Properties

Label 1152.2.w.b.143.6
Level $1152$
Weight $2$
Character 1152.143
Analytic conductor $9.199$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1152.w (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.19876631285\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 288)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 143.6
Character \(\chi\) \(=\) 1152.143
Dual form 1152.2.w.b.1007.6

$q$-expansion

\(f(q)\) \(=\) \(q+(0.366958 - 0.885915i) q^{5} +(-1.21471 + 1.21471i) q^{7} +O(q^{10})\) \(q+(0.366958 - 0.885915i) q^{5} +(-1.21471 + 1.21471i) q^{7} +(-0.545272 + 1.31640i) q^{11} +(0.0270492 - 0.0112041i) q^{13} +1.32687 q^{17} +(1.73653 + 4.19236i) q^{19} +(-0.934512 + 0.934512i) q^{23} +(2.88535 + 2.88535i) q^{25} +(9.35195 - 3.87371i) q^{29} +9.74390i q^{31} +(0.630382 + 1.52188i) q^{35} +(-6.28278 - 2.60241i) q^{37} +(3.42377 + 3.42377i) q^{41} +(-0.997463 - 0.413163i) q^{43} -6.21143i q^{47} +4.04896i q^{49} +(2.94741 + 1.22086i) q^{53} +(0.966130 + 0.966130i) q^{55} +(10.4533 + 4.32990i) q^{59} +(2.76809 + 6.68277i) q^{61} -0.0280747i q^{65} +(10.1069 - 4.18640i) q^{67} +(-7.38725 - 7.38725i) q^{71} +(-8.30156 + 8.30156i) q^{73} +(-0.936700 - 2.26139i) q^{77} -5.54363 q^{79} +(11.4571 - 4.74570i) q^{83} +(0.486907 - 1.17550i) q^{85} +(-7.93127 + 7.93127i) q^{89} +(-0.0192471 + 0.0464667i) q^{91} +4.35131 q^{95} +12.5582 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + O(q^{10}) \) \( 32 q + 8 q^{11} - 16 q^{29} - 24 q^{35} - 16 q^{53} + 32 q^{55} - 32 q^{59} + 32 q^{61} + 16 q^{67} - 16 q^{71} - 16 q^{77} + 32 q^{79} + 40 q^{83} + 48 q^{91} + 80 q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(641\) \(901\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{1}{8}\right)\)

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 0
\(4\) 0 0
\(5\) 0.366958 0.885915i 0.164109 0.396193i −0.820338 0.571880i \(-0.806214\pi\)
0.984446 + 0.175686i \(0.0562144\pi\)
\(6\) 0 0
\(7\) −1.21471 + 1.21471i −0.459117 + 0.459117i −0.898366 0.439249i \(-0.855245\pi\)
0.439249 + 0.898366i \(0.355245\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −0.545272 + 1.31640i −0.164406 + 0.396910i −0.984516 0.175295i \(-0.943912\pi\)
0.820110 + 0.572206i \(0.193912\pi\)
\(12\) 0 0
\(13\) 0.0270492 0.0112041i 0.00750210 0.00310747i −0.378929 0.925426i \(-0.623708\pi\)
0.386431 + 0.922318i \(0.373708\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.32687 0.321814 0.160907 0.986970i \(-0.448558\pi\)
0.160907 + 0.986970i \(0.448558\pi\)
\(18\) 0 0
\(19\) 1.73653 + 4.19236i 0.398388 + 0.961793i 0.988049 + 0.154142i \(0.0492614\pi\)
−0.589661 + 0.807651i \(0.700739\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −0.934512 + 0.934512i −0.194859 + 0.194859i −0.797792 0.602933i \(-0.793999\pi\)
0.602933 + 0.797792i \(0.293999\pi\)
\(24\) 0 0
\(25\) 2.88535 + 2.88535i 0.577069 + 0.577069i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 9.35195 3.87371i 1.73661 0.719329i 0.737586 0.675253i \(-0.235966\pi\)
0.999028 0.0440761i \(-0.0140344\pi\)
\(30\) 0 0
\(31\) 9.74390i 1.75006i 0.484072 + 0.875028i \(0.339157\pi\)
−0.484072 + 0.875028i \(0.660843\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0.630382 + 1.52188i 0.106554 + 0.257244i
\(36\) 0 0
\(37\) −6.28278 2.60241i −1.03288 0.427834i −0.199131 0.979973i \(-0.563812\pi\)
−0.833752 + 0.552139i \(0.813812\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 3.42377 + 3.42377i 0.534703 + 0.534703i 0.921968 0.387266i \(-0.126580\pi\)
−0.387266 + 0.921968i \(0.626580\pi\)
\(42\) 0 0
\(43\) −0.997463 0.413163i −0.152112 0.0630067i 0.305329 0.952247i \(-0.401234\pi\)
−0.457440 + 0.889240i \(0.651234\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 6.21143i 0.906031i −0.891503 0.453015i \(-0.850348\pi\)
0.891503 0.453015i \(-0.149652\pi\)
\(48\) 0 0
