Properties

Label 869.1.j.a.394.5
Level $869$
Weight $1$
Character 869.394
Analytic conductor $0.434$
Analytic rank $0$
Dimension $20$
Projective image $D_{25}$
CM discriminant -79
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 869 = 11 \cdot 79 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 869.j (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.433687495978\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(5\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\Q(\zeta_{50})\)
Defining polynomial: \(x^{20} - x^{15} + x^{10} - x^{5} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{25}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{25} - \cdots)\)

Embedding invariants

Embedding label 394.5
Root \(0.425779 - 0.904827i\) of defining polynomial
Character \(\chi\) \(=\) 869.394
Dual form 869.1.j.a.236.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.541587 - 1.66683i) q^{2} +(-1.67600 - 1.21769i) q^{4} +(0.598617 + 1.84235i) q^{5} +(-1.51949 + 1.10397i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\) \(q+(0.541587 - 1.66683i) q^{2} +(-1.67600 - 1.21769i) q^{4} +(0.598617 + 1.84235i) q^{5} +(-1.51949 + 1.10397i) q^{8} +(0.309017 - 0.951057i) q^{9} +3.39510 q^{10} +(0.876307 - 0.481754i) q^{11} +(-0.263146 + 0.809880i) q^{13} +(0.377030 + 1.16038i) q^{16} +(-1.41789 - 1.03016i) q^{18} +(1.50441 - 1.09302i) q^{19} +(1.24013 - 3.81672i) q^{20} +(-0.328407 - 1.72157i) q^{22} -1.85955 q^{23} +(-2.22691 + 1.61795i) q^{25} +(1.20742 + 0.877242i) q^{26} +(-0.115808 + 0.356420i) q^{31} +0.260160 q^{32} +(-1.67600 + 1.21769i) q^{36} +(-1.00711 - 3.09957i) q^{38} +(-2.94351 - 2.13858i) q^{40} +(-2.05532 - 0.259647i) q^{44} +1.93717 q^{45} +(-1.00711 + 3.09957i) q^{46} +(0.309017 + 0.951057i) q^{49} +(1.49078 + 4.58815i) q^{50} +(1.42721 - 1.03693i) q^{52} +(1.41213 + 1.32608i) q^{55} +(0.531374 + 0.386066i) q^{62} +(-0.236131 + 0.726735i) q^{64} -1.64961 q^{65} -1.27485 q^{67} +(0.580394 + 1.78627i) q^{72} +(-0.866986 - 0.629902i) q^{73} -3.85235 q^{76} +(0.309017 - 0.951057i) q^{79} +(-1.91213 + 1.38925i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(0.190983 + 0.587785i) q^{83} +(-0.799696 + 1.69944i) q^{88} -1.98423 q^{89} +(1.04914 - 3.22894i) q^{90} +(3.11662 + 2.26435i) q^{92} +(2.91429 + 2.11736i) q^{95} +(0.0388067 - 0.119435i) q^{97} +1.75261 q^{98} +(-0.187381 - 0.982287i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 5q^{4} - 5q^{9} + O(q^{10}) \) \( 20q - 5q^{4} - 5q^{9} - 5q^{16} + 15q^{20} - 5q^{22} - 5q^{25} + 15q^{26} - 10q^{32} - 5q^{36} - 10q^{40} - 5q^{49} - 10q^{50} - 10q^{62} - 5q^{64} - 10q^{76} - 5q^{79} - 10q^{80} - 5q^{81} + 15q^{83} - 5q^{88} + 15q^{92} + 15q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/869\mathbb{Z}\right)^\times\).

