Properties

Label 1152.2.w.a.1007.8
Level $1152$
Weight $2$
Character 1152.1007
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 1007.8
Character \(\chi\) \(=\) 1152.1007
Dual form 1152.2.w.a.143.8

$q$-expansion

\(f(q)\) \(=\) \(q+(1.39555 + 3.36915i) q^{5} +(1.05755 + 1.05755i) q^{7} +O(q^{10})\) \(q+(1.39555 + 3.36915i) q^{5} +(1.05755 + 1.05755i) q^{7} +(1.50977 + 3.64490i) q^{11} +(-2.23818 - 0.927086i) q^{13} +7.49610 q^{17} +(-0.818262 + 1.97546i) q^{19} +(-5.80392 - 5.80392i) q^{23} +(-5.86809 + 5.86809i) q^{25} +(-0.326633 - 0.135296i) q^{29} +1.71021i q^{31} +(-2.08718 + 5.03889i) q^{35} +(0.387384 - 0.160460i) q^{37} +(1.50401 - 1.50401i) q^{41} +(-7.40227 + 3.06612i) q^{43} +7.27404i q^{47} -4.76319i q^{49} +(-3.94866 + 1.63559i) q^{53} +(-10.1733 + 10.1733i) q^{55} +(12.7979 - 5.30105i) q^{59} +(-0.579943 + 1.40011i) q^{61} -8.83457i q^{65} +(7.96385 + 3.29874i) q^{67} +(4.75505 - 4.75505i) q^{71} +(-7.99854 - 7.99854i) q^{73} +(-2.25800 + 5.45130i) q^{77} -14.3967 q^{79} +(1.35250 + 0.560224i) q^{83} +(10.4612 + 25.2555i) q^{85} +(4.75638 + 4.75638i) q^{89} +(-1.38655 - 3.34742i) q^{91} -7.79754 q^{95} -1.28856 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + O(q^{10}) \) \( 32 q - 8 q^{11} + 16 q^{29} + 24 q^{35} + 16 q^{53} + 32 q^{55} + 32 q^{59} + 32 q^{61} + 16 q^{67} + 16 q^{71} + 16 q^{77} + 32 q^{79} - 40 q^{83} + 48 q^{91} - 80 q^{95} + O(q^{100}) \)

Character values

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

\(n\) \(127\) \(641\) \(901\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{7}{8}\right)\)

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
\(5\) 1.39555 + 3.36915i 0.624108 + 1.50673i 0.846839 + 0.531850i \(0.178503\pi\)
−0.222731 + 0.974880i \(0.571497\pi\)
\(6\) 0 0
\(7\) 1.05755 + 1.05755i 0.399715 + 0.399715i 0.878133 0.478417i \(-0.158789\pi\)
−0.478417 + 0.878133i \(0.658789\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1.50977 + 3.64490i 0.455211 + 1.09898i 0.970314 + 0.241849i \(0.0777539\pi\)
−0.515102 + 0.857129i \(0.672246\pi\)
\(12\) 0 0
\(13\) −2.23818 0.927086i −0.620761 0.257127i 0.0500610 0.998746i \(-0.484058\pi\)
−0.670822 + 0.741619i \(0.734058\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 7.49610 1.81807 0.909036 0.416717i \(-0.136820\pi\)
0.909036 + 0.416717i \(0.136820\pi\)
\(18\) 0 0
\(19\) −0.818262 + 1.97546i −0.187722 + 0.453201i −0.989520 0.144393i \(-0.953877\pi\)
0.801798 + 0.597595i \(0.203877\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −5.80392 5.80392i −1.21020 1.21020i −0.970960 0.239241i \(-0.923102\pi\)
−0.239241 0.970960i \(-0.576898\pi\)
\(24\) 0 0
\(25\) −5.86809 + 5.86809i −1.17362 + 1.17362i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −0.326633 0.135296i −0.0606542 0.0251238i 0.352150 0.935944i \(-0.385451\pi\)
−0.412804 + 0.910820i \(0.635451\pi\)
\(30\) 0 0
\(31\) 1.71021i 0.307163i 0.988136 + 0.153582i \(0.0490808\pi\)
−0.988136 + 0.153582i \(0.950919\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −2.08718 + 5.03889i −0.352797 + 0.851728i
\(36\) 0 0
\(37\) 0.387384 0.160460i 0.0636856 0.0263794i −0.350613 0.936520i \(-0.614027\pi\)
0.414299 + 0.910141i \(0.364027\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 1.50401 1.50401i 0.234887 0.234887i −0.579842 0.814729i \(-0.696886\pi\)
0.814729 + 0.579842i \(0.196886\pi\)
\(42\) 0 0
\(43\) −7.40227 + 3.06612i −1.12884 + 0.467579i −0.867385 0.497638i \(-0.834201\pi\)
−0.261450 + 0.965217i \(0.584201\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 7.27404i 1.06103i 0.847676 + 0.530514i \(0.178001\pi\)
−0.847676 + 0.530514i \(0.821999\pi\)
\(48\) 0 0
\(49\) 4.76319i 0.680455i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −3.94866 + 1.63559i −0.542390 + 0.224665i −0.637020 0.770847i \(-0.719833\pi\)
0.0946303 + 0.995512i \(0.469833\pi\)
