Properties

Label 1152.2.w.a.143.5
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 143.5
Character \(\chi\) \(=\) 1152.143
Dual form 1152.2.w.a.1007.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.0963530 + 0.232617i) q^{5} +(-0.617536 + 0.617536i) q^{7} +O(q^{10})\) \(q+(-0.0963530 + 0.232617i) q^{5} +(-0.617536 + 0.617536i) q^{7} +(-0.505112 + 1.21945i) q^{11} +(3.41575 - 1.41485i) q^{13} +2.76109 q^{17} +(-0.189895 - 0.458448i) q^{19} +(-4.46959 + 4.46959i) q^{23} +(3.49071 + 3.49071i) q^{25} +(-0.0101033 + 0.00418494i) q^{29} -4.03370i q^{31} +(-0.0841477 - 0.203151i) q^{35} +(6.30586 + 2.61197i) q^{37} +(5.34633 + 5.34633i) q^{41} +(10.1719 + 4.21336i) q^{43} +11.5870i q^{47} +6.23730i q^{49} +(-9.04956 - 3.74845i) q^{53} +(-0.234995 - 0.234995i) q^{55} +(-0.939369 - 0.389099i) q^{59} +(-2.97084 - 7.17223i) q^{61} +0.930884i q^{65} +(7.40244 - 3.06619i) q^{67} +(1.20890 + 1.20890i) q^{71} +(3.73875 - 3.73875i) q^{73} +(-0.441128 - 1.06498i) q^{77} +7.22016 q^{79} +(11.2970 - 4.67935i) q^{83} +(-0.266039 + 0.642275i) q^{85} +(-3.70197 + 3.70197i) q^{89} +(-1.23563 + 2.98307i) q^{91} +0.124940 q^{95} -14.0257 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q+O(q^{10}) \) 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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).

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

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
\(5\) −0.0963530 + 0.232617i −0.0430904 + 0.104029i −0.943959 0.330062i \(-0.892930\pi\)
0.900869 + 0.434091i \(0.142930\pi\)
\(6\) 0 0
\(7\) −0.617536 + 0.617536i −0.233407 + 0.233407i −0.814113 0.580706i \(-0.802776\pi\)
0.580706 + 0.814113i \(0.302776\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −0.505112 + 1.21945i −0.152297 + 0.367677i −0.981553 0.191192i \(-0.938765\pi\)
0.829256 + 0.558869i \(0.188765\pi\)
\(12\) 0 0
\(13\) 3.41575 1.41485i 0.947358 0.392408i 0.145121 0.989414i \(-0.453643\pi\)
0.802237 + 0.597006i \(0.203643\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.76109 0.669662 0.334831 0.942278i \(-0.391321\pi\)
0.334831 + 0.942278i \(0.391321\pi\)
\(18\) 0 0
\(19\) −0.189895 0.458448i −0.0435650 0.105175i 0.900599 0.434651i \(-0.143128\pi\)
−0.944164 + 0.329475i \(0.893128\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −4.46959 + 4.46959i −0.931975 + 0.931975i −0.997829 0.0658547i \(-0.979023\pi\)
0.0658547 + 0.997829i \(0.479023\pi\)
\(24\) 0 0
\(25\) 3.49071 + 3.49071i 0.698141 + 0.698141i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −0.0101033 + 0.00418494i −0.00187614 + 0.000777123i −0.383621 0.923490i \(-0.625323\pi\)
0.381745 + 0.924268i \(0.375323\pi\)
\(30\) 0 0
\(31\) 4.03370i 0.724474i −0.932086 0.362237i \(-0.882013\pi\)
0.932086 0.362237i \(-0.117987\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −0.0841477 0.203151i −0.0142236 0.0343387i
\(36\) 0 0
\(37\) 6.30586 + 2.61197i 1.03668 + 0.429406i 0.835118 0.550071i \(-0.185399\pi\)
0.201559 + 0.979476i \(0.435399\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 5.34633 + 5.34633i 0.834957 + 0.834957i 0.988190 0.153233i \(-0.0489686\pi\)
−0.153233 + 0.988190i \(0.548969\pi\)
\(42\) 0 0
\(43\) 10.1719 + 4.21336i 1.55121 + 0.642531i 0.983534 0.180724i \(-0.0578440\pi\)
0.567673 + 0.823254i \(0.307844\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 11.5870i 1.69013i 0.534660 + 0.845067i \(0.320440\pi\)
−0.534660 + 0.845067i \(0.679560\pi\)
\(48\) 0 0
\(49\) 6.23730i 0.891043i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −9.04956 3.74845i −1.24305 0.514889i −0.338385 0.941008i \(-0.609881\pi\)
−0.904667 + 0.426119i \(0.859881\pi\)
\(54\) 0 0
\(55\) −0.234995 0.234995i −0.0316867 0.0316867i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −0.939369 0.389099i −0.122295 0.0506564i 0.320697 0.947182i \(-0.396083\pi\)
