Properties

Label 1152.2.w.a.719.5
Level $1152$
Weight $2$
Character 1152.719
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 719.5
Character \(\chi\) \(=\) 1152.719
Dual form 1152.2.w.a.431.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.0913223 + 0.0378270i) q^{5} +(3.05457 - 3.05457i) q^{7} +O(q^{10})\) \(q+(0.0913223 + 0.0378270i) q^{5} +(3.05457 - 3.05457i) q^{7} +(-5.25649 - 2.17731i) q^{11} +(-1.57202 - 3.79519i) q^{13} +2.56471 q^{17} +(-2.64058 + 1.09376i) q^{19} +(-4.03079 + 4.03079i) q^{23} +(-3.52863 - 3.52863i) q^{25} +(-2.06984 - 4.99704i) q^{29} +1.44203i q^{31} +(0.394496 - 0.163406i) q^{35} +(-2.07758 + 5.01573i) q^{37} +(-0.296726 - 0.296726i) q^{41} +(2.72382 - 6.57588i) q^{43} +7.42367i q^{47} -11.6608i q^{49} +(-1.53235 + 3.69941i) q^{53} +(-0.397674 - 0.397674i) q^{55} +(0.988255 - 2.38586i) q^{59} +(10.4346 - 4.32215i) q^{61} -0.406051i q^{65} +(0.690522 + 1.66707i) q^{67} +(-2.97957 - 2.97957i) q^{71} +(9.22401 - 9.22401i) q^{73} +(-22.7071 + 9.40558i) q^{77} +1.12181 q^{79} +(-4.13529 - 9.98348i) q^{83} +(0.234216 + 0.0970152i) q^{85} +(12.0590 - 12.0590i) q^{89} +(-16.3945 - 6.79084i) q^{91} -0.282518 q^{95} -18.5545 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 8 q^{11} + 16 q^{29} + 24 q^{35} + 16 q^{53} + 32 q^{55} + 32 q^{59} + 32 q^{61} + 16 q^{67} + 16 q^{71} + 16 q^{77} + 32 q^{79} - 40 q^{83} + 48 q^{91} - 80 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(127\) \(641\) \(901\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{5}{8}\right)\)

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
\(5\) 0.0913223 + 0.0378270i 0.0408406 + 0.0169167i 0.403010 0.915195i \(-0.367964\pi\)
−0.362170 + 0.932112i \(0.617964\pi\)
\(6\) 0 0
\(7\) 3.05457 3.05457i 1.15452 1.15452i 0.168884 0.985636i \(-0.445984\pi\)
0.985636 0.168884i \(-0.0540163\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −5.25649 2.17731i −1.58489 0.656483i −0.595712 0.803198i \(-0.703130\pi\)
−0.989179 + 0.146715i \(0.953130\pi\)
\(12\) 0 0
\(13\) −1.57202 3.79519i −0.436000 1.05260i −0.977318 0.211779i \(-0.932074\pi\)
0.541317 0.840818i \(-0.317926\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.56471 0.622034 0.311017 0.950404i \(-0.399330\pi\)
0.311017 + 0.950404i \(0.399330\pi\)
\(18\) 0 0
\(19\) −2.64058 + 1.09376i −0.605791 + 0.250927i −0.664428 0.747353i \(-0.731325\pi\)
0.0586367 + 0.998279i \(0.481325\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −4.03079 + 4.03079i −0.840477 + 0.840477i −0.988921 0.148443i \(-0.952574\pi\)
0.148443 + 0.988921i \(0.452574\pi\)
\(24\) 0 0
\(25\) −3.52863 3.52863i −0.705725 0.705725i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −2.06984 4.99704i −0.384360 0.927927i −0.991111 0.133035i \(-0.957528\pi\)
0.606752 0.794892i \(-0.292472\pi\)
\(30\) 0 0
\(31\) 1.44203i 0.258996i 0.991580 + 0.129498i \(0.0413366\pi\)
−0.991580 + 0.129498i \(0.958663\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0.394496 0.163406i 0.0666820 0.0276206i
\(36\) 0 0
\(37\) −2.07758 + 5.01573i −0.341552 + 0.824581i 0.656007 + 0.754755i \(0.272244\pi\)
−0.997559 + 0.0698256i \(0.977756\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −0.296726 0.296726i −0.0463409 0.0463409i 0.683557 0.729897i \(-0.260432\pi\)
−0.729897 + 0.683557i \(0.760432\pi\)
\(42\) 0 0
\(43\) 2.72382 6.57588i 0.415378 1.00281i −0.568291 0.822828i \(-0.692395\pi\)
0.983669 0.179984i \(-0.0576047\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 7.42367i 1.08285i 0.840748 + 0.541427i \(0.182116\pi\)
−0.840748 + 0.541427i \(0.817884\pi\)
\(48\) 0 0
\(49\) 11.6608i 1.66583i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −1.53235 + 3.69941i −0.210484 + 0.508153i −0.993498 0.113851i \(-0.963681\pi\)
0.783014 + 0.622004i \(0.213681\pi\)
\(54\) 0 0