\(54\) 0 0
\(55\) −10.1733 + 10.1733i −1.37176 + 1.37176i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 12.7979 5.30105i 1.66614 0.690138i 0.667619 0.744503i \(-0.267313\pi\)
0.998521 + 0.0543646i \(0.0173133\pi\)
\(60\) 0 0
\(61\) −0.579943 + 1.40011i −0.0742542 + 0.179265i −0.956648 0.291245i \(-0.905930\pi\)
0.882394 + 0.470511i \(0.155930\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 8.83457i 1.09579i
\(66\) 0 0
\(67\) 7.96385 + 3.29874i 0.972940 + 0.403005i 0.811806 0.583928i \(-0.198485\pi\)
0.161134 + 0.986933i \(0.448485\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 4.75505 4.75505i 0.564320 0.564320i −0.366211 0.930532i \(-0.619345\pi\)
0.930532 + 0.366211i \(0.119345\pi\)
\(72\) 0 0
\(73\) −7.99854 7.99854i −0.936158 0.936158i 0.0619229 0.998081i \(-0.480277\pi\)
−0.998081 + 0.0619229i \(0.980277\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −2.25800 + 5.45130i −0.257323 + 0.621233i
\(78\) 0 0
\(79\) −14.3967 −1.61975 −0.809877 0.586600i \(-0.800466\pi\)
−0.809877 + 0.586600i \(0.800466\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 1.35250 + 0.560224i 0.148456 + 0.0614926i 0.455674 0.890147i \(-0.349398\pi\)
−0.307218 + 0.951639i \(0.599398\pi\)
\(84\) 0 0
\(85\) 10.4612 + 25.2555i 1.13467 + 2.73934i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 4.75638 + 4.75638i 0.504176 + 0.504176i 0.912733 0.408557i \(-0.133968\pi\)
−0.408557 + 0.912733i \(0.633968\pi\)
\(90\) 0 0
\(91\) −1.38655 3.34742i −0.145350 0.350905i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −7.79754 −0.800011
\(96\) 0 0
\(97\) −1.28856 −0.130834 −0.0654168 0.997858i \(-0.520838\pi\)
−0.0654168 + 0.997858i \(0.520838\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 4.56084 + 11.0109i 0.453821 + 1.09562i 0.970858 + 0.239657i \(0.0770351\pi\)
−0.517037 + 0.855963i \(0.672965\pi\)
\(102\) 0 0
\(103\) 8.69287 + 8.69287i 0.856533 + 0.856533i 0.990928 0.134394i \(-0.0429089\pi\)
−0.134394 + 0.990928i \(0.542909\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 6.21290 + 14.9993i 0.600624 + 1.45003i 0.872940 + 0.487827i \(0.162210\pi\)
−0.272316 + 0.962208i \(0.587790\pi\)
\(108\) 0 0
\(109\) 1.20531 + 0.499254i 0.115447 + 0.0478198i 0.439659 0.898165i \(-0.355099\pi\)
−0.324212 + 0.945984i \(0.605099\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −4.83947 −0.455259 −0.227630 0.973748i \(-0.573098\pi\)
−0.227630 + 0.973748i \(0.573098\pi\)
\(114\) 0 0
\(115\) 11.4546 27.6539i 1.06815 2.57874i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 7.92748 + 7.92748i 0.726711 + 0.726711i
\(120\) 0 0
\(121\) −3.22771 + 3.22771i −0.293428 + 0.293428i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −11.1139 4.60353i −0.994059 0.411753i
\(126\) 0 0
\(127\) 1.85060i 0.164214i −0.996624 0.0821069i \(-0.973835\pi\)
0.996624 0.0821069i \(-0.0261649\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 2.44102 5.89314i 0.213273 0.514886i −0.780650 0.624969i \(-0.785112\pi\)
0.993922 + 0.110083i \(0.0351116\pi\)
\(132\) 0 0
\(133\) −2.95449 + 1.22379i −0.256187 + 0.106116i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −2.65921 + 2.65921i −0.227192 + 0.227192i −0.811519 0.584327i \(-0.801359\pi\)
0.584327 + 0.811519i \(0.301359\pi\)
\(138\) 0 0
\(139\) 11.7567 4.86980i 0.997193 0.413051i 0.176426 0.984314i \(-0.443546\pi\)
0.820767 + 0.571263i \(0.193546\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 9.55763i 0.799250i
\(144\) 0 0
\(145\) 1.28929i 0.107070i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 8.23656 3.41170i 0.674765 0.279497i −0.0188714 0.999822i \(-0.506007\pi\)
0.693637 + 0.720325i \(0.256007\pi\)
\(150\) 0 0
\(151\) 11.9992 11.9992i 0.976478 0.976478i −0.0232512 0.999730i \(-0.507402\pi\)