\(49\) 4.04896i 0.578423i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 2.94741 + 1.22086i 0.404858 + 0.167698i 0.575814 0.817581i \(-0.304685\pi\)
−0.170955 + 0.985279i \(0.554685\pi\)
\(54\) 0 0
\(55\) 0.966130 + 0.966130i 0.130273 + 0.130273i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 10.4533 + 4.32990i 1.36090 + 0.563704i 0.939306 0.343079i \(-0.111470\pi\)
0.421596 + 0.906784i \(0.361470\pi\)
\(60\) 0 0
\(61\) 2.76809 + 6.68277i 0.354418 + 0.855641i 0.996064 + 0.0886397i \(0.0282520\pi\)
−0.641646 + 0.767001i \(0.721748\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0.0280747i 0.00348224i
\(66\) 0 0
\(67\) 10.1069 4.18640i 1.23475 0.511450i 0.332680 0.943040i \(-0.392047\pi\)
0.902070 + 0.431590i \(0.142047\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −7.38725 7.38725i −0.876705 0.876705i 0.116487 0.993192i \(-0.462837\pi\)
−0.993192 + 0.116487i \(0.962837\pi\)
\(72\) 0 0
\(73\) −8.30156 + 8.30156i −0.971625 + 0.971625i −0.999608 0.0279838i \(-0.991091\pi\)
0.0279838 + 0.999608i \(0.491091\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −0.936700 2.26139i −0.106747 0.257710i
\(78\) 0 0
\(79\) −5.54363 −0.623707 −0.311853 0.950130i \(-0.600950\pi\)
−0.311853 + 0.950130i \(0.600950\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 11.4571 4.74570i 1.25758 0.520909i 0.348417 0.937340i \(-0.386719\pi\)
0.909167 + 0.416431i \(0.136719\pi\)
\(84\) 0 0
\(85\) 0.486907 1.17550i 0.0528125 0.127501i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −7.93127 + 7.93127i −0.840713 + 0.840713i −0.988952 0.148238i \(-0.952640\pi\)
0.148238 + 0.988952i \(0.452640\pi\)
\(90\) 0 0
\(91\) −0.0192471 + 0.0464667i −0.00201765 + 0.00487103i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 4.35131 0.446435
\(96\) 0 0
\(97\) 12.5582 1.27509 0.637545 0.770413i \(-0.279950\pi\)
0.637545 + 0.770413i \(0.279950\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1.67080 4.03367i 0.166251 0.401365i −0.818695 0.574229i \(-0.805302\pi\)
0.984946 + 0.172864i \(0.0553020\pi\)
\(102\) 0 0
\(103\) 2.18742 2.18742i 0.215533 0.215533i −0.591080 0.806613i \(-0.701298\pi\)
0.806613 + 0.591080i \(0.201298\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −3.09671 + 7.47611i −0.299370 + 0.722743i 0.700588 + 0.713566i \(0.252921\pi\)
−0.999958 + 0.00917704i \(0.997079\pi\)
\(108\) 0 0
\(109\) −0.499988 + 0.207102i −0.0478902 + 0.0198368i −0.406500 0.913651i \(-0.633251\pi\)
0.358610 + 0.933488i \(0.383251\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −19.7112 −1.85427 −0.927137 0.374722i \(-0.877738\pi\)
−0.927137 + 0.374722i \(0.877738\pi\)
\(114\) 0 0
\(115\) 0.484972 + 1.17083i 0.0452239 + 0.109180i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −1.61177 + 1.61177i −0.147750 + 0.147750i
\(120\) 0 0
\(121\) 6.34258 + 6.34258i 0.576598 + 0.576598i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 8.04455 3.33216i 0.719526 0.298038i
\(126\) 0 0
\(127\) 12.1620i 1.07920i 0.841920 + 0.539602i \(0.181425\pi\)
−0.841920 + 0.539602i \(0.818575\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 1.68416 + 4.06591i 0.147145 + 0.355240i 0.980217 0.197924i \(-0.0634200\pi\)
−0.833072 + 0.553165i \(0.813420\pi\)
\(132\) 0 0
\(133\) −7.20188 2.98312i −0.624482 0.258669i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 7.05217 + 7.05217i 0.602508 + 0.602508i 0.940977 0.338470i \(-0.109909\pi\)
−0.338470 + 0.940977i \(0.609909\pi\)
\(138\) 0 0
\(139\) −13.5567 5.61536i −1.14986 0.476288i −0.275374 0.961337i \(-0.588802\pi\)
−0.874487 + 0.485049i \(0.838802\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0.0417169i 0.00348855i
\(144\) 0 0
\(145\) 9.70653i 0.806083i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −8.14803 3.37503i −0.667513 0.276493i 0.0230832 0.999734i \(-0.492652\pi\)
−0.690596 + 0.723241i \(0.742652\pi\)
\(150\) 0 0