\(55\) −0.397674 0.397674i −0.0536223 0.0536223i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0.988255 2.38586i 0.128660 0.310612i −0.846402 0.532544i \(-0.821236\pi\)
0.975062 + 0.221931i \(0.0712361\pi\)
\(60\) 0 0
\(61\) 10.4346 4.32215i 1.33601 0.553395i 0.403649 0.914914i \(-0.367742\pi\)
0.932365 + 0.361519i \(0.117742\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0.406051i 0.0503644i
\(66\) 0 0
\(67\) 0.690522 + 1.66707i 0.0843606 + 0.203665i 0.960431 0.278519i \(-0.0898437\pi\)
−0.876070 + 0.482184i \(0.839844\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −2.97957 2.97957i −0.353610 0.353610i 0.507841 0.861451i \(-0.330444\pi\)
−0.861451 + 0.507841i \(0.830444\pi\)
\(72\) 0 0
\(73\) 9.22401 9.22401i 1.07959 1.07959i 0.0830429 0.996546i \(-0.473536\pi\)
0.996546 0.0830429i \(-0.0264638\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −22.7071 + 9.40558i −2.58771 + 1.07187i
\(78\) 0 0
\(79\) 1.12181 0.126213 0.0631065 0.998007i \(-0.479899\pi\)
0.0631065 + 0.998007i \(0.479899\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −4.13529 9.98348i −0.453907 1.09583i −0.970824 0.239794i \(-0.922920\pi\)
0.516916 0.856036i \(-0.327080\pi\)
\(84\) 0 0
\(85\) 0.234216 + 0.0970152i 0.0254042 + 0.0105228i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 12.0590 12.0590i 1.27825 1.27825i 0.336609 0.941644i \(-0.390720\pi\)
0.941644 0.336609i \(-0.109280\pi\)
\(90\) 0 0
\(91\) −16.3945 6.79084i −1.71862 0.711874i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −0.282518 −0.0289857
\(96\) 0 0
\(97\) −18.5545 −1.88393 −0.941963 0.335717i \(-0.891022\pi\)
−0.941963 + 0.335717i \(0.891022\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −5.24603 2.17298i −0.521999 0.216219i 0.106096 0.994356i \(-0.466165\pi\)
−0.628095 + 0.778137i \(0.716165\pi\)
\(102\) 0 0
\(103\) 11.0095 11.0095i 1.08479 1.08479i 0.0887398 0.996055i \(-0.471716\pi\)
0.996055 0.0887398i \(-0.0282839\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0.182628 + 0.0756468i 0.0176553 + 0.00731305i 0.391494 0.920181i \(-0.371959\pi\)
−0.373838 + 0.927494i \(0.621959\pi\)
\(108\) 0 0
\(109\) 2.10265 + 5.07626i 0.201398 + 0.486217i 0.992019 0.126088i \(-0.0402423\pi\)
−0.790621 + 0.612305i \(0.790242\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −5.91777 −0.556697 −0.278348 0.960480i \(-0.589787\pi\)
−0.278348 + 0.960480i \(0.589787\pi\)
\(114\) 0 0
\(115\) −0.520573 + 0.215629i −0.0485437 + 0.0201075i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 7.83410 7.83410i 0.718151 0.718151i
\(120\) 0 0
\(121\) 15.1118 + 15.1118i 1.37380 + 1.37380i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −0.377900 0.912331i −0.0338004 0.0816014i
\(126\) 0 0
\(127\) 9.70061i 0.860790i −0.902641 0.430395i \(-0.858374\pi\)
0.902641 0.430395i \(-0.141626\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 12.7327 5.27407i 1.11246 0.460798i 0.250678 0.968070i \(-0.419346\pi\)
0.861786 + 0.507273i \(0.169346\pi\)
\(132\) 0 0
\(133\) −4.72486 + 11.4068i −0.409698 + 0.989098i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 5.62861 + 5.62861i 0.480884 + 0.480884i 0.905414 0.424530i \(-0.139561\pi\)
−0.424530 + 0.905414i \(0.639561\pi\)
\(138\) 0 0
\(139\) −0.202389 + 0.488610i −0.0171664 + 0.0414434i −0.932230 0.361865i \(-0.882140\pi\)
0.915064 + 0.403309i \(0.132140\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 23.3722i 1.95448i
\(144\) 0 0
\(145\) 0.534637i 0.0443992i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1.35052 + 3.26046i −0.110639 + 0.267107i −0.969495 0.245110i \(-0.921176\pi\)
0.858856 + 0.512217i \(0.171176\pi\)
\(150\) 0 0
\(151\) 13.6492 + 13.6492i 1.11076 + 1.11076i 0.993048 + 0.117709i \(0.0375552\pi\)
0.117709 + 0.993048i \(0.462445\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −0.0545476 + 0.131690i −0.00438137 + 0.0105776i