−0.442992 + 0.896526i \(0.646083\pi\)
\(60\) 0 0
\(61\) −2.97084 7.17223i −0.380377 0.918311i −0.991893 0.127078i \(-0.959440\pi\)
0.611516 0.791232i \(-0.290560\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0.930884i 0.115462i
\(66\) 0 0
\(67\) 7.40244 3.06619i 0.904352 0.374595i 0.118460 0.992959i \(-0.462204\pi\)
0.785892 + 0.618364i \(0.212204\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 1.20890 + 1.20890i 0.143470 + 0.143470i 0.775194 0.631724i \(-0.217652\pi\)
−0.631724 + 0.775194i \(0.717652\pi\)
\(72\) 0 0
\(73\) 3.73875 3.73875i 0.437588 0.437588i −0.453612 0.891199i \(-0.649865\pi\)
0.891199 + 0.453612i \(0.149865\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −0.441128 1.06498i −0.0502712 0.121366i
\(78\) 0 0
\(79\) 7.22016 0.812331 0.406166 0.913800i \(-0.366866\pi\)
0.406166 + 0.913800i \(0.366866\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 11.2970 4.67935i 1.24000 0.513626i 0.336287 0.941760i \(-0.390829\pi\)
0.903715 + 0.428134i \(0.140829\pi\)
\(84\) 0 0
\(85\) −0.266039 + 0.642275i −0.0288560 + 0.0696645i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −3.70197 + 3.70197i −0.392408 + 0.392408i −0.875545 0.483137i \(-0.839497\pi\)
0.483137 + 0.875545i \(0.339497\pi\)
\(90\) 0 0
\(91\) −1.23563 + 2.98307i −0.129529 + 0.312710i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0.124940 0.0128185
\(96\) 0 0
\(97\) −14.0257 −1.42409 −0.712046 0.702133i \(-0.752231\pi\)
−0.712046 + 0.702133i \(0.752231\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −4.26734 + 10.3023i −0.424616 + 1.02511i 0.556352 + 0.830947i \(0.312201\pi\)
−0.980968 + 0.194168i \(0.937799\pi\)
\(102\) 0 0
\(103\) −8.34273 + 8.34273i −0.822034 + 0.822034i −0.986399 0.164366i \(-0.947442\pi\)
0.164366 + 0.986399i \(0.447442\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1.28476 3.10168i 0.124202 0.299850i −0.849533 0.527536i \(-0.823116\pi\)
0.973735 + 0.227686i \(0.0731159\pi\)
\(108\) 0 0
\(109\) 8.00684 3.31654i 0.766916 0.317667i 0.0352935 0.999377i \(-0.488763\pi\)
0.731623 + 0.681710i \(0.238763\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 5.12115 0.481757 0.240879 0.970555i \(-0.422564\pi\)
0.240879 + 0.970555i \(0.422564\pi\)
\(114\) 0 0
\(115\) −0.609043 1.47036i −0.0567936 0.137112i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −1.70507 + 1.70507i −0.156304 + 0.156304i
\(120\) 0 0
\(121\) 6.54626 + 6.54626i 0.595114 + 0.595114i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −2.31142 + 0.957421i −0.206740 + 0.0856344i
\(126\) 0 0
\(127\) 8.28564i 0.735232i −0.929978 0.367616i \(-0.880174\pi\)
0.929978 0.367616i \(-0.119826\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −7.82244 18.8850i −0.683450 1.64999i −0.757578 0.652745i \(-0.773617\pi\)
0.0741279 0.997249i \(-0.476383\pi\)
\(132\) 0 0
\(133\) 0.400375 + 0.165841i 0.0347169 + 0.0143802i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 13.3963 + 13.3963i 1.14452 + 1.14452i 0.987613 + 0.156906i \(0.0501521\pi\)
0.156906 + 0.987613i \(0.449848\pi\)
\(138\) 0 0
\(139\) 18.0954 + 7.49538i 1.53484 + 0.635750i 0.980496 0.196540i \(-0.0629706\pi\)
0.554340 + 0.832290i \(0.312971\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 4.87998i 0.408085i
\(144\) 0 0
\(145\) 0.00275343i 0.000228660i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −14.0938 5.83786i −1.15461 0.478256i −0.278535 0.960426i \(-0.589849\pi\)
−0.876078 + 0.482170i \(0.839849\pi\)
\(150\) 0 0
\(151\) −3.91247 3.91247i −0.318392 0.318392i 0.529757 0.848149i \(-0.322283\pi\)
−0.848149 + 0.529757i \(0.822283\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0.938306 + 0.388659i 0.0753665 + 0.0312178i
\(156\) 0 0
\(157\) −7.38756 17.8351i −0.589591 1.42340i −0.883894 0.467687i \(-0.845088\pi\)