\(151\) −13.4470 13.4470i −1.09430 1.09430i −0.995064 0.0992395i \(-0.968359\pi\)
−0.0992395 0.995064i \(-0.531641\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 8.63227 + 3.57560i 0.693361 + 0.287199i
\(156\) 0 0
\(157\) 1.17205 + 2.82959i 0.0935400 + 0.225826i 0.963724 0.266902i \(-0.0860000\pi\)
−0.870184 + 0.492727i \(0.836000\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 2.27032i 0.178926i
\(162\) 0 0
\(163\) 14.7015 6.08955i 1.15151 0.476970i 0.276469 0.961023i \(-0.410836\pi\)
0.875039 + 0.484052i \(0.160836\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −8.30270 8.30270i −0.642482 0.642482i 0.308683 0.951165i \(-0.400112\pi\)
−0.951165 + 0.308683i \(0.900112\pi\)
\(168\) 0 0
\(169\) −9.19178 + 9.19178i −0.707060 + 0.707060i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −5.16308 12.4648i −0.392542 0.947680i −0.989384 0.145322i \(-0.953578\pi\)
0.596843 0.802358i \(-0.296422\pi\)
\(174\) 0 0
\(175\) −7.00971 −0.529885
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −1.43728 + 0.595340i −0.107427 + 0.0444978i −0.435750 0.900068i \(-0.643517\pi\)
0.328323 + 0.944566i \(0.393517\pi\)
\(180\) 0 0
\(181\) 5.57818 13.4669i 0.414623 1.00099i −0.569258 0.822159i \(-0.692769\pi\)
0.983880 0.178828i \(-0.0572307\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −4.61104 + 4.61104i −0.339010 + 0.339010i
\(186\) 0 0
\(187\) −0.723507 + 1.74670i −0.0529081 + 0.127731i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 7.01680 0.507718 0.253859 0.967241i \(-0.418300\pi\)
0.253859 + 0.967241i \(0.418300\pi\)
\(192\) 0 0
\(193\) 21.3761 1.53868 0.769342 0.638837i \(-0.220584\pi\)
0.769342 + 0.638837i \(0.220584\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −4.34168 + 10.4817i −0.309332 + 0.746793i 0.690395 + 0.723432i \(0.257437\pi\)
−0.999727 + 0.0233605i \(0.992563\pi\)
\(198\) 0 0
\(199\) 9.04307 9.04307i 0.641047 0.641047i −0.309766 0.950813i \(-0.600251\pi\)
0.950813 + 0.309766i \(0.100251\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −6.65448 + 16.0653i −0.467053 + 1.12757i
\(204\) 0 0
\(205\) 4.28955 1.77679i 0.299595 0.124096i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −6.46572 −0.447243
\(210\) 0 0
\(211\) −5.73872 13.8545i −0.395070 0.953783i −0.988817 0.149132i \(-0.952352\pi\)
0.593747 0.804652i \(-0.297648\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −0.732055 + 0.732055i −0.0499257 + 0.0499257i
\(216\) 0 0
\(217\) −11.8360 11.8360i −0.803480 0.803480i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0.0358909 0.0148665i 0.00241428 0.00100003i
\(222\) 0 0
\(223\) 0.0857822i 0.00574440i −0.999996 0.00287220i \(-0.999086\pi\)
0.999996 0.00287220i \(-0.000914251\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −9.62555 23.2381i −0.638870 1.54237i −0.828187 0.560452i \(-0.810627\pi\)
0.189317 0.981916i \(-0.439373\pi\)
\(228\) 0 0
\(229\) −24.5201 10.1566i −1.62034 0.671165i −0.626237 0.779633i \(-0.715406\pi\)
−0.994100 + 0.108468i \(0.965406\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −2.44973 2.44973i −0.160487 0.160487i 0.622295 0.782782i \(-0.286200\pi\)
−0.782782 + 0.622295i \(0.786200\pi\)
\(234\) 0 0
\(235\) −5.50280 2.27934i −0.358963 0.148687i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 11.3256i 0.732589i 0.930499 + 0.366295i \(0.119374\pi\)
−0.930499 + 0.366295i \(0.880626\pi\)
\(240\) 0 0
\(241\) 13.4166i 0.864239i −0.901816 0.432119i \(-0.857766\pi\)
0.901816 0.432119i \(-0.142234\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 3.58704 + 1.48580i 0.229167 + 0.0949243i
\(246\) 0 0
\(247\) 0.0939436 + 0.0939436i 0.00597749 + 0.00597749i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −15.2970 6.33621i −0.965535 0.399938i −0.156487 0.987680i \(-0.550017\pi\)
−0.809048 + 0.587742i \(0.800017\pi\)
\(252\) 0 0