0.999730 + 0.0232512i \(0.00740175\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −5.76197 + 2.38669i −0.462812 + 0.191703i
\(156\) 0 0
\(157\) 5.47915 13.2278i 0.437284 1.05570i −0.539599 0.841922i \(-0.681424\pi\)
0.976883 0.213775i \(-0.0685759\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 12.2758i 0.967471i
\(162\) 0 0
\(163\) −10.3137 4.27206i −0.807828 0.334614i −0.0597412 0.998214i \(-0.519028\pi\)
−0.748087 + 0.663600i \(0.769028\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 6.27058 6.27058i 0.485232 0.485232i −0.421566 0.906798i \(-0.638519\pi\)
0.906798 + 0.421566i \(0.138519\pi\)
\(168\) 0 0
\(169\) −5.04241 5.04241i −0.387878 0.387878i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −9.58864 + 23.1490i −0.729011 + 1.75999i −0.0831448 + 0.996537i \(0.526496\pi\)
−0.645866 + 0.763451i \(0.723504\pi\)
\(174\) 0 0
\(175\) −12.4116 −0.938226
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 6.32195 + 2.61864i 0.472524 + 0.195726i 0.606221 0.795296i \(-0.292685\pi\)
−0.133697 + 0.991022i \(0.542685\pi\)
\(180\) 0 0
\(181\) −1.02155 2.46625i −0.0759314 0.183315i 0.881356 0.472453i \(-0.156631\pi\)
−0.957287 + 0.289138i \(0.906631\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1.08123 + 1.08123i 0.0794934 + 0.0794934i
\(186\) 0 0
\(187\) 11.3174 + 27.3225i 0.827607 + 1.99802i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −20.7890 −1.50424 −0.752121 0.659025i \(-0.770969\pi\)
−0.752121 + 0.659025i \(0.770969\pi\)
\(192\) 0 0
\(193\) 14.9444 1.07572 0.537861 0.843034i \(-0.319233\pi\)
0.537861 + 0.843034i \(0.319233\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −9.50419 22.9451i −0.677145 1.63477i −0.769191 0.639019i \(-0.779341\pi\)
0.0920460 0.995755i \(-0.470659\pi\)
\(198\) 0 0
\(199\) 1.24926 + 1.24926i 0.0885579 + 0.0885579i 0.749998 0.661440i \(-0.230054\pi\)
−0.661440 + 0.749998i \(0.730054\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −0.202348 0.488512i −0.0142021 0.0342868i
\(204\) 0 0
\(205\) 7.16615 + 2.96832i 0.500506 + 0.207316i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −8.43573 −0.583512
\(210\) 0 0
\(211\) 4.04903 9.77521i 0.278746 0.672953i −0.721055 0.692878i \(-0.756343\pi\)
0.999801 + 0.0199244i \(0.00634254\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −20.6604 20.6604i −1.40903 1.40903i
\(216\) 0 0
\(217\) −1.80863 + 1.80863i −0.122778 + 0.122778i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −16.7777 6.94954i −1.12859 0.467476i
\(222\) 0 0
\(223\) 19.2531i 1.28928i −0.764485 0.644641i \(-0.777007\pi\)
0.764485 0.644641i \(-0.222993\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 5.98915 14.4591i 0.397514 0.959684i −0.590740 0.806862i \(-0.701164\pi\)
0.988254 0.152822i \(-0.0488361\pi\)
\(228\) 0 0
\(229\) −7.93338 + 3.28612i −0.524253 + 0.217153i −0.629084 0.777337i \(-0.716570\pi\)
0.104831 + 0.994490i \(0.466570\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 12.2337 12.2337i 0.801455 0.801455i −0.181868 0.983323i \(-0.558214\pi\)
0.983323 + 0.181868i \(0.0582145\pi\)
\(234\) 0 0
\(235\) −24.5073 + 10.1513i −1.59868 + 0.662196i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 10.3650i 0.670459i −0.942137 0.335229i \(-0.891186\pi\)
0.942137 0.335229i \(-0.108814\pi\)
\(240\) 0 0
\(241\) 14.1048i 0.908572i 0.890856 + 0.454286i \(0.150106\pi\)
−0.890856 + 0.454286i \(0.849894\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 16.0479 6.64726i 1.02526 0.424678i
\(246\) 0 0
\(247\) 3.66284 3.66284i 0.233061 0.233061i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −4.92406 + 2.03961i −0.310804 + 0.128739i −0.532633 0.846346i \(-0.678797\pi\)
0.221829 + 0.975086i \(0.428797\pi\)
\(252\) 0 0
\(253\) 12.3921 29.9172i 0.779087 1.88088i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 20.2370i 1.26235i −0.775640 0.631175i \(-0.782573\pi\)
0.775640 0.631175i \(-0.217427\pi\)
