Properties

Label 1152.2.w.b.1007.4
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 1007.4
Character \(\chi\) \(=\) 1152.1007
Dual form 1152.2.w.b.143.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.0963530 + 0.232617i) q^{5} +(-0.617536 - 0.617536i) q^{7} +O(q^{10})\) \(q+(0.0963530 + 0.232617i) q^{5} +(-0.617536 - 0.617536i) q^{7} +(0.505112 + 1.21945i) q^{11} +(3.41575 + 1.41485i) q^{13} -2.76109 q^{17} +(-0.189895 + 0.458448i) q^{19} +(4.46959 + 4.46959i) q^{23} +(3.49071 - 3.49071i) q^{25} +(0.0101033 + 0.00418494i) q^{29} +4.03370i q^{31} +(0.0841477 - 0.203151i) q^{35} +(6.30586 - 2.61197i) q^{37} +(-5.34633 + 5.34633i) q^{41} +(10.1719 - 4.21336i) q^{43} +11.5870i q^{47} -6.23730i q^{49} +(9.04956 - 3.74845i) q^{53} +(-0.234995 + 0.234995i) q^{55} +(0.939369 - 0.389099i) q^{59} +(-2.97084 + 7.17223i) q^{61} +0.930884i q^{65} +(7.40244 + 3.06619i) q^{67} +(-1.20890 + 1.20890i) q^{71} +(3.73875 + 3.73875i) q^{73} +(0.441128 - 1.06498i) q^{77} +7.22016 q^{79} +(-11.2970 - 4.67935i) q^{83} +(-0.266039 - 0.642275i) q^{85} +(3.70197 + 3.70197i) q^{89} +(-1.23563 - 2.98307i) q^{91} -0.124940 q^{95} -14.0257 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + O(q^{10}) \) \( 32 q + 8 q^{11} - 16 q^{29} - 24 q^{35} - 16 q^{53} + 32 q^{55} - 32 q^{59} + 32 q^{61} + 16 q^{67} - 16 q^{71} - 16 q^{77} + 32 q^{79} + 40 q^{83} + 48 q^{91} + 80 q^{95} + O(q^{100}) \)

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
\(5\) 0.0963530 + 0.232617i 0.0430904 + 0.104029i 0.943959 0.330062i \(-0.107070\pi\)
−0.900869 + 0.434091i \(0.857070\pi\)
\(6\) 0 0
\(7\) −0.617536 0.617536i −0.233407 0.233407i 0.580706 0.814113i \(-0.302776\pi\)
−0.814113 + 0.580706i \(0.802776\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0.505112 + 1.21945i 0.152297 + 0.367677i 0.981553 0.191192i \(-0.0612353\pi\)
−0.829256 + 0.558869i \(0.811235\pi\)
\(12\) 0 0
\(13\) 3.41575 + 1.41485i 0.947358 + 0.392408i 0.802237 0.597006i \(-0.203643\pi\)
0.145121 + 0.989414i \(0.453643\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −2.76109 −0.669662 −0.334831 0.942278i \(-0.608679\pi\)
−0.334831 + 0.942278i \(0.608679\pi\)
\(18\) 0 0
\(19\) −0.189895 + 0.458448i −0.0435650 + 0.105175i −0.944164 0.329475i \(-0.893128\pi\)
0.900599 + 0.434651i \(0.143128\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 4.46959 + 4.46959i 0.931975 + 0.931975i 0.997829 0.0658547i \(-0.0209774\pi\)
−0.0658547 + 0.997829i \(0.520977\pi\)
\(24\) 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 \(-0.374677\pi\)
−0.381745 + 0.924268i \(0.624677\pi\)
\(30\) 0 0
\(31\) 4.03370i 0.724474i 0.932086 + 0.362237i \(0.117987\pi\)
−0.932086 + 0.362237i \(0.882013\pi\)
\(32\) 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 0.201559 0.979476i \(-0.435399\pi\)
0.835118 + 0.550071i \(0.185399\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −5.34633 + 5.34633i −0.834957 + 0.834957i −0.988190 0.153233i \(-0.951031\pi\)
0.153233 + 0.988190i \(0.451031\pi\)
\(42\) 0 0
\(43\) 10.1719 4.21336i 1.55121 0.642531i 0.567673 0.823254i \(-0.307844\pi\)
0.983534 + 0.180724i \(0.0578440\pi\)
\(44\) 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 \(-0.390119\pi\)
0.904667 + 0.426119i \(0.140119\pi\)
\(54\) 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 \(-0.603917\pi\)
0.442992 + 0.896526i \(0.353917\pi\)
\(60\) 0 0
\(61\) −2.97084 + 7.17223i −0.380377 + 0.918311i 0.611516 + 0.791232i \(0.290560\pi\)
−0.991893 + 0.127078i \(0.959440\pi\)