0.294303 0.955712i \(-0.404912\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 5.52027i 0.435058i
\(162\) 0 0
\(163\) −17.9611 + 7.43971i −1.40682 + 0.582723i −0.951512 0.307611i \(-0.900470\pi\)
−0.455307 + 0.890335i \(0.650470\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −13.9383 13.9383i −1.07858 1.07858i −0.996637 0.0819391i \(-0.973889\pi\)
−0.0819391 0.996637i \(-0.526111\pi\)
\(168\) 0 0
\(169\) 0.473139 0.473139i 0.0363953 0.0363953i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −1.06460 2.57018i −0.0809402 0.195407i 0.878229 0.478241i \(-0.158725\pi\)
−0.959169 + 0.282834i \(0.908725\pi\)
\(174\) 0 0
\(175\) −4.31128 −0.325902
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 14.3931 5.96183i 1.07579 0.445608i 0.226761 0.973950i \(-0.427186\pi\)
0.849031 + 0.528342i \(0.177186\pi\)
\(180\) 0 0
\(181\) −2.56470 + 6.19174i −0.190633 + 0.460229i −0.990079 0.140509i \(-0.955126\pi\)
0.799446 + 0.600737i \(0.205126\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1.21518 + 1.21518i −0.0893415 + 0.0893415i
\(186\) 0 0
\(187\) −1.39466 + 3.36700i −0.101988 + 0.246220i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 15.0419 1.08840 0.544198 0.838957i \(-0.316834\pi\)
0.544198 + 0.838957i \(0.316834\pi\)
\(192\) 0 0
\(193\) −19.6537 −1.41470 −0.707352 0.706861i \(-0.750111\pi\)
−0.707352 + 0.706861i \(0.750111\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 3.28693 7.93534i 0.234184 0.565370i −0.762478 0.647015i \(-0.776017\pi\)
0.996661 + 0.0816448i \(0.0260173\pi\)
\(198\) 0 0
\(199\) −14.6374 + 14.6374i −1.03761 + 1.03761i −0.0383500 + 0.999264i \(0.512210\pi\)
−0.999264 + 0.0383500i \(0.987790\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0.00365482 0.00882352i 0.000256518 0.000619290i
\(204\) 0 0
\(205\) −1.75878 + 0.728511i −0.122839 + 0.0508814i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0.654971 0.0453053
\(210\) 0 0
\(211\) −6.76173 16.3243i −0.465497 1.12381i −0.966108 0.258137i \(-0.916891\pi\)
0.500612 0.865672i \(-0.333109\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −1.96019 + 1.96019i −0.133684 + 0.133684i
\(216\) 0 0
\(217\) 2.49096 + 2.49096i 0.169097 + 0.169097i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 9.43118 3.90652i 0.634410 0.262781i
\(222\) 0 0
\(223\) 15.8618i 1.06219i −0.847313 0.531093i \(-0.821781\pi\)
0.847313 0.531093i \(-0.178219\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 2.50806 + 6.05500i 0.166466 + 0.401884i 0.984995 0.172580i \(-0.0552104\pi\)
−0.818530 + 0.574464i \(0.805210\pi\)
\(228\) 0 0
\(229\) −7.60466 3.14995i −0.502530 0.208155i 0.116994 0.993133i \(-0.462674\pi\)
−0.619524 + 0.784978i \(0.712674\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −5.99464 5.99464i −0.392722 0.392722i 0.482935 0.875656i \(-0.339571\pi\)
−0.875656 + 0.482935i \(0.839571\pi\)
\(234\) 0 0
\(235\) −2.69532 1.11644i −0.175824 0.0728285i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1.11236i 0.0719527i 0.999353 + 0.0359763i \(0.0114541\pi\)
−0.999353 + 0.0359763i \(0.988546\pi\)
\(240\) 0 0
\(241\) 0.709331i 0.0456920i 0.999739 + 0.0228460i \(0.00727274\pi\)
−0.999739 + 0.0228460i \(0.992727\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −1.45090 0.600982i −0.0926946 0.0383953i
\(246\) 0 0
\(247\) −1.29727 1.29727i −0.0825432 0.0825432i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −10.3657 4.29361i −0.654276 0.271010i 0.0307514 0.999527i \(-0.490210\pi\)
−0.685028 + 0.728517i \(0.740210\pi\)
\(252\) 0 0
\(253\) −3.19279 7.70808i −0.200729 0.484603i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 29.1264i 1.81686i −0.418042 0.908428i \(-0.637284\pi\)
0.418042 0.908428i \(-0.362716\pi\)
\(258\) 0 0
\(259\) −5.50708 + 2.28111i −0.342194 + 0.141741i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 1.87052 + 1.87052i 0.115341 + 0.115341i 0.762422 0.647080i \(-0.224010\pi\)