\(156\) 0 0
\(157\) −15.4587 + 6.40321i −1.23374 + 0.511032i −0.901753 0.432252i \(-0.857719\pi\)
−0.331987 + 0.943284i \(0.607719\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 24.6247i 1.94070i
\(162\) 0 0
\(163\) 6.04288 + 14.5888i 0.473315 + 1.14268i 0.962689 + 0.270609i \(0.0872252\pi\)
−0.489374 + 0.872074i \(0.662775\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 6.58872 + 6.58872i 0.509850 + 0.509850i 0.914480 0.404630i \(-0.132600\pi\)
−0.404630 + 0.914480i \(0.632600\pi\)
\(168\) 0 0
\(169\) −2.73986 + 2.73986i −0.210759 + 0.210759i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 17.8204 7.38143i 1.35486 0.561200i 0.417216 0.908807i \(-0.363006\pi\)
0.937640 + 0.347608i \(0.113006\pi\)
\(174\) 0 0
\(175\) −21.5569 −1.62955
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −4.07369 9.83475i −0.304482 0.735084i −0.999865 0.0164446i \(-0.994765\pi\)
0.695383 0.718639i \(-0.255235\pi\)
\(180\) 0 0
\(181\) 8.06280 + 3.33972i 0.599303 + 0.248239i 0.661647 0.749815i \(-0.269858\pi\)
−0.0623442 + 0.998055i \(0.519858\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −0.379459 + 0.379459i −0.0278984 + 0.0278984i
\(186\) 0 0
\(187\) −13.4814 5.58417i −0.985856 0.408355i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 13.0520 0.944411 0.472205 0.881489i \(-0.343458\pi\)
0.472205 + 0.881489i \(0.343458\pi\)
\(192\) 0 0
\(193\) −3.05926 −0.220210 −0.110105 0.993920i \(-0.535119\pi\)
−0.110105 + 0.993920i \(0.535119\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 5.46774 + 2.26481i 0.389560 + 0.161361i 0.568862 0.822433i \(-0.307384\pi\)
−0.179302 + 0.983794i \(0.557384\pi\)
\(198\) 0 0
\(199\) 4.48835 4.48835i 0.318170 0.318170i −0.529894 0.848064i \(-0.677768\pi\)
0.848064 + 0.529894i \(0.177768\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −21.5863 8.94133i −1.51506 0.627559i
\(204\) 0 0
\(205\) −0.0158735 0.0383220i −0.00110865 0.00267652i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 16.2617 1.12484
\(210\) 0 0
\(211\) −0.322439 + 0.133558i −0.0221976 + 0.00919454i −0.393755 0.919216i \(-0.628824\pi\)
0.371557 + 0.928410i \(0.378824\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0.497491 0.497491i 0.0339286 0.0339286i
\(216\) 0 0
\(217\) 4.40478 + 4.40478i 0.299016 + 0.299016i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −4.03178 9.73358i −0.271207 0.654752i
\(222\) 0 0
\(223\) 19.1612i 1.28313i 0.767068 + 0.641566i \(0.221715\pi\)
−0.767068 + 0.641566i \(0.778285\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 19.4451 8.05441i 1.29061 0.534590i 0.371446 0.928455i \(-0.378862\pi\)
0.919169 + 0.393864i \(0.128862\pi\)
\(228\) 0 0
\(229\) −6.97193 + 16.8317i −0.460718 + 1.11227i 0.507385 + 0.861719i \(0.330612\pi\)
−0.968103 + 0.250552i \(0.919388\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −16.7768 16.7768i −1.09909 1.09909i −0.994518 0.104569i \(-0.966654\pi\)
−0.104569 0.994518i \(-0.533346\pi\)
\(234\) 0 0
\(235\) −0.280815 + 0.677947i −0.0183183 + 0.0442244i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 9.10976i 0.589261i −0.955611 0.294631i \(-0.904803\pi\)
0.955611 0.294631i \(-0.0951966\pi\)
\(240\) 0 0
\(241\) 7.39995i 0.476673i −0.971183 0.238336i \(-0.923398\pi\)
0.971183 0.238336i \(-0.0766020\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0.441093 1.06489i 0.0281804 0.0680336i
\(246\) 0 0
\(247\) 8.30210 + 8.30210i 0.528250 + 0.528250i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −4.84250 + 11.6908i −0.305656 + 0.737919i 0.694180 + 0.719802i \(0.255767\pi\)
−0.999836 + 0.0181174i \(0.994233\pi\)
\(252\) 0 0
\(253\) 29.9641 12.4115i 1.88382 0.780306i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 6.02571i 0.375873i −0.982181 0.187937i \(-0.939820\pi\)
0.982181 0.187937i \(-0.0601800\pi\)