\(258\) 0 0
\(259\) 0.579371 + 0.239983i 0.0360004 + 0.0149118i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −3.63751 + 3.63751i −0.224299 + 0.224299i −0.810306 0.586007i \(-0.800699\pi\)
0.586007 + 0.810306i \(0.300699\pi\)
\(264\) 0 0
\(265\) −11.0211 11.0211i −0.677019 0.677019i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −2.92241 + 7.05531i −0.178182 + 0.430170i −0.987585 0.157083i \(-0.949791\pi\)
0.809403 + 0.587254i \(0.199791\pi\)
\(270\) 0 0
\(271\) 7.63925 0.464052 0.232026 0.972710i \(-0.425465\pi\)
0.232026 + 0.972710i \(0.425465\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −30.2480 12.5291i −1.82402 0.755535i
\(276\) 0 0
\(277\) −6.85371 16.5463i −0.411799 0.994172i −0.984655 0.174515i \(-0.944164\pi\)
0.572855 0.819657i \(-0.305836\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 13.5776 + 13.5776i 0.809969 + 0.809969i 0.984629 0.174660i \(-0.0558826\pi\)
−0.174660 + 0.984629i \(0.555883\pi\)
\(282\) 0 0
\(283\) −7.17080 17.3118i −0.426260 1.02908i −0.980463 0.196701i \(-0.936977\pi\)
0.554204 0.832381i \(-0.313023\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 3.18112 0.187776
\(288\) 0 0
\(289\) 39.1916 2.30539
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1.11909 + 2.70172i 0.0653780 + 0.157836i 0.953192 0.302367i \(-0.0977767\pi\)
−0.887814 + 0.460203i \(0.847777\pi\)
\(294\) 0 0
\(295\) 35.7201 + 35.7201i 2.07970 + 2.07970i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 7.60951 + 18.3710i 0.440069 + 1.06242i
\(300\) 0 0
\(301\) −11.0708 4.58568i −0.638111 0.264314i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −5.52651 −0.316447
\(306\) 0 0
\(307\) −0.597072 + 1.44146i −0.0340767 + 0.0822684i −0.940002 0.341170i \(-0.889177\pi\)
0.905925 + 0.423438i \(0.139177\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 16.3415 + 16.3415i 0.926640 + 0.926640i 0.997487 0.0708472i \(-0.0225703\pi\)
−0.0708472 + 0.997487i \(0.522570\pi\)
\(312\) 0 0
\(313\) 11.0100 11.0100i 0.622320 0.622320i −0.323804 0.946124i \(-0.604962\pi\)
0.946124 + 0.323804i \(0.104962\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 6.87945 + 2.84956i 0.386388 + 0.160047i 0.567417 0.823430i \(-0.307943\pi\)
−0.181029 + 0.983478i \(0.557943\pi\)
\(318\) 0 0
\(319\) 1.39481i 0.0780943i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −6.13378 + 14.8082i −0.341292 + 0.823953i
\(324\) 0 0
\(325\) 18.5741 7.69364i 1.03030 0.426766i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −7.69264 + 7.69264i −0.424109 + 0.424109i
\(330\) 0 0
\(331\) −3.18235 + 1.31817i −0.174918 + 0.0724533i −0.468424 0.883504i \(-0.655178\pi\)
0.293506 + 0.955957i \(0.405178\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 31.4350i 1.71748i
\(336\) 0 0
\(337\) 33.5837i 1.82942i −0.404110 0.914710i \(-0.632419\pi\)
0.404110 0.914710i \(-0.367581\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −6.23355 + 2.58202i −0.337566 + 0.139824i
\(342\) 0 0
\(343\) 12.4401 12.4401i 0.671704 0.671704i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −10.5727 + 4.37938i −0.567575 + 0.235097i −0.647970 0.761666i \(-0.724382\pi\)
0.0803952 + 0.996763i \(0.474382\pi\)
\(348\) 0 0
\(349\) −1.93540 + 4.67246i −0.103599 + 0.250111i −0.967176 0.254106i \(-0.918219\pi\)
0.863577 + 0.504217i \(0.168219\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 11.8710i 0.631829i 0.948788 + 0.315915i \(0.102311\pi\)
−0.948788 + 0.315915i \(0.897689\pi\)
\(354\) 0 0
\(355\) 22.6564 + 9.38458i 1.20248 + 0.498082i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 7.19895 7.19895i 0.379946 0.379946i −0.491137 0.871083i \(-0.663418\pi\)
0.871083 + 0.491137i \(0.163418\pi\)
\(360\) 0 0
\(361\) 10.2021 + 10.2021i 0.536955 + 0.536955i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 15.7859 38.1106i 0.826274 1.99480i