−0.647080 + 0.762422i \(0.724010\pi\)
\(264\) 0 0
\(265\) 1.74390 1.74390i 0.107127 0.107127i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1.63828 3.95517i −0.0998879 0.241151i 0.866034 0.499986i \(-0.166661\pi\)
−0.965922 + 0.258835i \(0.916661\pi\)
\(270\) 0 0
\(271\) −0.865193 −0.0525567 −0.0262784 0.999655i \(-0.508366\pi\)
−0.0262784 + 0.999655i \(0.508366\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −6.01993 + 2.49354i −0.363016 + 0.150366i
\(276\) 0 0
\(277\) −10.8442 + 26.1801i −0.651563 + 1.57301i 0.158948 + 0.987287i \(0.449190\pi\)
−0.810510 + 0.585724i \(0.800810\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 3.20552 3.20552i 0.191225 0.191225i −0.605000 0.796225i \(-0.706827\pi\)
0.796225 + 0.605000i \(0.206827\pi\)
\(282\) 0 0
\(283\) 0.808604 1.95214i 0.0480665 0.116043i −0.898023 0.439949i \(-0.854996\pi\)
0.946089 + 0.323907i \(0.104996\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −6.60311 −0.389769
\(288\) 0 0
\(289\) −9.37639 −0.551552
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 2.84084 6.85839i 0.165964 0.400671i −0.818916 0.573914i \(-0.805424\pi\)
0.984879 + 0.173242i \(0.0554244\pi\)
\(294\) 0 0
\(295\) 0.181022 0.181022i 0.0105395 0.0105395i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −8.94320 + 21.5908i −0.517199 + 1.24863i
\(300\) 0 0
\(301\) −8.88344 + 3.67964i −0.512033 + 0.212091i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1.95463 0.111922
\(306\) 0 0
\(307\) −5.75328 13.8897i −0.328357 0.792724i −0.998715 0.0506860i \(-0.983859\pi\)
0.670357 0.742038i \(-0.266141\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 9.92757 9.92757i 0.562941 0.562941i −0.367201 0.930142i \(-0.619684\pi\)
0.930142 + 0.367201i \(0.119684\pi\)
\(312\) 0 0
\(313\) −6.07029 6.07029i −0.343113 0.343113i 0.514423 0.857536i \(-0.328006\pi\)
−0.857536 + 0.514423i \(0.828006\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 28.8754 11.9606i 1.62180 0.671773i 0.627525 0.778596i \(-0.284068\pi\)
0.994278 + 0.106823i \(0.0340678\pi\)
\(318\) 0 0
\(319\) 0.0144343i 0.000808168i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −0.524318 1.26581i −0.0291738 0.0704318i
\(324\) 0 0
\(325\) 16.8622 + 6.98455i 0.935346 + 0.387433i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −7.15538 7.15538i −0.394489 0.394489i
\(330\) 0 0
\(331\) −13.5735 5.62233i −0.746067 0.309031i −0.0229312 0.999737i \(-0.507300\pi\)
−0.723136 + 0.690706i \(0.757300\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 2.01737i 0.110221i
\(336\) 0 0
\(337\) 7.22397i 0.393515i 0.980452 + 0.196757i \(0.0630411\pi\)
−0.980452 + 0.196757i \(0.936959\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 4.91889 + 2.03747i 0.266373 + 0.110335i
\(342\) 0 0
\(343\) −8.17451 8.17451i −0.441382 0.441382i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −6.78836 2.81183i −0.364418 0.150947i 0.192958 0.981207i \(-0.438192\pi\)
−0.557376 + 0.830260i \(0.688192\pi\)
\(348\) 0 0
\(349\) 0.0989263 + 0.238829i 0.00529540 + 0.0127842i 0.926505 0.376282i \(-0.122798\pi\)
−0.921210 + 0.389066i \(0.872798\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 1.04908i 0.0558369i −0.999610 0.0279184i \(-0.991112\pi\)
0.999610 0.0279184i \(-0.00888787\pi\)
\(354\) 0 0
\(355\) −0.397691 + 0.164729i −0.0211072 + 0.00874290i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −10.9586 10.9586i −0.578375 0.578375i 0.356080 0.934455i \(-0.384113\pi\)
−0.934455 + 0.356080i \(0.884113\pi\)
\(360\) 0 0
\(361\) 13.2609 13.2609i 0.697943 0.697943i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0.509456 + 1.22994i 0.0266662 + 0.0643778i
\(366\) 0 0
\(367\) 14.0919 0.735589 0.367795 0.929907i \(-0.380113\pi\)