\(258\) 0 0
\(259\) 8.97478 + 21.6670i 0.557666 + 1.34632i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −6.79218 6.79218i −0.418824 0.418824i 0.465974 0.884798i \(-0.345704\pi\)
−0.884798 + 0.465974i \(0.845704\pi\)
\(264\) 0 0
\(265\) −0.279875 + 0.279875i −0.0171926 + 0.0171926i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −13.8548 + 5.73883i −0.844740 + 0.349903i −0.762721 0.646728i \(-0.776137\pi\)
−0.0820193 + 0.996631i \(0.526137\pi\)
\(270\) 0 0
\(271\) −5.62497 −0.341692 −0.170846 0.985298i \(-0.554650\pi\)
−0.170846 + 0.985298i \(0.554650\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 10.8653 + 26.2311i 0.655201 + 1.58179i
\(276\) 0 0
\(277\) −1.00843 0.417706i −0.0605908 0.0250975i 0.352182 0.935931i \(-0.385440\pi\)
−0.412773 + 0.910834i \(0.635440\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 21.7589 21.7589i 1.29803 1.29803i 0.368335 0.929693i \(-0.379928\pi\)
0.929693 0.368335i \(-0.120072\pi\)
\(282\) 0 0
\(283\) 22.3614 + 9.26239i 1.32925 + 0.550592i 0.930441 0.366443i \(-0.119424\pi\)
0.398807 + 0.917035i \(0.369424\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −1.81274 −0.107003
\(288\) 0 0
\(289\) −10.4223 −0.613074
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 29.2423 + 12.1126i 1.70835 + 0.707623i 0.999998 + 0.00176683i \(0.000562400\pi\)
0.708355 + 0.705856i \(0.249438\pi\)
\(294\) 0 0
\(295\) 0.180500 0.180500i 0.0105091 0.0105091i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 21.6341 + 8.96114i 1.25113 + 0.518236i
\(300\) 0 0
\(301\) −11.7664 28.4066i −0.678204 1.63733i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1.11641 0.0639252
\(306\) 0 0
\(307\) −13.7854 + 5.71009i −0.786773 + 0.325892i −0.739645 0.672997i \(-0.765007\pi\)
−0.0471275 + 0.998889i \(0.515007\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −11.4220 + 11.4220i −0.647684 + 0.647684i −0.952433 0.304749i \(-0.901427\pi\)
0.304749 + 0.952433i \(0.401427\pi\)
\(312\) 0 0
\(313\) 2.24707 + 2.24707i 0.127012 + 0.127012i 0.767755 0.640743i \(-0.221374\pi\)
−0.640743 + 0.767755i \(0.721374\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.05906 + 2.55679i 0.0594826 + 0.143604i 0.950826 0.309724i \(-0.100237\pi\)
−0.891344 + 0.453328i \(0.850237\pi\)
\(318\) 0 0
\(319\) 30.7736i 1.72299i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −6.77233 + 2.80519i −0.376823 + 0.156085i
\(324\) 0 0
\(325\) −7.84475 + 18.9389i −0.435148 + 1.05054i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 22.6761 + 22.6761i 1.25018 + 1.25018i
\(330\) 0 0
\(331\) 0.123439 0.298008i 0.00678481 0.0163800i −0.920451 0.390858i \(-0.872178\pi\)
0.927236 + 0.374478i \(0.122178\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0.178361i 0.00974489i
\(336\) 0 0
\(337\) 16.5067i 0.899179i 0.893235 + 0.449590i \(0.148430\pi\)
−0.893235 + 0.449590i \(0.851570\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 3.13974 7.58001i 0.170027 0.410481i
\(342\) 0 0
\(343\) −14.2368 14.2368i −0.768716 0.768716i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −5.96248 + 14.3947i −0.320083 + 0.772748i 0.679166 + 0.733985i \(0.262342\pi\)
−0.999248 + 0.0387633i \(0.987658\pi\)
\(348\) 0 0
\(349\) 1.57618 0.652873i 0.0843707 0.0349475i −0.340099 0.940390i \(-0.610461\pi\)
0.424470 + 0.905442i \(0.360461\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 18.7091i 0.995786i −0.867239 0.497893i \(-0.834107\pi\)
0.867239 0.497893i \(-0.165893\pi\)
\(354\) 0 0
\(355\) −0.159393 0.384810i −0.00845972 0.0204236i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −23.5065 23.5065i −1.24062 1.24062i −0.959742 0.280882i \(-0.909373\pi\)
−0.280882 0.959742i \(-0.590627\pi\)
\(360\) 0 0
\(361\) −7.65868 + 7.65868i −0.403088 + 0.403088i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1.19127 0.493442i 0.0623542 0.0258279i