\(366\) 0 0
\(367\) −5.49636 −0.286908 −0.143454 0.989657i \(-0.545821\pi\)
−0.143454 + 0.989657i \(0.545821\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −5.90560 2.44618i −0.306603 0.126999i
\(372\) 0 0
\(373\) 9.45992 + 22.8383i 0.489816 + 1.18252i 0.954813 + 0.297208i \(0.0960556\pi\)
−0.464996 + 0.885313i \(0.653944\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0.605634 + 0.605634i 0.0311917 + 0.0311917i
\(378\) 0 0
\(379\) 5.26808 + 12.7183i 0.270603 + 0.653293i 0.999509 0.0313200i \(-0.00997110\pi\)
−0.728906 + 0.684613i \(0.759971\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0.651517 0.0332910 0.0166455 0.999861i \(-0.494701\pi\)
0.0166455 + 0.999861i \(0.494701\pi\)
\(384\) 0 0
\(385\) −21.5174 −1.09663
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 6.58251 + 15.8916i 0.333747 + 0.805736i 0.998288 + 0.0584844i \(0.0186268\pi\)
−0.664542 + 0.747251i \(0.731373\pi\)
\(390\) 0 0
\(391\) −43.5068 43.5068i −2.20023 2.20023i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −20.0913 48.5046i −1.01090 2.44053i
\(396\) 0 0
\(397\) −23.5792 9.76681i −1.18340 0.490182i −0.297802 0.954628i \(-0.596254\pi\)
−0.885602 + 0.464446i \(0.846254\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 5.64431 0.281864 0.140932 0.990019i \(-0.454990\pi\)
0.140932 + 0.990019i \(0.454990\pi\)
\(402\) 0 0
\(403\) 1.58552 3.82777i 0.0789802 0.190675i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1.16972 + 1.16972i 0.0579808 + 0.0579808i
\(408\) 0 0
\(409\) −15.4062 + 15.4062i −0.761790 + 0.761790i −0.976646 0.214856i \(-0.931072\pi\)
0.214856 + 0.976646i \(0.431072\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 19.1405 + 7.92824i 0.941840 + 0.390123i
\(414\) 0 0
\(415\) 5.33860i 0.262061i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 9.62264 23.2311i 0.470097 1.13491i −0.494024 0.869449i \(-0.664474\pi\)
0.964120 0.265466i \(-0.0855257\pi\)
\(420\) 0 0
\(421\) −2.00854 + 0.831963i −0.0978901 + 0.0405474i −0.431091 0.902308i \(-0.641871\pi\)
0.333201 + 0.942856i \(0.391871\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −43.9878 + 43.9878i −2.13372 + 2.13372i
\(426\) 0 0
\(427\) −2.09400 + 0.867362i −0.101336 + 0.0419746i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 16.8804i 0.813100i 0.913628 + 0.406550i \(0.133268\pi\)
−0.913628 + 0.406550i \(0.866732\pi\)
\(432\) 0 0
\(433\) 0.162457i 0.00780716i −0.999992 0.00390358i \(-0.998757\pi\)
0.999992 0.00390358i \(-0.00124255\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 16.2145 6.71628i 0.775646 0.321283i
\(438\) 0 0
\(439\) 0.853136 0.853136i 0.0407180 0.0407180i −0.686455 0.727173i \(-0.740834\pi\)
0.727173 + 0.686455i \(0.240834\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 22.2491 9.21590i 1.05709 0.437860i 0.214672 0.976686i \(-0.431132\pi\)
0.842417 + 0.538826i \(0.181132\pi\)
\(444\) 0 0
\(445\) −9.38721 + 22.6627i −0.444996 + 1.07432i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 23.1544i 1.09272i 0.837549 + 0.546362i \(0.183988\pi\)
−0.837549 + 0.546362i \(0.816012\pi\)
\(450\) 0 0
\(451\) 7.75266 + 3.21126i 0.365059 + 0.151212i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 9.34298 9.34298i 0.438006 0.438006i
\(456\) 0 0
\(457\) 15.2233 + 15.2233i 0.712114 + 0.712114i 0.966977 0.254863i \(-0.0820304\pi\)
−0.254863 + 0.966977i \(0.582030\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 12.2190 29.4992i 0.569093 1.37391i −0.333227 0.942847i \(-0.608138\pi\)
0.902320 0.431066i \(-0.141862\pi\)
\(462\) 0 0
\(463\) −0.577924 −0.0268584 −0.0134292 0.999910i \(-0.504275\pi\)
−0.0134292 + 0.999910i \(0.504275\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −25.0132 10.3608i −1.15747 0.479441i −0.280440 0.959872i \(-0.590480\pi\)
−0.877033 + 0.480431i \(0.840480\pi\)
\(468\) 0 0