0.367795 + 0.929907i \(0.380113\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 7.90323 3.27363i 0.410315 0.169958i
\(372\) 0 0
\(373\) 0.973904 2.35121i 0.0504268 0.121741i −0.896659 0.442723i \(-0.854013\pi\)
0.947086 + 0.320981i \(0.104013\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −0.0285894 + 0.0285894i −0.00147243 + 0.00147243i
\(378\) 0 0
\(379\) −7.22577 + 17.4446i −0.371163 + 0.896067i 0.622391 + 0.782707i \(0.286161\pi\)
−0.993554 + 0.113360i \(0.963839\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 4.91841 0.251319 0.125660 0.992073i \(-0.459895\pi\)
0.125660 + 0.992073i \(0.459895\pi\)
\(384\) 0 0
\(385\) 0.290236 0.0147918
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −6.57039 + 15.8623i −0.333132 + 0.804252i 0.665208 + 0.746658i \(0.268343\pi\)
−0.998340 + 0.0575939i \(0.981657\pi\)
\(390\) 0 0
\(391\) −12.3409 + 12.3409i −0.624108 + 0.624108i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −0.695683 + 1.67953i −0.0350036 + 0.0845062i
\(396\) 0 0
\(397\) 1.49381 0.618757i 0.0749723 0.0310545i −0.344882 0.938646i \(-0.612081\pi\)
0.419854 + 0.907591i \(0.362081\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −29.8271 −1.48949 −0.744747 0.667347i \(-0.767430\pi\)
−0.744747 + 0.667347i \(0.767430\pi\)
\(402\) 0 0
\(403\) −5.70708 13.7781i −0.284290 0.686336i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −6.37033 + 6.37033i −0.315765 + 0.315765i
\(408\) 0 0
\(409\) 9.09883 + 9.09883i 0.449908 + 0.449908i 0.895324 0.445416i \(-0.146944\pi\)
−0.445416 + 0.895324i \(0.646944\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0.820377 0.339811i 0.0403681 0.0167210i
\(414\) 0 0
\(415\) 3.07873i 0.151129i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 3.94681 + 9.52845i 0.192814 + 0.465495i 0.990489 0.137593i \(-0.0439366\pi\)
−0.797674 + 0.603088i \(0.793937\pi\)
\(420\) 0 0
\(421\) 2.91334 + 1.20674i 0.141987 + 0.0588131i 0.452546 0.891741i \(-0.350516\pi\)
−0.310558 + 0.950554i \(0.600516\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 9.63815 + 9.63815i 0.467519 + 0.467519i
\(426\) 0 0
\(427\) 6.26371 + 2.59451i 0.303122 + 0.125557i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 23.1792i 1.11650i −0.829672 0.558252i \(-0.811472\pi\)
0.829672 0.558252i \(-0.188528\pi\)
\(432\) 0 0
\(433\) 25.2987i 1.21578i −0.794023 0.607888i \(-0.792017\pi\)
0.794023 0.607888i \(-0.207983\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2.89783 + 1.20032i 0.138622 + 0.0574191i
\(438\) 0 0
\(439\) 28.3833 + 28.3833i 1.35466 + 1.35466i 0.880365 + 0.474297i \(0.157298\pi\)
0.474297 + 0.880365i \(0.342702\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 19.8722 + 8.23132i 0.944155 + 0.391082i 0.801031 0.598623i \(-0.204285\pi\)
0.143124 + 0.989705i \(0.454285\pi\)
\(444\) 0 0
\(445\) −0.504444 1.21784i −0.0239130 0.0577310i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 12.5843i 0.593889i 0.954895 + 0.296944i \(0.0959676\pi\)
−0.954895 + 0.296944i \(0.904032\pi\)
\(450\) 0 0
\(451\) −9.22007 + 3.81908i −0.434156 + 0.179833i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −0.574855 0.574855i −0.0269496 0.0269496i
\(456\) 0 0
\(457\) 8.93449 8.93449i 0.417938 0.417938i −0.466554 0.884492i \(-0.654505\pi\)
0.884492 + 0.466554i \(0.154505\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 12.9213 + 31.1949i 0.601807 + 1.45289i 0.871720 + 0.490005i \(0.163005\pi\)
−0.269913 + 0.962885i \(0.586995\pi\)
\(462\) 0 0
\(463\) 1.78637 0.0830196 0.0415098 0.999138i \(-0.486783\pi\)
0.0415098 + 0.999138i \(0.486783\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −37.9374 + 15.7142i −1.75553 + 0.727166i −0.758376 + 0.651818i \(0.774007\pi\)
−0.997157 + 0.0753479i \(0.975993\pi\)
\(468\) 0 0
\(469\) −2.67779 + 6.46476i −0.123649 + 0.298515i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −10.2759 + 10.2759i −0.472488 + 0.472488i