\(253\) −0.720632 1.73976i −0.0453057 0.109378i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 2.43408i 0.151833i 0.997114 + 0.0759167i \(0.0241883\pi\)
−0.997114 + 0.0759167i \(0.975812\pi\)
\(258\) 0 0
\(259\) 10.7929 4.47058i 0.670640 0.277788i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −15.2250 15.2250i −0.938816 0.938816i 0.0594176 0.998233i \(-0.481076\pi\)
−0.998233 + 0.0594176i \(0.981076\pi\)
\(264\) 0 0
\(265\) 2.16316 2.16316i 0.132882 0.132882i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 2.29849 + 5.54904i 0.140141 + 0.338331i 0.978331 0.207048i \(-0.0663857\pi\)
−0.838190 + 0.545379i \(0.816386\pi\)
\(270\) 0 0
\(271\) 10.5866 0.643088 0.321544 0.946895i \(-0.395798\pi\)
0.321544 + 0.946895i \(0.395798\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −5.37158 + 2.22498i −0.323918 + 0.134171i
\(276\) 0 0
\(277\) 5.91980 14.2917i 0.355686 0.858702i −0.640210 0.768200i \(-0.721153\pi\)
0.995896 0.0905024i \(-0.0288473\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 12.0206 12.0206i 0.717087 0.717087i −0.250921 0.968008i \(-0.580733\pi\)
0.968008 + 0.250921i \(0.0807334\pi\)
\(282\) 0 0
\(283\) 5.86696 14.1641i 0.348754 0.841968i −0.648013 0.761629i \(-0.724400\pi\)
0.996768 0.0803386i \(-0.0256002\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −8.31776 −0.490982
\(288\) 0 0
\(289\) −15.2394 −0.896436
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −6.02149 + 14.5372i −0.351779 + 0.849270i 0.644622 + 0.764502i \(0.277015\pi\)
−0.996401 + 0.0847682i \(0.972985\pi\)
\(294\) 0 0
\(295\) 7.67184 7.67184i 0.446672 0.446672i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −0.0148074 + 0.0357482i −0.000856334 + 0.00206737i
\(300\) 0 0
\(301\) 1.71350 0.709755i 0.0987645 0.0409096i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 6.93614 0.397162
\(306\) 0 0
\(307\) 10.0677 + 24.3055i 0.574592 + 1.38719i 0.897608 + 0.440795i \(0.145303\pi\)
−0.323016 + 0.946394i \(0.604697\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −22.5777 + 22.5777i −1.28027 + 1.28027i −0.339751 + 0.940516i \(0.610343\pi\)
−0.940516 + 0.339751i \(0.889657\pi\)
\(312\) 0 0
\(313\) −9.91862 9.91862i −0.560633 0.560633i 0.368854 0.929487i \(-0.379750\pi\)
−0.929487 + 0.368854i \(0.879750\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 10.4152 4.31414i 0.584979 0.242306i −0.0705101 0.997511i \(-0.522463\pi\)
0.655489 + 0.755205i \(0.272463\pi\)
\(318\) 0 0
\(319\) 14.4232i 0.807542i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 2.30416 + 5.56273i 0.128207 + 0.309519i
\(324\) 0 0
\(325\) 0.110374 + 0.0457185i 0.00612245 + 0.00253600i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 7.54509 + 7.54509i 0.415974 + 0.415974i
\(330\) 0 0
\(331\) −13.0127 5.39006i −0.715245 0.296264i −0.00477208 0.999989i \(-0.501519\pi\)
−0.710473 + 0.703724i \(0.751519\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 10.4901i 0.573133i
\(336\) 0 0
\(337\) 16.7271i 0.911182i −0.890189 0.455591i \(-0.849428\pi\)
0.890189 0.455591i \(-0.150572\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −12.8269 5.31308i −0.694616 0.287719i
\(342\) 0 0
\(343\) −13.4213 13.4213i −0.724681 0.724681i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −17.4060 7.20981i −0.934404 0.387043i −0.137056 0.990563i \(-0.543764\pi\)
−0.797347 + 0.603521i \(0.793764\pi\)
\(348\) 0 0
\(349\) 8.01279 + 19.3446i 0.428915 + 1.03549i 0.979632 + 0.200800i \(0.0643541\pi\)
−0.550718 + 0.834692i \(0.685646\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 29.2201i 1.55523i −0.628743 0.777613i \(-0.716430\pi\)
0.628743 0.777613i \(-0.283570\pi\)
\(354\) 0 0
\(355\) −9.25529 + 3.83367i −0.491220 + 0.203470i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 23.8752 + 23.8752i 1.26008 + 1.26008i 0.951052 + 0.309032i \(0.100005\pi\)
0.309032 + 0.951052i \(0.399995\pi\)
\(360\) 0 0