\(469\) 4.93358 + 11.9107i 0.227812 + 0.549986i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −22.3514 22.3514i −1.02772 1.02772i
\(474\) 0 0
\(475\) −6.79053 16.3938i −0.311571 0.752199i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 20.6865 0.945188 0.472594 0.881280i \(-0.343318\pi\)
0.472594 + 0.881280i \(0.343318\pi\)
\(480\) 0 0
\(481\) −1.01580 −0.0463164
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1.79825 4.34136i −0.0816543 0.197131i
\(486\) 0 0
\(487\) 17.8979 + 17.8979i 0.811031 + 0.811031i 0.984788 0.173757i \(-0.0555909\pi\)
−0.173757 + 0.984788i \(0.555591\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −0.919341 2.21949i −0.0414893 0.100164i 0.901776 0.432203i \(-0.142264\pi\)
−0.943266 + 0.332039i \(0.892264\pi\)
\(492\) 0 0
\(493\) −2.44848 1.01419i −0.110274 0.0456769i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 10.0574 0.451135
\(498\) 0 0
\(499\) −8.65228 + 20.8884i −0.387329 + 0.935095i 0.603175 + 0.797609i \(0.293902\pi\)
−0.990504 + 0.137486i \(0.956098\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 9.91458 + 9.91458i 0.442069 + 0.442069i 0.892707 0.450638i \(-0.148803\pi\)
−0.450638 + 0.892707i \(0.648803\pi\)
\(504\) 0 0
\(505\) −30.7323 + 30.7323i −1.36757 + 1.36757i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −8.70757 3.60679i −0.385956 0.159868i 0.181264 0.983434i \(-0.441981\pi\)
−0.567220 + 0.823566i \(0.691981\pi\)
\(510\) 0 0
\(511\) 16.9177i 0.748393i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −17.1563 + 41.4189i −0.755995 + 1.82513i
\(516\) 0 0
\(517\) −26.5131 + 10.9821i −1.16605 + 0.482992i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −0.843541 + 0.843541i −0.0369562 + 0.0369562i −0.725343 0.688387i \(-0.758319\pi\)
0.688387 + 0.725343i \(0.258319\pi\)
\(522\) 0 0
\(523\) −0.0207812 + 0.00860784i −0.000908697 + 0.000376395i −0.383138 0.923691i \(-0.625157\pi\)
0.382229 + 0.924068i \(0.375157\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 12.8199i 0.558445i
\(528\) 0 0
\(529\) 44.3710i 1.92917i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −4.76060 + 1.97190i −0.206204 + 0.0854126i
\(534\) 0 0
\(535\) −41.8644 + 41.8644i −1.80996 + 1.80996i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 17.3613 7.19130i 0.747805 0.309751i
\(540\) 0 0
\(541\) 1.78856 4.31796i 0.0768961 0.185644i −0.880757 0.473569i \(-0.842965\pi\)
0.957653 + 0.287925i \(0.0929655\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 4.75759i 0.203793i
\(546\) 0 0
\(547\) −26.9790 11.1751i −1.15354 0.477811i −0.277819 0.960633i \(-0.589612\pi\)
−0.875718 + 0.482823i \(0.839612\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0.534543 0.534543i 0.0227723 0.0227723i
\(552\) 0 0
\(553\) −15.2252 15.2252i −0.647440 0.647440i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 2.15147 5.19412i 0.0911609 0.220082i −0.871722 0.490000i \(-0.836997\pi\)
0.962883 + 0.269918i \(0.0869967\pi\)
\(558\) 0 0
\(559\) 19.4102 0.820964
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 15.9450 + 6.60465i 0.672003 + 0.278353i 0.692479 0.721438i \(-0.256518\pi\)
−0.0204766 + 0.999790i \(0.506518\pi\)
\(564\) 0 0
\(565\) −6.75372 16.3049i −0.284131 0.685953i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 1.67703 + 1.67703i 0.0703046 + 0.0703046i 0.741385 0.671080i \(-0.234169\pi\)
−0.671080 + 0.741385i \(0.734169\pi\)
\(570\) 0 0
\(571\) 2.41843 + 5.83861i 0.101208 + 0.244338i 0.966371 0.257154i \(-0.0827847\pi\)
−0.865162 + 0.501492i \(0.832785\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 68.1158 2.84063
\(576\) 0 0
\(577\) 10.8983 0.453703 0.226851 0.973929i \(-0.427157\pi\)
0.226851 + 0.973929i \(0.427157\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0.837869 + 2.02280i 0.0347607 + 0.0839197i
\(582\) 0 0