\(62\) 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 0.785892 0.618364i \(-0.212204\pi\)
0.118460 + 0.992959i \(0.462204\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −1.20890 + 1.20890i −0.143470 + 0.143470i −0.775194 0.631724i \(-0.782348\pi\)
0.631724 + 0.775194i \(0.282348\pi\)
\(72\) 0 0
\(73\) 3.73875 + 3.73875i 0.437588 + 0.437588i 0.891199 0.453612i \(-0.149865\pi\)
−0.453612 + 0.891199i \(0.649865\pi\)
\(74\) 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 \(-0.609171\pi\)
−0.903715 + 0.428134i \(0.859171\pi\)
\(84\) 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 \(-0.160503\pi\)
−0.483137 + 0.875545i \(0.660503\pi\)
\(90\) 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 0.980968 + 0.194168i \(0.0622006\pi\)
−0.556352 + 0.830947i \(0.687799\pi\)
\(102\) 0 0
\(103\) −8.34273 8.34273i −0.822034 0.822034i 0.164366 0.986399i \(-0.447442\pi\)
−0.986399 + 0.164366i \(0.947442\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1.28476 3.10168i −0.124202 0.299850i 0.849533 0.527536i \(-0.176884\pi\)
−0.973735 + 0.227686i \(0.926884\pi\)
\(108\) 0 0
\(109\) 8.00684 + 3.31654i 0.766916 + 0.317667i 0.731623 0.681710i \(-0.238763\pi\)
0.0352935 + 0.999377i \(0.488763\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −5.12115 −0.481757 −0.240879 0.970555i \(-0.577436\pi\)
−0.240879 + 0.970555i \(0.577436\pi\)
\(114\) 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 \(0.119826\pi\)
−0.929978 + 0.367616i \(0.880174\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 7.82244 18.8850i 0.683450 1.64999i −0.0741279 0.997249i \(-0.523617\pi\)
0.757578 0.652745i \(-0.226383\pi\)
\(132\) 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 −0.156906 + 0.987613i \(0.550152\pi\)
−0.987613 + 0.156906i \(0.949848\pi\)
\(138\) 0 0
\(139\) 18.0954 7.49538i 1.53484 0.635750i 0.554340 0.832290i \(-0.312971\pi\)
0.980496 + 0.196540i \(0.0629706\pi\)
\(140\) 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 \(-0.410151\pi\)
0.876078 + 0.482170i \(0.160151\pi\)
\(150\) 0 0
\(151\) −3.91247 + 3.91247i −0.318392 + 0.318392i −0.848149 0.529757i \(-0.822283\pi\)
0.529757 + 0.848149i \(0.322283\pi\)
\(152\) 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 0.294303 + 0.955712i \(0.404912\pi\)
−0.883894 + 0.467687i \(0.845088\pi\)
\(158\) 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 −0.455307 0.890335i \(-0.650470\pi\)
−0.951512 + 0.307611i \(0.900470\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 13.9383 13.9383i 1.07858 1.07858i 0.0819391 0.996637i \(-0.473889\pi\)
0.996637 0.0819391i \(-0.0261113\pi\)
\(168\) 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 \(-0.841275\pi\)
0.959169 + 0.282834i \(0.0912746\pi\)
\(174\) 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 \(-0.572814\pi\)
−0.849031 + 0.528342i \(0.822814\pi\)
\(180\) 0 0
\(181\) −2.56470 6.19174i −0.190633 0.460229i 0.799446 0.600737i \(-0.205126\pi\)
−0.990079 + 0.140509i \(0.955126\pi\)
\(182\) 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 \(-0.683166\pi\)
−0.544198 + 0.838957i \(0.683166\pi\)
\(192\) 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 \(-0.223983\pi\)
−0.996661 + 0.0816448i \(0.973983\pi\)
\(198\) 0 0
\(199\) −14.6374 14.6374i −1.03761 1.03761i −0.999264 0.0383500i \(-0.987790\pi\)
−0.0383500 0.999264i \(-0.512210\pi\)
\(200\) 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 0.500612 + 0.865672i \(0.333109\pi\)
−0.966108 + 0.258137i \(0.916891\pi\)
\(212\) 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 \(0.178219\pi\)