\(474\) 0 0
\(475\) 0.937438 2.26318i 0.0430126 0.103842i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 30.3196 1.38534 0.692669 0.721256i \(-0.256435\pi\)
0.692669 + 0.721256i \(0.256435\pi\)
\(480\) 0 0
\(481\) 25.2348 1.15061
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1.35142 3.26260i 0.0613646 0.148147i
\(486\) 0 0
\(487\) 23.2907 23.2907i 1.05540 1.05540i 0.0570287 0.998373i \(-0.481837\pi\)
0.998373 0.0570287i \(-0.0181627\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −4.68275 + 11.3052i −0.211330 + 0.510195i −0.993628 0.112709i \(-0.964047\pi\)
0.782298 + 0.622904i \(0.214047\pi\)
\(492\) 0 0
\(493\) −0.0278962 + 0.0115550i −0.00125638 + 0.000520410i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1.49308 −0.0669736
\(498\) 0 0
\(499\) 8.69892 + 21.0011i 0.389417 + 0.940136i 0.990063 + 0.140621i \(0.0449100\pi\)
−0.600646 + 0.799515i \(0.705090\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 27.4548 27.4548i 1.22415 1.22415i 0.258004 0.966144i \(-0.416935\pi\)
0.966144 0.258004i \(-0.0830649\pi\)
\(504\) 0 0
\(505\) −1.98531 1.98531i −0.0883451 0.0883451i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −16.5641 + 6.86109i −0.734193 + 0.304113i −0.718274 0.695761i \(-0.755067\pi\)
−0.0159191 + 0.999873i \(0.505067\pi\)
\(510\) 0 0
\(511\) 4.61763i 0.204272i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1.13681 2.74451i −0.0500939 0.120937i
\(516\) 0 0
\(517\) −14.1297 5.85272i −0.621424 0.257402i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −24.2903 24.2903i −1.06418 1.06418i −0.997794 0.0663854i \(-0.978853\pi\)
−0.0663854 0.997794i \(-0.521147\pi\)
\(522\) 0 0
\(523\) −3.09598 1.28240i −0.135378 0.0560753i 0.313966 0.949434i \(-0.398342\pi\)
−0.449344 + 0.893359i \(0.648342\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 11.1374i 0.485153i
\(528\) 0 0
\(529\) 16.9545i 0.737153i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 25.8260 + 10.6975i 1.11865 + 0.463359i
\(534\) 0 0
\(535\) 0.597711 + 0.597711i 0.0258413 + 0.0258413i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −7.60606 3.15053i −0.327616 0.135703i
\(540\) 0 0
\(541\) 12.7340 + 30.7426i 0.547477 + 1.32173i 0.919349 + 0.393443i \(0.128716\pi\)
−0.371872 + 0.928284i \(0.621284\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 2.18208i 0.0934701i
\(546\) 0 0
\(547\) −1.08569 + 0.449709i −0.0464209 + 0.0192282i −0.405773 0.913974i \(-0.632998\pi\)
0.359352 + 0.933202i \(0.382998\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0.00383715 + 0.00383715i 0.000163468 + 0.000163468i
\(552\) 0 0
\(553\) −4.45871 + 4.45871i −0.189604 + 0.189604i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 9.36569 + 22.6108i 0.396837 + 0.958049i 0.988411 + 0.151799i \(0.0485066\pi\)
−0.591574 + 0.806250i \(0.701493\pi\)
\(558\) 0 0
\(559\) 40.7060 1.72168
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 25.1131 10.4022i 1.05839 0.438400i 0.215511 0.976501i \(-0.430858\pi\)
0.842880 + 0.538101i \(0.180858\pi\)
\(564\) 0 0
\(565\) −0.493438 + 1.19126i −0.0207591 + 0.0501169i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −21.7622 + 21.7622i −0.912319 + 0.912319i −0.996454 0.0841358i \(-0.973187\pi\)
0.0841358 + 0.996454i \(0.473187\pi\)
\(570\) 0 0
\(571\) 12.7421 30.7622i 0.533241 1.28736i −0.396124 0.918197i \(-0.629645\pi\)
0.929365 0.369161i \(-0.120355\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −31.2041 −1.30130
\(576\) 0 0
\(577\) 9.17163 0.381820 0.190910 0.981608i \(-0.438856\pi\)
0.190910 + 0.981608i \(0.438856\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −4.08661 + 9.86595i −0.169541 + 0.409308i
\(582\) 0 0