\(583\) −11.9231 11.9231i −0.493804 0.493804i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 12.0840 + 29.1734i 0.498760 + 1.20411i 0.950152 + 0.311788i \(0.100928\pi\)
−0.451392 + 0.892326i \(0.649072\pi\)
\(588\) 0 0
\(589\) −3.37846 1.39940i −0.139207 0.0576614i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −25.8516 −1.06160 −0.530800 0.847497i \(-0.678108\pi\)
−0.530800 + 0.847497i \(0.678108\pi\)
\(594\) 0 0
\(595\) −15.6457 + 37.7721i −0.641411 + 1.54850i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −7.76404 7.76404i −0.317230 0.317230i 0.530472 0.847702i \(-0.322015\pi\)
−0.847702 + 0.530472i \(0.822015\pi\)
\(600\) 0 0
\(601\) 27.7695 27.7695i 1.13274 1.13274i 0.143020 0.989720i \(-0.454319\pi\)
0.989720 0.143020i \(-0.0456812\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −15.3790 6.37021i −0.625247 0.258986i
\(606\) 0 0
\(607\) 6.83755i 0.277527i −0.990326 0.138764i \(-0.955687\pi\)
0.990326 0.138764i \(-0.0443129\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 6.74366 16.2806i 0.272819 0.658644i
\(612\) 0 0
\(613\) 1.88592 0.781173i 0.0761716 0.0315513i −0.344272 0.938870i \(-0.611874\pi\)
0.420444 + 0.907319i \(0.361874\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 16.5582 16.5582i 0.666610 0.666610i −0.290320 0.956930i \(-0.593762\pi\)
0.956930 + 0.290320i \(0.0937617\pi\)
\(618\) 0 0
\(619\) −34.0627 + 14.1093i −1.36910 + 0.567099i −0.941544 0.336891i \(-0.890625\pi\)
−0.427554 + 0.903990i \(0.640625\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 10.0602i 0.403053i
\(624\) 0 0
\(625\) 2.37526i 0.0950104i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 2.90387 1.20282i 0.115785 0.0479597i
\(630\) 0 0
\(631\) 18.8332 18.8332i 0.749737 0.749737i −0.224693 0.974430i \(-0.572138\pi\)
0.974430 + 0.224693i \(0.0721379\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 6.23494 2.58260i 0.247426 0.102487i
\(636\) 0 0
\(637\) −4.41589 + 10.6609i −0.174964 + 0.422400i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 34.0636i 1.34543i 0.739900 + 0.672716i \(0.234873\pi\)
−0.739900 + 0.672716i \(0.765127\pi\)
\(642\) 0 0
\(643\) −8.14924 3.37552i −0.321374 0.133118i 0.216164 0.976357i \(-0.430646\pi\)
−0.537538 + 0.843239i \(0.680646\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −15.9458 + 15.9458i −0.626894 + 0.626894i −0.947285 0.320391i \(-0.896186\pi\)
0.320391 + 0.947285i \(0.396186\pi\)
\(648\) 0 0
\(649\) 38.6436 + 38.6436i 1.51689 + 1.51689i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −10.3560 + 25.0017i −0.405263 + 0.978391i 0.581104 + 0.813829i \(0.302621\pi\)
−0.986367 + 0.164562i \(0.947379\pi\)
\(654\) 0 0
\(655\) 23.2614 0.908900
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0.976716 + 0.404569i 0.0380475 + 0.0157598i 0.401626 0.915804i \(-0.368445\pi\)
−0.363579 + 0.931564i \(0.618445\pi\)
\(660\) 0 0
\(661\) −10.6003 25.5914i −0.412304 0.995389i −0.984518 0.175285i \(-0.943915\pi\)
0.572214 0.820104i \(-0.306085\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −8.24627 8.24627i −0.319777 0.319777i
\(666\) 0 0
\(667\) 1.11051 + 2.68100i 0.0429990 + 0.103809i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −5.97883 −0.230810
\(672\) 0 0
\(673\) −17.3400 −0.668409 −0.334205 0.942501i \(-0.608468\pi\)
−0.334205 + 0.942501i \(0.608468\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 1.10411 + 2.66556i 0.0424344 + 0.102446i 0.943676 0.330872i \(-0.107343\pi\)
−0.901241 + 0.433318i \(0.857343\pi\)
\(678\) 0 0
\(679\) −1.36271 1.36271i −0.0522962 0.0522962i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −9.51934 22.9817i −0.364247 0.879371i −0.994669 0.103118i \(-0.967118\pi\)
0.630422 0.776253i \(-0.282882\pi\)
\(684\) 0 0
\(685\) −12.6703 5.24823i −0.484109 0.200525i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 10.3542 0.394462
\(690\) 0 0