−0.847313 + 0.531093i \(0.821781\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −2.50806 + 6.05500i −0.166466 + 0.401884i −0.984995 0.172580i \(-0.944790\pi\)
0.818530 + 0.574464i \(0.194790\pi\)
\(228\) 0 0
\(229\) −7.60466 + 3.14995i −0.502530 + 0.208155i −0.619524 0.784978i \(-0.712674\pi\)
0.116994 + 0.993133i \(0.462674\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 5.99464 5.99464i 0.392722 0.392722i −0.482935 0.875656i \(-0.660429\pi\)
0.875656 + 0.482935i \(0.160429\pi\)
\(234\) 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 \(-0.992727\pi\)
0.999739 0.0228460i \(-0.00727274\pi\)
\(242\) 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 \(-0.509790\pi\)
0.685028 + 0.728517i \(0.259790\pi\)
\(252\) 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 \(-0.775990\pi\)
0.647080 + 0.762422i \(0.275990\pi\)
\(264\) 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 \(-0.833339\pi\)
0.965922 + 0.258835i \(0.0833386\pi\)
\(270\) 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 −0.810510 0.585724i \(-0.800810\pi\)
0.158948 0.987287i \(-0.449190\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −3.20552 3.20552i −0.191225 0.191225i 0.605000 0.796225i \(-0.293173\pi\)
−0.796225 + 0.605000i \(0.793173\pi\)
\(282\) 0 0
\(283\) 0.808604 + 1.95214i 0.0480665 + 0.116043i 0.946089 0.323907i \(-0.104996\pi\)
−0.898023 + 0.439949i \(0.854996\pi\)
\(284\) 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 \(-0.194576\pi\)
−0.984879 + 0.173242i \(0.944576\pi\)
\(294\) 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 0.670357 + 0.742038i \(0.266141\pi\)
−0.998715 + 0.0506860i \(0.983859\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −9.92757 9.92757i −0.562941 0.562941i 0.367201 0.930142i \(-0.380316\pi\)
−0.930142 + 0.367201i \(0.880316\pi\)
\(312\) 0 0
\(313\) −6.07029 + 6.07029i −0.343113 + 0.343113i −0.857536 0.514423i \(-0.828006\pi\)
0.514423 + 0.857536i \(0.328006\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −28.8754 11.9606i −1.62180 0.671773i −0.627525 0.778596i \(-0.715932\pi\)
−0.994278 + 0.106823i \(0.965932\pi\)
\(318\) 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 −0.723136 0.690706i \(-0.757300\pi\)
−0.0229312 + 0.999737i \(0.507300\pi\)
\(332\) 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 \(-0.936959\pi\)
0.980452 0.196757i \(-0.0630411\pi\)
\(338\) 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 \(-0.561808\pi\)
0.557376 + 0.830260i \(0.311808\pi\)
\(348\) 0 0
\(349\) 0.0989263 0.238829i 0.00529540 0.0127842i −0.921210 0.389066i \(-0.872798\pi\)
0.926505 + 0.376282i \(0.122798\pi\)
\(350\) 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 \(-0.615887\pi\)
0.934455 + 0.356080i \(0.115887\pi\)
\(360\) 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 0.947086 0.320981i \(-0.104013\pi\)
−0.896659 + 0.442723i \(0.854013\pi\)
\(374\) 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 −0.993554 0.113360i \(-0.963839\pi\)
0.622391 0.782707i \(-0.286161\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −4.91841 −0.251319 −0.125660 0.992073i \(-0.540105\pi\)
−0.125660 + 0.992073i \(0.540105\pi\)
\(384\) 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 0.998340 + 0.0575939i \(0.0183429\pi\)
−0.665208 + 0.746658i \(0.731657\pi\)
\(390\) 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 0.419854 0.907591i \(-0.362081\pi\)
−0.344882 + 0.938646i \(0.612081\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 29.8271 1.48949 0.744747 0.667347i \(-0.232570\pi\)