\(583\) 9.14208 9.14208i 0.378626 0.378626i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −10.6350 + 25.6751i −0.438953 + 1.05973i 0.537359 + 0.843354i \(0.319422\pi\)
−0.976311 + 0.216371i \(0.930578\pi\)
\(588\) 0 0
\(589\) −1.84924 + 0.765981i −0.0761966 + 0.0315617i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 10.8973 0.447497 0.223748 0.974647i \(-0.428171\pi\)
0.223748 + 0.974647i \(0.428171\pi\)
\(594\) 0 0
\(595\) −0.232339 0.560917i −0.00952498 0.0229953i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −7.15470 + 7.15470i −0.292333 + 0.292333i −0.838001 0.545668i \(-0.816276\pi\)
0.545668 + 0.838001i \(0.316276\pi\)
\(600\) 0 0
\(601\) −16.0354 16.0354i −0.654098 0.654098i 0.299879 0.953977i \(-0.403054\pi\)
−0.953977 + 0.299879i \(0.903054\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −2.15352 + 0.892017i −0.0875530 + 0.0362657i
\(606\) 0 0
\(607\) 26.1378i 1.06090i 0.847716 + 0.530450i \(0.177977\pi\)
−0.847716 + 0.530450i \(0.822023\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 16.3938 + 39.5782i 0.663223 + 1.60116i
\(612\) 0 0
\(613\) −0.264513 0.109565i −0.0106836 0.00442529i 0.377335 0.926077i \(-0.376840\pi\)
−0.388019 + 0.921651i \(0.626840\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −9.11322 9.11322i −0.366884 0.366884i 0.499455 0.866340i \(-0.333533\pi\)
−0.866340 + 0.499455i \(0.833533\pi\)
\(618\) 0 0
\(619\) 4.31772 + 1.78846i 0.173544 + 0.0718842i 0.467764 0.883854i \(-0.345060\pi\)
−0.294220 + 0.955738i \(0.595060\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 4.57221i 0.183182i
\(624\) 0 0
\(625\) 24.0531i 0.962124i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 17.4110 + 7.21189i 0.694223 + 0.287557i
\(630\) 0 0
\(631\) 24.3839 + 24.3839i 0.970707 + 0.970707i 0.999583 0.0288764i \(-0.00919293\pi\)
−0.0288764 + 0.999583i \(0.509193\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 1.92738 + 0.798346i 0.0764856 + 0.0316814i
\(636\) 0 0
\(637\) 8.82483 + 21.3050i 0.349653 + 0.844136i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 8.45729i 0.334043i 0.985953 + 0.167022i \(0.0534149\pi\)
−0.985953 + 0.167022i \(0.946585\pi\)
\(642\) 0 0
\(643\) 34.7117 14.3781i 1.36890 0.567015i 0.427407 0.904059i \(-0.359427\pi\)
0.941489 + 0.337044i \(0.109427\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 26.4083 + 26.4083i 1.03822 + 1.03822i 0.999240 + 0.0389780i \(0.0124102\pi\)
0.0389780 + 0.999240i \(0.487590\pi\)
\(648\) 0 0
\(649\) 0.948973 0.948973i 0.0372504 0.0372504i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −11.3223 27.3345i −0.443076 1.06968i −0.974864 0.222802i \(-0.928480\pi\)
0.531788 0.846878i \(-0.321520\pi\)
\(654\) 0 0
\(655\) 5.14669 0.201098
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −35.5774 + 14.7366i −1.38590 + 0.574058i −0.946052 0.324015i \(-0.894967\pi\)
−0.439847 + 0.898073i \(0.644967\pi\)
\(660\) 0 0
\(661\) 11.9242 28.7874i 0.463796 1.11970i −0.503031 0.864268i \(-0.667782\pi\)
0.966827 0.255434i \(-0.0822182\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −0.0771547 + 0.0771547i −0.00299193 + 0.00299193i
\(666\) 0 0
\(667\) 0.0264528 0.0638627i 0.00102426 0.00247278i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 10.2468 0.395572
\(672\) 0 0
\(673\) 4.89312 0.188616 0.0943080 0.995543i \(-0.469936\pi\)
0.0943080 + 0.995543i \(0.469936\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −3.36496 + 8.12372i −0.129326 + 0.312220i −0.975258 0.221071i \(-0.929045\pi\)
0.845932 + 0.533291i \(0.179045\pi\)
\(678\) 0 0
\(679\) 8.66136 8.66136i 0.332392 0.332392i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 13.0545 31.5165i 0.499518 1.20594i −0.450225 0.892915i \(-0.648656\pi\)
0.949744 0.313029i \(-0.101344\pi\)
\(684\) 0 0
\(685\) −4.40696 + 1.82542i −0.168381 + 0.0697459i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −36.2145 −1.37966
\(690\) 0 0