\(361\) −1.12530 + 1.12530i −0.0592262 + 0.0592262i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 4.30816 + 10.4008i 0.225499 + 0.544403i
\(366\) 0 0
\(367\) 7.91904 0.413370 0.206685 0.978408i \(-0.433732\pi\)
0.206685 + 0.978408i \(0.433732\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −5.06324 + 2.09726i −0.262870 + 0.108884i
\(372\) 0 0
\(373\) −0.910870 + 2.19904i −0.0471631 + 0.113862i −0.945705 0.325025i \(-0.894627\pi\)
0.898542 + 0.438887i \(0.144627\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0.209561 0.209561i 0.0107930 0.0107930i
\(378\) 0 0
\(379\) −8.94487 + 21.5948i −0.459467 + 1.10925i 0.509146 + 0.860680i \(0.329961\pi\)
−0.968613 + 0.248572i \(0.920039\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 8.41070 0.429767 0.214883 0.976640i \(-0.431063\pi\)
0.214883 + 0.976640i \(0.431063\pi\)
\(384\) 0 0
\(385\) −2.34713 −0.119621
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −4.66887 + 11.2717i −0.236721 + 0.571496i −0.996940 0.0781715i \(-0.975092\pi\)
0.760219 + 0.649667i \(0.225092\pi\)
\(390\) 0 0
\(391\) −1.23998 + 1.23998i −0.0627085 + 0.0627085i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −2.03428 + 4.91118i −0.102356 + 0.247108i
\(396\) 0 0
\(397\) 13.1886 5.46289i 0.661916 0.274175i −0.0263285 0.999653i \(-0.508382\pi\)
0.688245 + 0.725479i \(0.258382\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 3.87685 0.193601 0.0968004 0.995304i \(-0.469139\pi\)
0.0968004 + 0.995304i \(0.469139\pi\)
\(402\) 0 0
\(403\) 0.109172 + 0.263565i 0.00543825 + 0.0131291i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 6.85165 6.85165i 0.339624 0.339624i
\(408\) 0 0
\(409\) 6.61246 + 6.61246i 0.326965 + 0.326965i 0.851431 0.524466i \(-0.175735\pi\)
−0.524466 + 0.851431i \(0.675735\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −17.9573 + 7.43815i −0.883620 + 0.366007i
\(414\) 0 0
\(415\) 11.8915i 0.583732i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −7.69097 18.5676i −0.375729 0.907089i −0.992756 0.120147i \(-0.961663\pi\)
0.617028 0.786942i \(-0.288337\pi\)
\(420\) 0 0
\(421\) 15.8875 + 6.58080i 0.774307 + 0.320729i 0.734616 0.678483i \(-0.237362\pi\)
0.0396916 + 0.999212i \(0.487362\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 3.82849 + 3.82849i 0.185709 + 0.185709i
\(426\) 0 0
\(427\) −11.4800 4.75519i −0.555558 0.230120i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 12.7583i 0.614548i 0.951621 + 0.307274i \(0.0994168\pi\)
−0.951621 + 0.307274i \(0.900583\pi\)
\(432\) 0 0
\(433\) 1.18066i 0.0567390i −0.999598 0.0283695i \(-0.990968\pi\)
0.999598 0.0283695i \(-0.00903150\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −5.54062 2.29500i −0.265044 0.109785i
\(438\) 0 0
\(439\) 8.88783 + 8.88783i 0.424193 + 0.424193i 0.886644 0.462452i \(-0.153030\pi\)
−0.462452 + 0.886644i \(0.653030\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 12.1498 + 5.03262i 0.577255 + 0.239107i 0.652157 0.758084i \(-0.273864\pi\)
−0.0749018 + 0.997191i \(0.523864\pi\)
\(444\) 0 0
\(445\) 4.11599 + 9.93688i 0.195117 + 0.471053i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0.529631i 0.0249948i 0.999922 + 0.0124974i \(0.00397815\pi\)
−0.999922 + 0.0124974i \(0.996022\pi\)
\(450\) 0 0
\(451\) −6.37394 + 2.64017i −0.300137 + 0.124321i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0.0341027 + 0.0341027i 0.00159876 + 0.00159876i
\(456\) 0 0
\(457\) −5.43494 + 5.43494i −0.254236 + 0.254236i −0.822705 0.568469i \(-0.807536\pi\)
0.568469 + 0.822705i \(0.307536\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −7.55433 18.2378i −0.351840 0.849418i −0.996393 0.0848579i \(-0.972956\pi\)
0.644553 0.764560i \(-0.277044\pi\)
\(462\) 0 0
\(463\) −4.63562 −0.215436 −0.107718 0.994182i \(-0.534354\pi\)
−0.107718 + 0.994182i \(0.534354\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 18.9494 7.84910i 0.876874 0.363213i 0.101590 0.994826i \(-0.467607\pi\)
