0
\(772\) 27.2588i 0.981067i
\(773\) 31.6336i 1.13778i 0.822413 + 0.568891i \(0.192627\pi\)
−0.822413 + 0.568891i \(0.807373\pi\)
\(774\) 0 0
\(775\) 18.0731i 0.649204i
\(776\) 2.63611 0.0946310
\(777\) 0 0
\(778\) 30.9585i 1.10992i
\(779\) −2.29426 −0.0822005
\(780\) 0 0
\(781\) 12.9704 0.464117
\(782\) 137.432i 4.91456i
\(783\) 0 0
\(784\) −3.76587 −0.134495
\(785\) 14.3426i 0.511911i
\(786\) 0 0
\(787\) 23.2041i 0.827137i 0.910473 + 0.413569i \(0.135718\pi\)
−0.910473 + 0.413569i \(0.864282\pi\)
\(788\) 30.7559i 1.09563i
\(789\) 0 0
\(790\) 2.79432 0.0994175
\(791\) 1.47526i 0.0524542i
\(792\) 0 0
\(793\) −1.28254 + 3.02229i −0.0455443 + 0.107325i
\(794\) −32.0974 −1.13909
\(795\) 0 0
\(796\) 45.7533 1.62168
\(797\) 16.5706 0.586960 0.293480 0.955965i \(-0.405187\pi\)
0.293480 + 0.955965i \(0.405187\pi\)
\(798\) 0 0
\(799\) 86.2946i 3.05288i