\(366\) 0 0
\(367\) 2.95190 0.154088 0.0770440 0.997028i \(-0.475452\pi\)
0.0770440 + 0.997028i \(0.475452\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 6.61945 + 15.9808i 0.343665 + 0.829680i
\(372\) 0 0
\(373\) −19.7552 8.18287i −1.02289 0.423693i −0.192746 0.981249i \(-0.561739\pi\)
−0.830140 + 0.557556i \(0.811739\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −15.7109 + 15.7109i −0.809152 + 0.809152i
\(378\) 0 0
\(379\) −4.26476 1.76652i −0.219066 0.0907402i 0.270451 0.962734i \(-0.412827\pi\)
−0.489518 + 0.871993i \(0.662827\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 9.45328 0.483040 0.241520 0.970396i \(-0.422354\pi\)
0.241520 + 0.970396i \(0.422354\pi\)
\(384\) 0 0
\(385\) −2.42945 −0.123816
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 20.8554 + 8.63860i 1.05741 + 0.437994i 0.842532 0.538646i \(-0.181064\pi\)
0.214880 + 0.976640i \(0.431064\pi\)
\(390\) 0 0
\(391\) −10.3378 + 10.3378i −0.522806 + 0.522806i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0.102446 + 0.0424345i 0.00515461 + 0.00213511i
\(396\) 0 0
\(397\) 3.29268 + 7.94922i 0.165255 + 0.398960i 0.984714 0.174177i \(-0.0557264\pi\)
−0.819460 + 0.573137i \(0.805726\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −32.5903 −1.62748 −0.813740 0.581229i \(-0.802572\pi\)
−0.813740 + 0.581229i \(0.802572\pi\)
\(402\) 0 0
\(403\) 5.47278 2.26690i 0.272619 0.112922i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 21.8416 21.8416i 1.08265 1.08265i
\(408\) 0 0
\(409\) 5.41708 + 5.41708i 0.267858 + 0.267858i 0.828236 0.560379i \(-0.189344\pi\)
−0.560379 + 0.828236i \(0.689344\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −4.26908 10.3065i −0.210068 0.507149i
\(414\) 0 0
\(415\) 1.06814i 0.0524329i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −22.0298 + 9.12504i −1.07623 + 0.445787i −0.849184 0.528097i \(-0.822906\pi\)
−0.227042 + 0.973885i \(0.572906\pi\)
\(420\) 0 0
\(421\) 2.82553 6.82144i 0.137708 0.332457i −0.839948 0.542667i \(-0.817415\pi\)
0.977656 + 0.210210i \(0.0674147\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −9.04991 9.04991i −0.438985 0.438985i
\(426\) 0 0
\(427\) 18.6709 45.0756i 0.903549 2.18136i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 6.73112i 0.324226i −0.986772 0.162113i \(-0.948169\pi\)
0.986772 0.162113i \(-0.0518310\pi\)
\(432\) 0 0
\(433\) 12.1160i 0.582257i 0.956684 + 0.291129i \(0.0940308\pi\)
−0.956684 + 0.291129i \(0.905969\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 6.23489 15.0524i 0.298255 0.720052i
\(438\) 0 0
\(439\) −14.0767 14.0767i −0.671843 0.671843i 0.286298 0.958141i \(-0.407575\pi\)
−0.958141 + 0.286298i \(0.907575\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 14.5313 35.0817i 0.690404 1.66678i −0.0535615 0.998565i \(-0.517057\pi\)
0.743965 0.668218i \(-0.232943\pi\)
\(444\) 0 0
\(445\) 1.55741 0.645102i 0.0738285 0.0305808i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 25.9809i 1.22611i 0.790039 + 0.613056i \(0.210060\pi\)
−0.790039 + 0.613056i \(0.789940\pi\)
\(450\) 0 0
\(451\) 0.913674 + 2.20580i 0.0430232 + 0.103867i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −1.24031 1.24031i −0.0581467 0.0581467i
\(456\) 0 0
\(457\) 6.23785 6.23785i 0.291794 0.291794i −0.545994 0.837789i \(-0.683848\pi\)
0.837789 + 0.545994i \(0.183848\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 23.3278 9.66269i 1.08648 0.450036i 0.233704 0.972308i \(-0.424915\pi\)
0.852779 + 0.522271i \(0.174915\pi\)
\(462\) 0 0
\(463\) −3.99595 −0.185707 −0.0928537 0.995680i \(-0.529599\pi\)
−0.0928537 + 0.995680i \(0.529599\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −7.26272 17.5338i −0.336079 0.811366i −0.998084 0.0618671i \(-0.980294\pi\)
0.662006 0.749499i \(-0.269706\pi\)
\(468\) 0 0