0.775284 + 0.631613i \(0.217607\pi\)
\(468\) 0 0
\(469\) −7.19164 + 17.3622i −0.332079 + 0.801710i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 1.08778 1.08778i 0.0500161 0.0500161i
\(474\) 0 0
\(475\) −7.08591 + 17.1069i −0.325124 + 0.784918i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 41.5437 1.89818 0.949089 0.315008i \(-0.102007\pi\)
0.949089 + 0.315008i \(0.102007\pi\)
\(480\) 0 0
\(481\) −0.199102 −0.00907827
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 4.60833 11.1255i 0.209253 0.505182i
\(486\) 0 0
\(487\) 18.8137 18.8137i 0.852529 0.852529i −0.137915 0.990444i \(-0.544040\pi\)
0.990444 + 0.137915i \(0.0440400\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 7.29239 17.6054i 0.329101 0.794520i −0.669559 0.742759i \(-0.733517\pi\)
0.998660 0.0517607i \(-0.0164833\pi\)
\(492\) 0 0
\(493\) 12.4089 5.13992i 0.558867 0.231490i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 17.9467 0.805020
\(498\) 0 0
\(499\) 2.21640 + 5.35086i 0.0992197 + 0.239537i 0.965693 0.259685i \(-0.0836189\pi\)
−0.866474 + 0.499223i \(0.833619\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 13.1494 13.1494i 0.586303 0.586303i −0.350325 0.936628i \(-0.613929\pi\)
0.936628 + 0.350325i \(0.113929\pi\)
\(504\) 0 0
\(505\) −2.96038 2.96038i −0.131735 0.131735i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −11.1362 + 4.61276i −0.493603 + 0.204457i −0.615578 0.788076i \(-0.711077\pi\)
0.121975 + 0.992533i \(0.461077\pi\)
\(510\) 0 0
\(511\) 20.1680i 0.892179i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1.13518 2.74056i −0.0500219 0.120764i
\(516\) 0 0
\(517\) 8.17675 + 3.38692i 0.359613 + 0.148957i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −12.8812 12.8812i −0.564338 0.564338i 0.366199 0.930537i \(-0.380659\pi\)
−0.930537 + 0.366199i \(0.880659\pi\)
\(522\) 0 0
\(523\) 14.3454 + 5.94206i 0.627280 + 0.259828i 0.673597 0.739099i \(-0.264748\pi\)
−0.0463167 + 0.998927i \(0.514748\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 12.9289i 0.563193i
\(528\) 0 0
\(529\) 21.2534i 0.924060i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0.130971 + 0.0542498i 0.00567296 + 0.00234982i
\(534\) 0 0
\(535\) 5.48684 + 5.48684i 0.237217 + 0.237217i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −5.33007 2.20779i −0.229582 0.0950961i
\(540\) 0 0
\(541\) 5.53641 + 13.3661i 0.238029 + 0.574653i 0.997079 0.0763798i \(-0.0243361\pi\)
−0.759050 + 0.651033i \(0.774336\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0.518945i 0.0222292i
\(546\) 0 0
\(547\) −34.8390 + 14.4308i −1.48961 + 0.617016i −0.971232 0.238137i \(-0.923463\pi\)
−0.518376 + 0.855153i \(0.673463\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 32.4799 + 32.4799i 1.38369 + 1.38369i
\(552\) 0 0
\(553\) 6.73389 6.73389i 0.286354 0.286354i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 12.6874 + 30.6300i 0.537581 + 1.29784i 0.926407 + 0.376524i \(0.122881\pi\)
−0.388826 + 0.921311i \(0.627119\pi\)
\(558\) 0 0
\(559\) −0.0316097 −0.00133695
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −35.8986 + 14.8697i −1.51294 + 0.626682i −0.976163 0.217040i \(-0.930360\pi\)
−0.536781 + 0.843722i \(0.680360\pi\)
\(564\) 0 0
\(565\) −7.23319 + 17.4625i −0.304302 + 0.734651i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 19.9044 19.9044i 0.834436 0.834436i −0.153684 0.988120i \(-0.549114\pi\)
0.988120 + 0.153684i \(0.0491137\pi\)
\(570\) 0 0
\(571\) 2.51768 6.07821i 0.105361 0.254365i −0.862403 0.506223i \(-0.831041\pi\)
0.967764 + 0.251857i \(0.0810414\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −5.39278 −0.224895
\(576\) 0 0
\(577\) −18.7117 −0.778980 −0.389490 0.921031i \(-0.627349\pi\)
−0.389490 + 0.921031i \(0.627349\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −8.15244 + 19.6817i −0.338220 + 0.816536i
\(582\) 0 0