0.744747 + 0.667347i \(0.232570\pi\)
\(402\) 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 −0.445416 0.895324i \(-0.646944\pi\)
0.895324 + 0.445416i \(0.146944\pi\)
\(410\) 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 \(-0.956063\pi\)
0.797674 + 0.603088i \(0.206063\pi\)
\(420\) 0 0
\(421\) 2.91334 1.20674i 0.141987 0.0588131i −0.310558 0.950554i \(-0.600516\pi\)
0.452546 + 0.891741i \(0.350516\pi\)
\(422\) 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 \(0.207983\pi\)
−0.794023 + 0.607888i \(0.792017\pi\)
\(434\) 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 0.474297 0.880365i \(-0.342702\pi\)
0.880365 0.474297i \(-0.157298\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −19.8722 + 8.23132i −0.944155 + 0.391082i −0.801031 0.598623i \(-0.795715\pi\)
−0.143124 + 0.989705i \(0.545715\pi\)
\(444\) 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 0.884492 0.466554i \(-0.154505\pi\)
−0.466554 + 0.884492i \(0.654505\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −12.9213 + 31.1949i −0.601807 + 1.45289i 0.269913 + 0.962885i \(0.413005\pi\)
−0.871720 + 0.490005i \(0.836995\pi\)
\(462\) 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 0.997157 + 0.0753479i \(0.0240067\pi\)
0.758376 + 0.651818i \(0.225993\pi\)
\(468\) 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 \(-0.743565\pi\)
−0.692669 + 0.721256i \(0.743565\pi\)
\(480\) 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 0.998373 + 0.0570287i \(0.0181627\pi\)
0.0570287 + 0.998373i \(0.481837\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 4.68275 + 11.3052i 0.211330 + 0.510195i 0.993628 0.112709i \(-0.0359528\pi\)
−0.782298 + 0.622904i \(0.785953\pi\)
\(492\) 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 −0.600646 0.799515i \(-0.705090\pi\)
0.990063 0.140621i \(-0.0449100\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −27.4548 27.4548i −1.22415 1.22415i −0.966144 0.258004i \(-0.916935\pi\)
−0.258004 0.966144i \(-0.583065\pi\)
\(504\) 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 \(-0.244933\pi\)
0.0159191 + 0.999873i \(0.494933\pi\)
\(510\) 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 0.0663854 0.997794i \(-0.478853\pi\)
0.997794 0.0663854i \(-0.0211467\pi\)
\(522\) 0 0
\(523\) −3.09598 + 1.28240i −0.135378 + 0.0560753i −0.449344 0.893359i \(-0.648342\pi\)
0.313966 + 0.949434i \(0.398342\pi\)
\(524\) 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 −0.371872 0.928284i \(-0.621284\pi\)
0.919349 0.393443i \(-0.128716\pi\)
\(542\) 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 0.359352 0.933202i \(-0.382998\pi\)
−0.405773 + 0.913974i \(0.632998\pi\)
\(548\) 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 0.591574 + 0.806250i \(0.298507\pi\)
−0.988411 + 0.151799i \(0.951493\pi\)
\(558\) 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 \(-0.569142\pi\)
−0.842880 + 0.538101i \(0.819142\pi\)
\(564\) 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 \(-0.0268129\pi\)
−0.0841358 + 0.996454i \(0.526813\pi\)
\(570\) 0 0
\(571\) 12.7421 + 30.7622i 0.533241 + 1.28736i 0.929365 + 0.369161i \(0.120355\pi\)
−0.396124 + 0.918197i \(0.629645\pi\)
\(572\) 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 0.976311 + 0.216371i \(0.0694222\pi\)
−0.537359 + 0.843354i \(0.680578\pi\)
\(588\) 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 \(-0.571829\pi\)
−0.223748 + 0.974647i \(0.571829\pi\)
\(594\) 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 \(-0.183724\pi\)
−0.545668 + 0.838001i \(0.683724\pi\)