\(469\) 7.20142 + 2.98293i 0.332531 + 0.137739i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −28.6354 + 28.6354i −1.31666 + 1.31666i
\(474\) 0 0
\(475\) 13.1771 + 5.45814i 0.604607 + 0.250437i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −21.7665 −0.994537 −0.497268 0.867597i \(-0.665664\pi\)
−0.497268 + 0.867597i \(0.665664\pi\)
\(480\) 0 0
\(481\) 22.3017 1.01687
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1.69444 0.701861i −0.0769407 0.0318699i
\(486\) 0 0
\(487\) 9.10128 9.10128i 0.412419 0.412419i −0.470162 0.882580i \(-0.655804\pi\)
0.882580 + 0.470162i \(0.155804\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −15.2645 6.32276i −0.688876 0.285342i 0.0106556 0.999943i \(-0.496608\pi\)
−0.699532 + 0.714601i \(0.746608\pi\)
\(492\) 0 0
\(493\) −5.30855 12.8160i −0.239085 0.577202i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −18.2026 −0.816500
\(498\) 0 0
\(499\) 32.2595 13.3623i 1.44413 0.598180i 0.483337 0.875434i \(-0.339425\pi\)
0.960796 + 0.277255i \(0.0894246\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 7.34111 7.34111i 0.327324 0.327324i −0.524244 0.851568i \(-0.675652\pi\)
0.851568 + 0.524244i \(0.175652\pi\)
\(504\) 0 0
\(505\) −0.396882 0.396882i −0.0176610 0.0176610i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 7.55299 + 18.2345i 0.334780 + 0.808231i 0.998199 + 0.0599832i \(0.0191047\pi\)
−0.663419 + 0.748248i \(0.730895\pi\)
\(510\) 0 0
\(511\) 56.3508i 2.49281i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 1.42186 0.588955i 0.0626548 0.0259525i
\(516\) 0 0
\(517\) 16.1636 39.0225i 0.710876 1.71621i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −26.3209 26.3209i −1.15314 1.15314i −0.985920 0.167218i \(-0.946522\pi\)
−0.167218 0.985920i \(-0.553478\pi\)
\(522\) 0 0
\(523\) −5.50275 + 13.2848i −0.240619 + 0.580905i −0.997345 0.0728276i \(-0.976798\pi\)
0.756726 + 0.653732i \(0.226798\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 3.69839i 0.161104i
\(528\) 0 0
\(529\) 9.49450i 0.412805i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −0.659674 + 1.59259i −0.0285737 + 0.0689829i
\(534\) 0 0
\(535\) 0.0138165 + 0.0138165i 0.000597339 + 0.000597339i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −25.3892 + 61.2950i −1.09359 + 2.64016i
\(540\) 0 0
\(541\) 1.34772 0.558245i 0.0579431 0.0240008i −0.353524 0.935426i \(-0.615017\pi\)
0.411467 + 0.911425i \(0.365017\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0.543113i 0.0232644i
\(546\) 0 0
\(547\) −3.11417 7.51828i −0.133152 0.321458i 0.843215 0.537577i \(-0.180660\pi\)
−0.976367 + 0.216119i \(0.930660\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 10.9312 + 10.9312i 0.465683 + 0.465683i
\(552\) 0 0
\(553\) 3.42664 3.42664i 0.145715 0.145715i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −10.3810 + 4.29993i −0.439855 + 0.182194i −0.591610 0.806224i \(-0.701508\pi\)
0.151755 + 0.988418i \(0.451508\pi\)
\(558\) 0 0
\(559\) −29.2386 −1.23666
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 1.95005 + 4.70784i 0.0821848 + 0.198412i 0.959630 0.281265i \(-0.0907540\pi\)
−0.877445 + 0.479677i \(0.840754\pi\)
\(564\) 0 0
\(565\) −0.540424 0.223851i −0.0227358 0.00941749i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −3.12423 + 3.12423i −0.130974 + 0.130974i −0.769555 0.638581i \(-0.779522\pi\)
0.638581 + 0.769555i \(0.279522\pi\)
\(570\) 0 0
\(571\) −33.4029 13.8360i −1.39787 0.579017i −0.448672 0.893697i \(-0.648103\pi\)
−0.949198 + 0.314680i \(0.898103\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 28.4463 1.18629
\(576\) 0 0
\(577\) −14.0315 −0.584141 −0.292070 0.956397i \(-0.594344\pi\)
−0.292070 + 0.956397i \(0.594344\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −43.1268 17.8637i −1.78920 0.741112i
\(582\) 0 0