\(583\) −3.21428 + 3.21428i −0.133122 + 0.133122i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 12.8204 30.9512i 0.529155 1.27749i −0.402922 0.915234i \(-0.632005\pi\)
0.932077 0.362260i \(-0.117995\pi\)
\(588\) 0 0
\(589\) −40.8499 + 16.9206i −1.68319 + 0.697201i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 14.7730 0.606654 0.303327 0.952887i \(-0.401903\pi\)
0.303327 + 0.952887i \(0.401903\pi\)
\(594\) 0 0
\(595\) 0.836437 + 2.01934i 0.0342906 + 0.0827848i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 17.9159 17.9159i 0.732022 0.732022i −0.238998 0.971020i \(-0.576819\pi\)
0.971020 + 0.238998i \(0.0768189\pi\)
\(600\) 0 0
\(601\) 4.12098 + 4.12098i 0.168098 + 0.168098i 0.786143 0.618045i \(-0.212075\pi\)
−0.618045 + 0.786143i \(0.712075\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 7.94645 3.29153i 0.323069 0.133820i
\(606\) 0 0
\(607\) 25.4859i 1.03444i 0.855852 + 0.517220i \(0.173033\pi\)
−0.855852 + 0.517220i \(0.826967\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −0.0695938 0.168014i −0.00281546 0.00679713i
\(612\) 0 0
\(613\) 35.2820 + 14.6143i 1.42503 + 0.590265i 0.956118 0.292982i \(-0.0946476\pi\)
0.468908 + 0.883247i \(0.344648\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 13.7171 + 13.7171i 0.552229 + 0.552229i 0.927084 0.374855i \(-0.122307\pi\)
−0.374855 + 0.927084i \(0.622307\pi\)
\(618\) 0 0
\(619\) 21.5287 + 8.91748i 0.865311 + 0.358424i 0.770782 0.637099i \(-0.219866\pi\)
0.0945288 + 0.995522i \(0.469866\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 19.2684i 0.771971i
\(624\) 0 0
\(625\) 12.0529i 0.482117i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −8.33646 3.45307i −0.332396 0.137683i
\(630\) 0 0
\(631\) 16.8025 + 16.8025i 0.668896 + 0.668896i 0.957460 0.288565i \(-0.0931780\pi\)
−0.288565 + 0.957460i \(0.593178\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 10.7745 + 4.46295i 0.427573 + 0.177107i
\(636\) 0 0
\(637\) 0.0453652 + 0.109521i 0.00179743 + 0.00433939i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 10.7233i 0.423546i −0.977319 0.211773i \(-0.932076\pi\)
0.977319 0.211773i \(-0.0679238\pi\)
\(642\) 0 0
\(643\) 30.3018 12.5514i 1.19499 0.494980i 0.305612 0.952156i \(-0.401139\pi\)
0.889376 + 0.457176i \(0.151139\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −4.94231 4.94231i −0.194302 0.194302i 0.603250 0.797552i \(-0.293872\pi\)
−0.797552 + 0.603250i \(0.793872\pi\)
\(648\) 0 0
\(649\) −11.3998 + 11.3998i −0.447480 + 0.447480i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 5.01854 + 12.1158i 0.196391 + 0.474129i 0.991142 0.132806i \(-0.0423988\pi\)
−0.794751 + 0.606935i \(0.792399\pi\)
\(654\) 0 0
\(655\) 4.22007 0.164892
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 29.1760 12.0851i 1.13653 0.470768i 0.266537 0.963825i \(-0.414121\pi\)
0.869997 + 0.493057i \(0.164121\pi\)
\(660\) 0 0
\(661\) −15.3024 + 36.9433i −0.595196 + 1.43693i 0.283231 + 0.959052i \(0.408594\pi\)
−0.878426 + 0.477877i \(0.841406\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −5.28557 + 5.28557i −0.204966 + 0.204966i
\(666\) 0 0
\(667\) −5.11949 + 12.3595i −0.198227 + 0.478563i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −10.3066 −0.397881
\(672\) 0 0
\(673\) −6.49552 −0.250384 −0.125192 0.992133i \(-0.539955\pi\)
−0.125192 + 0.992133i \(0.539955\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −2.62635 + 6.34057i −0.100939 + 0.243688i −0.966279 0.257497i \(-0.917102\pi\)
0.865340 + 0.501185i \(0.167102\pi\)
\(678\) 0 0
\(679\) −15.2545 + 15.2545i −0.585415 + 0.585415i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 4.22340 10.1962i 0.161604 0.390146i −0.822248 0.569129i \(-0.807281\pi\)
0.983852 + 0.178982i \(0.0572805\pi\)
\(684\) 0 0
\(685\) 8.83548 3.65978i 0.337586 0.139833i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0.0934039 0.00355840