\(691\) 13.7784 + 33.2640i 0.524155 + 1.26542i 0.935301 + 0.353853i \(0.115129\pi\)
−0.411146 + 0.911569i \(0.634871\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −3.48710 + 3.48710i −0.132273 + 0.132273i
\(696\) 0 0
\(697\) 14.7617 + 14.7617i 0.559139 + 0.559139i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −19.9772 + 8.27483i −0.754529 + 0.312536i −0.726588 0.687073i \(-0.758895\pi\)
−0.0279411 + 0.999610i \(0.508895\pi\)
\(702\) 0 0
\(703\) 3.38691i 0.127740i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −3.72679 8.99726i −0.140160 0.338377i
\(708\) 0 0
\(709\) 16.4355 + 6.80779i 0.617246 + 0.255672i 0.669323 0.742971i \(-0.266584\pi\)
−0.0520769 + 0.998643i \(0.516584\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 18.0290 + 18.0290i 0.675191 + 0.675191i
\(714\) 0 0
\(715\) −1.13516 0.470201i −0.0424528 0.0175845i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 13.9143i 0.518917i 0.965754 + 0.259458i \(0.0835440\pi\)
−0.965754 + 0.259458i \(0.916456\pi\)
\(720\) 0 0
\(721\) 10.3039i 0.383736i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −0.0498762 0.0206594i −0.00185235 0.000767270i
\(726\) 0 0
\(727\) −21.4548 21.4548i −0.795713 0.795713i 0.186703 0.982416i \(-0.440220\pi\)
−0.982416 + 0.186703i \(0.940220\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 28.0856 + 11.6334i 1.03878 + 0.430279i
\(732\) 0 0
\(733\) −6.82805 16.4844i −0.252200 0.608864i 0.746181 0.665743i \(-0.231885\pi\)
−0.998381 + 0.0568787i \(0.981885\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 10.5757i 0.389559i
\(738\) 0 0
\(739\) −6.45405 + 2.67336i −0.237416 + 0.0983410i −0.498219 0.867051i \(-0.666013\pi\)
0.260803 + 0.965392i \(0.416013\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −15.5864 15.5864i −0.571811 0.571811i 0.360823 0.932634i \(-0.382496\pi\)
−0.932634 + 0.360823i \(0.882496\pi\)
\(744\) 0 0
\(745\) 2.71597 2.71597i 0.0995053 0.0995053i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 1.12201 + 2.70878i 0.0409975 + 0.0989767i
\(750\) 0 0
\(751\) −42.0270 −1.53359 −0.766793 0.641894i \(-0.778149\pi\)
−0.766793 + 0.641894i \(0.778149\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 1.28708 0.533128i 0.0468418 0.0194025i
\(756\) 0 0
\(757\) −7.05779 + 17.0390i −0.256520 + 0.619294i −0.998704 0.0509027i \(-0.983790\pi\)
0.742184 + 0.670196i \(0.233790\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 26.7062 26.7062i 0.968098 0.968098i −0.0314086 0.999507i \(-0.509999\pi\)
0.999507 + 0.0314086i \(0.00999931\pi\)
\(762\) 0 0
\(763\) −2.89643 + 6.99260i −0.104858 + 0.253149i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −3.75916 −0.135735
\(768\) 0 0
\(769\) 44.3834 1.60051 0.800253 0.599662i \(-0.204698\pi\)
0.800253 + 0.599662i \(0.204698\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 14.1152 34.0770i 0.507687 1.22566i −0.437525 0.899206i \(-0.644145\pi\)
0.945212 0.326458i \(-0.105855\pi\)
\(774\) 0 0
\(775\) 14.0805 14.0805i 0.505785 0.505785i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 1.43577 3.46626i 0.0514418 0.124191i
\(780\) 0 0
\(781\) −2.08482 + 0.863560i −0.0746006 + 0.0309006i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 4.86056 0.173481
\(786\) 0 0
\(787\) −5.82978 14.0743i −0.207809 0.501696i 0.785269 0.619155i \(-0.212525\pi\)
−0.993078 + 0.117460i \(0.962525\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −3.16250 + 3.16250i −0.112445 + 0.112445i
\(792\) 0 0
\(793\) −20.2953 20.2953i −0.720705 0.720705i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 17.7102 7.33581i 0.627328 0.259848i −0.0462892 0.998928i \(-0.514740\pi\)
0.673617 + 0.739080i \(0.264740\pi\)
\(798\) 0 0
\(799\) 31.9927i 1.13182i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 2.67073 + 6.44770i 0.0942479 + 0.227535i
\(804\) 0 0