\(691\) −8.56212 + 20.6708i −0.325719 + 0.786354i 0.673182 + 0.739477i \(0.264927\pi\)
−0.998901 + 0.0468774i \(0.985073\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 32.8142 + 32.8142i 1.24471 + 1.24471i
\(696\) 0 0
\(697\) 11.2742 11.2742i 0.427041 0.427041i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 40.4517 + 16.7556i 1.52784 + 0.632852i 0.979143 0.203171i \(-0.0651247\pi\)
0.548695 + 0.836022i \(0.315125\pi\)
\(702\) 0 0
\(703\) 0.896560i 0.0338144i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −6.82119 + 16.4678i −0.256537 + 0.619335i
\(708\) 0 0
\(709\) −16.2624 + 6.73611i −0.610748 + 0.252980i −0.666548 0.745462i \(-0.732229\pi\)
0.0558005 + 0.998442i \(0.482229\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 9.92594 9.92594i 0.371730 0.371730i
\(714\) 0 0
\(715\) 32.2011 13.3381i 1.20425 0.498818i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 23.5642i 0.878796i −0.898292 0.439398i \(-0.855192\pi\)
0.898292 0.439398i \(-0.144808\pi\)
\(720\) 0 0
\(721\) 18.3862i 0.684739i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 2.71064 1.12278i 0.100671 0.0416991i
\(726\) 0 0
\(727\) 16.5208 16.5208i 0.612724 0.612724i −0.330931 0.943655i \(-0.607363\pi\)
0.943655 + 0.330931i \(0.107363\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −55.4882 + 22.9840i −2.05230 + 0.850092i
\(732\) 0 0
\(733\) −8.74219 + 21.1055i −0.322900 + 0.779550i 0.676183 + 0.736734i \(0.263633\pi\)
−0.999083 + 0.0428159i \(0.986367\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 34.0077i 1.25269i
\(738\) 0 0
\(739\) −41.5366 17.2050i −1.52795 0.632897i −0.548785 0.835964i \(-0.684909\pi\)
−0.979165 + 0.203066i \(0.934909\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −19.3232 + 19.3232i −0.708900 + 0.708900i −0.966304 0.257404i \(-0.917133\pi\)
0.257404 + 0.966304i \(0.417133\pi\)
\(744\) 0 0
\(745\) 22.9890 + 22.9890i 0.842253 + 0.842253i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −9.29200 + 22.4329i −0.339522 + 0.819679i
\(750\) 0 0
\(751\) 9.32371 0.340227 0.170114 0.985424i \(-0.445587\pi\)
0.170114 + 0.985424i \(0.445587\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 57.1724 + 23.6816i 2.08072 + 0.861861i
\(756\) 0 0
\(757\) −9.71720 23.4594i −0.353178 0.852647i −0.996224 0.0868193i \(-0.972330\pi\)
0.643046 0.765827i \(-0.277670\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 21.9092 + 21.9092i 0.794207 + 0.794207i 0.982175 0.187968i \(-0.0601902\pi\)
−0.187968 + 0.982175i \(0.560190\pi\)
\(762\) 0 0
\(763\) 0.746683 + 1.80265i 0.0270317 + 0.0652604i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −33.5585 −1.21173
\(768\) 0 0
\(769\) −11.9106 −0.429508 −0.214754 0.976668i \(-0.568895\pi\)
−0.214754 + 0.976668i \(0.568895\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −3.39696 8.20098i −0.122180 0.294969i 0.850942 0.525260i \(-0.176032\pi\)
−0.973122 + 0.230291i \(0.926032\pi\)
\(774\) 0 0
\(775\) −10.0357 10.0357i −0.360492 0.360492i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 1.74044 + 4.20178i 0.0623576 + 0.150545i
\(780\) 0 0
\(781\) 24.5107 + 10.1527i 0.877061 + 0.363290i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 52.2130 1.86356
\(786\) 0 0
\(787\) −6.32430 + 15.2682i −0.225437 + 0.544253i −0.995612 0.0935798i \(-0.970169\pi\)
0.770175 + 0.637833i \(0.220169\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −5.11797 5.11797i −0.181974 0.181974i
\(792\) 0 0
\(793\) 2.59604 2.59604i 0.0921881 0.0921881i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 13.4382 + 5.56628i 0.476005 + 0.197168i 0.607770 0.794113i \(-0.292064\pi\)
−0.131765 + 0.991281i \(0.542064\pi\)
\(798\) 0 0
\(799\) 54.5269i 1.92902i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 17.0779 41.2298i 0.602667 1.45497i
\(804\) 0 0
\(805\) 41.3591 17.1315i 1.45772 0.603807i