\(690\) 0 0
\(691\) 2.10014 + 5.07018i 0.0798931 + 0.192879i 0.958779 0.284153i \(-0.0917125\pi\)
−0.878886 + 0.477032i \(0.841712\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −9.94946 + 9.94946i −0.377404 + 0.377404i
\(696\) 0 0
\(697\) 4.54291 + 4.54291i 0.172075 + 0.172075i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −39.8651 + 16.5127i −1.50568 + 0.623675i −0.974662 0.223683i \(-0.928192\pi\)
−0.531022 + 0.847358i \(0.678192\pi\)
\(702\) 0 0
\(703\) 30.8588i 1.16386i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 2.87020 + 6.92928i 0.107945 + 0.260602i
\(708\) 0 0
\(709\) 13.6775 + 5.66541i 0.513670 + 0.212769i 0.624434 0.781078i \(-0.285330\pi\)
−0.110764 + 0.993847i \(0.535330\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −9.10580 9.10580i −0.341015 0.341015i
\(714\) 0 0
\(715\) 0.0369577 + 0.0153084i 0.00138214 + 0.000572501i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 38.0055i 1.41736i 0.705528 + 0.708682i \(0.250710\pi\)
−0.705528 + 0.708682i \(0.749290\pi\)
\(720\) 0 0
\(721\) 5.31416i 0.197910i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 38.1606 + 15.8066i 1.41725 + 0.587044i
\(726\) 0 0
\(727\) 3.50408 + 3.50408i 0.129959 + 0.129959i 0.769094 0.639135i \(-0.220708\pi\)
−0.639135 + 0.769094i \(0.720708\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −1.32351 0.548215i −0.0489517 0.0202765i
\(732\) 0 0
\(733\) −18.0521 43.5817i −0.666771 1.60973i −0.786980 0.616978i \(-0.788357\pi\)
0.120210 0.992749i \(-0.461643\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 15.5874i 0.574170i
\(738\) 0 0
\(739\) −39.4444 + 16.3384i −1.45098 + 0.601018i −0.962433 0.271518i \(-0.912474\pi\)
−0.488551 + 0.872535i \(0.662474\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 10.7638 + 10.7638i 0.394884 + 0.394884i 0.876424 0.481540i \(-0.159922\pi\)
−0.481540 + 0.876424i \(0.659922\pi\)
\(744\) 0 0
\(745\) −5.97997 + 5.97997i −0.219089 + 0.219089i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −5.31970 12.8429i −0.194378 0.469269i
\(750\) 0 0
\(751\) 20.8234 0.759856 0.379928 0.925016i \(-0.375949\pi\)
0.379928 + 0.925016i \(0.375949\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −16.8474 + 6.97843i −0.613140 + 0.253971i
\(756\) 0 0
\(757\) 4.51339 10.8963i 0.164042 0.396032i −0.820389 0.571806i \(-0.806243\pi\)
0.984431 + 0.175774i \(0.0562428\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 13.8159 13.8159i 0.500826 0.500826i −0.410868 0.911695i \(-0.634774\pi\)
0.911695 + 0.410868i \(0.134774\pi\)
\(762\) 0 0
\(763\) 0.355772 0.858909i 0.0128798 0.0310946i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0.331266 0.0119613
\(768\) 0 0
\(769\) 10.2754 0.370539 0.185270 0.982688i \(-0.440684\pi\)
0.185270 + 0.982688i \(0.440684\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 20.3918 49.2302i 0.733442 1.77069i 0.102674 0.994715i \(-0.467260\pi\)
0.630769 0.775971i \(-0.282740\pi\)
\(774\) 0 0
\(775\) −28.1145 + 28.1145i −1.00990 + 1.00990i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −8.40818 + 20.2991i −0.301254 + 0.727292i
\(780\) 0 0
\(781\) 13.7527 5.69654i 0.492109 0.203838i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 2.93687 0.104821
\(786\) 0 0
\(787\) −12.3657 29.8534i −0.440789 1.06416i −0.975672 0.219233i \(-0.929644\pi\)
0.534883 0.844926i \(-0.320356\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 23.9434 23.9434i 0.851329 0.851329i
\(792\) 0 0
\(793\) 0.149749 + 0.149749i 0.00531776 + 0.00531776i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −3.74523 + 1.55133i −0.132663 + 0.0549508i −0.448027 0.894020i \(-0.647873\pi\)
0.315364 + 0.948971i \(0.397873\pi\)
\(798\) 0 0
\(799\) 8.24179i 0.291574i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −6.40159 15.4548i −0.225907 0.545389i
\(804\) 0 0
\(805\) −2.01131 0.833113i −0.0708895 0.0293634i