\(583\) 16.1095 16.1095i 0.667188 0.667188i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 12.0165 + 4.97740i 0.495975 + 0.205439i 0.616627 0.787255i \(-0.288499\pi\)
−0.120652 + 0.992695i \(0.538499\pi\)
\(588\) 0 0
\(589\) −1.57724 3.80780i −0.0649891 0.156898i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −17.6528 −0.724914 −0.362457 0.932000i \(-0.618062\pi\)
−0.362457 + 0.932000i \(0.618062\pi\)
\(594\) 0 0
\(595\) 1.01177 0.419088i 0.0414785 0.0171809i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −5.25995 + 5.25995i −0.214916 + 0.214916i −0.806352 0.591436i \(-0.798561\pi\)
0.591436 + 0.806352i \(0.298561\pi\)
\(600\) 0 0
\(601\) 6.54574 + 6.54574i 0.267006 + 0.267006i 0.827893 0.560886i \(-0.189540\pi\)
−0.560886 + 0.827893i \(0.689540\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0.808413 + 1.95168i 0.0328667 + 0.0793472i
\(606\) 0 0
\(607\) 1.72276i 0.0699248i −0.999389 0.0349624i \(-0.988869\pi\)
0.999389 0.0349624i \(-0.0111311\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 28.1743 11.6702i 1.13981 0.472125i
\(612\) 0 0
\(613\) 16.6267 40.1405i 0.671547 1.62126i −0.107435 0.994212i \(-0.534264\pi\)
0.778982 0.627046i \(-0.215736\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −7.78933 7.78933i −0.313587 0.313587i 0.532711 0.846297i \(-0.321173\pi\)
−0.846297 + 0.532711i \(0.821173\pi\)
\(618\) 0 0
\(619\) −11.0171 + 26.5976i −0.442814 + 1.06905i 0.532143 + 0.846655i \(0.321387\pi\)
−0.974957 + 0.222394i \(0.928613\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 73.6703i 2.95154i
\(624\) 0 0
\(625\) 24.8535i 0.994141i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −5.32840 + 12.8639i −0.212457 + 0.512917i
\(630\) 0 0
\(631\) 21.0548 + 21.0548i 0.838177 + 0.838177i 0.988619 0.150442i \(-0.0480696\pi\)
−0.150442 + 0.988619i \(0.548070\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0.366944 0.885882i 0.0145617 0.0351552i
\(636\) 0 0
\(637\) −44.2551 + 18.3311i −1.75345 + 0.726303i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 5.65123i 0.223210i 0.993753 + 0.111605i \(0.0355992\pi\)
−0.993753 + 0.111605i \(0.964401\pi\)
\(642\) 0 0
\(643\) −17.0022 41.0470i −0.670502 1.61874i −0.780759 0.624833i \(-0.785167\pi\)
0.110256 0.993903i \(-0.464833\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0.0151270 + 0.0151270i 0.000594703 + 0.000594703i 0.707404 0.706809i \(-0.249866\pi\)
−0.706809 + 0.707404i \(0.749866\pi\)
\(648\) 0 0
\(649\) −10.3895 + 10.3895i −0.407824 + 0.407824i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 28.8575 11.9531i 1.12928 0.467763i 0.261744 0.965137i \(-0.415703\pi\)
0.867536 + 0.497375i \(0.165703\pi\)
\(654\) 0 0
\(655\) 1.36228 0.0532289
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 7.25678 + 17.5194i 0.282684 + 0.682459i 0.999896 0.0143952i \(-0.00458229\pi\)
−0.717212 + 0.696855i \(0.754582\pi\)
\(660\) 0 0
\(661\) −15.6310 6.47456i −0.607974 0.251831i 0.0573877 0.998352i \(-0.481723\pi\)
−0.665362 + 0.746521i \(0.731723\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −0.862971 + 0.862971i −0.0334646 + 0.0334646i
\(666\) 0 0
\(667\) 28.4851 + 11.7989i 1.10295 + 0.456856i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −64.2600 −2.48073
\(672\) 0 0
\(673\) 26.5987 1.02530 0.512652 0.858596i \(-0.328663\pi\)
0.512652 + 0.858596i \(0.328663\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −26.3000 10.8938i −1.01079 0.418683i −0.185047 0.982730i \(-0.559244\pi\)
−0.825743 + 0.564047i \(0.809244\pi\)
\(678\) 0 0
\(679\) −56.6761 + 56.6761i −2.17503 + 2.17503i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 29.9528 + 12.4069i 1.14611 + 0.474735i 0.873228 0.487312i \(-0.162022\pi\)
0.272884 + 0.962047i \(0.412022\pi\)
\(684\) 0 0
\(685\) 0.301105 + 0.726931i 0.0115046 + 0.0277746i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 16.4489 0.626652