\(600\) 0 0
\(601\) −16.0354 + 16.0354i −0.654098 + 0.654098i −0.953977 0.299879i \(-0.903054\pi\)
0.299879 + 0.953977i \(0.403054\pi\)
\(602\) 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 \(-0.822023\pi\)
0.847716 0.530450i \(-0.177977\pi\)
\(608\) 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 −0.388019 0.921651i \(-0.626840\pi\)
0.377335 + 0.926077i \(0.376840\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 9.11322 9.11322i 0.366884 0.366884i −0.499455 0.866340i \(-0.666467\pi\)
0.866340 + 0.499455i \(0.166467\pi\)
\(618\) 0 0
\(619\) 4.31772 1.78846i 0.173544 0.0718842i −0.294220 0.955738i \(-0.595060\pi\)
0.467764 + 0.883854i \(0.345060\pi\)
\(620\) 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 −0.0288764 0.999583i \(-0.509193\pi\)
0.999583 + 0.0288764i \(0.00919293\pi\)
\(632\) 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 0.941489 0.337044i \(-0.109427\pi\)
0.427407 + 0.904059i \(0.359427\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −26.4083 + 26.4083i −1.03822 + 1.03822i −0.0389780 + 0.999240i \(0.512410\pi\)
−0.999240 + 0.0389780i \(0.987590\pi\)
\(648\) 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 −0.531788 0.846878i \(-0.678480\pi\)
0.974864 0.222802i \(-0.0715205\pi\)
\(654\) 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 \(-0.105033\pi\)
0.439847 + 0.898073i \(0.355033\pi\)
\(660\) 0 0
\(661\) 11.9242 + 28.7874i 0.463796 + 1.11970i 0.966827 + 0.255434i \(0.0822182\pi\)
−0.503031 + 0.864268i \(0.667782\pi\)
\(662\) 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 \(-0.0709552\pi\)
−0.845932 + 0.533291i \(0.820955\pi\)
\(678\) 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 −0.949744 0.313029i \(-0.898656\pi\)
0.450225 0.892915i \(-0.351344\pi\)
\(684\) 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 −0.411146 0.911569i \(-0.634871\pi\)
0.935301 0.353853i \(-0.115129\pi\)
\(692\) 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 \(-0.241105\pi\)
0.0279411 + 0.999610i \(0.491105\pi\)
\(702\) 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 −0.0520769 0.998643i \(-0.516584\pi\)
0.669323 + 0.742971i \(0.266584\pi\)
\(710\) 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 −0.982416 0.186703i \(-0.940220\pi\)
0.186703 + 0.982416i \(0.440220\pi\)
\(728\) 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 −0.998381 0.0568787i \(-0.981885\pi\)
0.746181 + 0.665743i \(0.231885\pi\)
\(734\) 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 0.260803 0.965392i \(-0.416013\pi\)
−0.498219 + 0.867051i \(0.666013\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 15.5864 15.5864i 0.571811 0.571811i −0.360823 0.932634i \(-0.617504\pi\)
0.932634 + 0.360823i \(0.117504\pi\)
\(744\) 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 0.742184 0.670196i \(-0.233790\pi\)
−0.998704 + 0.0509027i \(0.983790\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −26.7062 26.7062i −0.968098 0.968098i 0.0314086 0.999507i \(-0.490001\pi\)
−0.999507 + 0.0314086i \(0.990001\pi\)
\(762\) 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 −0.945212 0.326458i \(-0.894145\pi\)
0.437525 0.899206i \(-0.355855\pi\)
\(774\) 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 −0.993078 0.117460i \(-0.962525\pi\)
0.785269 + 0.619155i \(0.212525\pi\)
\(788\) 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 \(-0.485260\pi\)
−0.673617 + 0.739080i \(0.735260\pi\)
\(798\) 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
\(805\) 1.28411 0.531894i 0.0452588