\(690\) 0 0
\(691\) 9.94272 4.11841i 0.378239 0.156672i −0.185460 0.982652i \(-0.559378\pi\)
0.563699 + 0.825980i \(0.309378\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −0.0369653 + 0.0369653i −0.00140217 + 0.00140217i
\(696\) 0 0
\(697\) −0.761018 0.761018i −0.0288256 0.0288256i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 5.59430 + 13.5058i 0.211294 + 0.510108i 0.993623 0.112757i \(-0.0359683\pi\)
−0.782329 + 0.622866i \(0.785968\pi\)
\(702\) 0 0
\(703\) 15.5168i 0.585228i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −22.6619 + 9.38686i −0.852288 + 0.353029i
\(708\) 0 0
\(709\) 4.92207 11.8829i 0.184852 0.446273i −0.804102 0.594491i \(-0.797354\pi\)
0.988955 + 0.148218i \(0.0473537\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −5.81252 5.81252i −0.217680 0.217680i
\(714\) 0 0
\(715\) −0.884098 + 2.13440i −0.0330634 + 0.0798221i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 16.1029i 0.600537i 0.953855 + 0.300268i \(0.0970762\pi\)
−0.953855 + 0.300268i \(0.902924\pi\)
\(720\) 0 0
\(721\) 67.2584i 2.50483i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −10.3290 + 24.9364i −0.383609 + 0.926113i
\(726\) 0 0
\(727\) −21.0560 21.0560i −0.780923 0.780923i 0.199064 0.979987i \(-0.436210\pi\)
−0.979987 + 0.199064i \(0.936210\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 6.98581 16.8652i 0.258379 0.623783i
\(732\) 0 0
\(733\) 41.2426 17.0832i 1.52333 0.630984i 0.545074 0.838388i \(-0.316501\pi\)
0.978255 + 0.207404i \(0.0665015\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 10.2664i 0.378168i
\(738\) 0 0
\(739\) −11.2262 27.1024i −0.412962 0.996977i −0.984338 0.176290i \(-0.943591\pi\)
0.571377 0.820688i \(-0.306409\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −15.8059 15.8059i −0.579863 0.579863i 0.355003 0.934865i \(-0.384480\pi\)
−0.934865 + 0.355003i \(0.884480\pi\)
\(744\) 0 0
\(745\) −0.246666 + 0.246666i −0.00903715 + 0.00903715i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0.788918 0.326780i 0.0288264 0.0119403i
\(750\) 0 0
\(751\) 12.4955 0.455969 0.227984 0.973665i \(-0.426787\pi\)
0.227984 + 0.973665i \(0.426787\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0.730170 + 1.76279i 0.0265736 + 0.0641544i
\(756\) 0 0
\(757\) 30.0398 + 12.4429i 1.09182 + 0.452245i 0.854639 0.519222i \(-0.173778\pi\)
0.237176 + 0.971467i \(0.423778\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 15.5032 15.5032i 0.561992 0.561992i −0.367881 0.929873i \(-0.619917\pi\)
0.929873 + 0.367881i \(0.119917\pi\)
\(762\) 0 0
\(763\) 21.9285 + 9.08308i 0.793865 + 0.328830i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −10.6084 −0.383046
\(768\) 0 0
\(769\) −7.08253 −0.255403 −0.127701 0.991813i \(-0.540760\pi\)
−0.127701 + 0.991813i \(0.540760\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 30.3534 + 12.5728i 1.09173 + 0.452211i 0.854611 0.519268i \(-0.173796\pi\)
0.237123 + 0.971480i \(0.423796\pi\)
\(774\) 0 0
\(775\) 5.08838 5.08838i 0.182780 0.182780i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 1.10808 + 0.458981i 0.0397011 + 0.0164447i
\(780\) 0 0
\(781\) 9.17464 + 22.1495i 0.328294 + 0.792573i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −1.65394 −0.0590316
\(786\) 0 0
\(787\) 37.1276 15.3788i 1.32346 0.548194i 0.394675 0.918821i \(-0.370857\pi\)
0.928782 + 0.370627i \(0.120857\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −18.0763 + 18.0763i −0.642718 + 0.642718i
\(792\) 0 0
\(793\) −32.8068 32.8068i −1.16500 1.16500i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 1.87919 + 4.53677i 0.0665644 + 0.160701i 0.953661 0.300883i \(-0.0972814\pi\)
−0.887097 + 0.461584i \(0.847281\pi\)
\(798\) 0 0
\(799\) 19.0396i 0.673572i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −68.5694 + 28.4024i −2.41976 + 1.00230i
\(804\) 0 0