\(n\) \(475\) \(793\)
\(\chi(n)\) \(e\left(\frac{3}{5}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.541587 1.66683i 0.541587 1.66683i −0.187381 0.982287i \(-0.560000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(3\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(4\) −1.67600 1.21769i −1.67600 1.21769i
\(5\) 0.598617 + 1.84235i 0.598617 + 1.84235i 0.535827 + 0.844328i \(0.320000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(6\) 0 0
\(7\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(8\) −1.51949 + 1.10397i −1.51949 + 1.10397i
\(9\) 0.309017 0.951057i 0.309017 0.951057i
\(10\) 3.39510 3.39510
\(11\) 0.876307 0.481754i 0.876307 0.481754i
\(12\) 0 0
\(13\) −0.263146 + 0.809880i −0.263146 + 0.809880i 0.728969 + 0.684547i \(0.240000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.377030 + 1.16038i 0.377030 + 1.16038i
\(17\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(18\) −1.41789 1.03016i −1.41789 1.03016i
\(19\) 1.50441 1.09302i 1.50441 1.09302i 0.535827 0.844328i \(-0.320000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(20\) 1.24013 3.81672i 1.24013 3.81672i
\(21\) 0 0
\(22\) −0.328407 1.72157i −0.328407 1.72157i
\(23\) −1.85955 −1.85955 −0.929776 0.368125i \(-0.880000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(24\) 0 0
\(25\) −2.22691 + 1.61795i −2.22691 + 1.61795i
\(26\) 1.20742 + 0.877242i 1.20742 + 0.877242i
\(27\) 0 0
\(28\) 0 0
\(29\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(30\) 0 0
\(31\) −0.115808 + 0.356420i −0.115808 + 0.356420i −0.992115 0.125333i \(-0.960000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(32\) 0.260160 0.260160
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) −1.67600 + 1.21769i −1.67600 + 1.21769i
\(37\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(38\) −1.00711 3.09957i −1.00711 3.09957i
\(39\) 0 0
\(40\) −2.94351 2.13858i −2.94351 2.13858i
\(41\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) −2.05532 0.259647i −2.05532 0.259647i
\(45\) 1.93717 1.93717
\(46\) −1.00711 + 3.09957i −1.00711 + 3.09957i
\(47\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(48\) 0 0
\(49\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(50\) 1.49078 + 4.58815i 1.49078 + 4.58815i
\(51\) 0 0
\(52\) 1.42721 1.03693i 1.42721 1.03693i
\(53\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(54\) 0 0
\(55\) 1.41213 + 1.32608i 1.41213 + 1.32608i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(60\) 0 0
\(61\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(62\) 0.531374 + 0.386066i 0.531374 + 0.386066i
\(63\) 0 0
\(64\) −0.236131 + 0.726735i −0.236131 + 0.726735i
\(65\) −1.64961 −1.64961
\(66\) 0 0
\(67\) −1.27485 −1.27485 −0.637424 0.770513i \(-0.720000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(72\) 0.580394 + 1.78627i 0.580394 + 1.78627i
\(73\) −0.866986 0.629902i −0.866986 0.629902i 0.0627905 0.998027i \(-0.480000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) −3.85235 −3.85235
\(77\) 0 0
\(78\) 0 0
\(79\) 0.309017 0.951057i 0.309017 0.951057i
\(80\) −1.91213 + 1.38925i −1.91213 + 1.38925i
\(81\) −0.809017 0.587785i −0.809017 0.587785i
\(82\) 0 0
\(83\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) −0.799696 + 1.69944i −0.799696 + 1.69944i
\(89\) −1.98423 −1.98423 −0.992115 0.125333i \(-0.960000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(90\) 1.04914 3.22894i 1.04914 3.22894i
\(91\) 0 0
\(92\) 3.11662 + 2.26435i 3.11662 + 2.26435i
\(93\) 0 0
\(94\) 0 0
\(95\) 2.91429 + 2.11736i 2.91429 + 2.11736i
\(96\) 0 0
\(97\) 0.0388067 0.119435i 0.0388067 0.119435i −0.929776 0.368125i \(-0.880000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(98\) 1.75261 1.75261
\(99\) −0.187381 0.982287i −0.187381 0.982287i
\(100\) 5.70246 5.70246
\(101\) −0.613161 + 1.88711i −0.613161 + 1.88711i −0.187381 + 0.982287i \(0.560000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(102\) 0 0
\(103\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(104\) −0.494239 1.52111i −0.494239 1.52111i
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 2.97515 1.63560i 2.97515 1.63560i
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(114\) 0 0
\(115\) −1.11316 3.42596i −1.11316 3.42596i
\(116\) 0 0
\(117\) 0.688925 + 0.500534i 0.688925 + 0.500534i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 0.535827 0.844328i 0.535827 0.844328i
\(122\) 0 0
\(123\) 0 0
\(124\) 0.628103 0.456344i 0.628103 0.456344i
\(125\) −2.74670 1.99559i −2.74670 1.99559i
\(126\) 0 0
\(127\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(128\) 1.29394 + 0.940099i 1.29394 + 0.940099i
\(129\) 0 0
\(130\) −0.893408 + 2.74963i −0.893408 + 2.74963i
\(131\) 1.07165 1.07165 0.535827 0.844328i \(-0.320000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −0.690441 + 2.12496i −0.690441 + 2.12496i
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(138\) 0 0
\(139\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0.159566 + 0.836475i 0.159566 + 0.836475i
\(144\) 1.22010 1.22010
\(145\) 0 0
\(146\) −1.51949 + 1.10397i −1.51949 + 1.10397i
\(147\) 0 0
\(148\) 0 0
\(149\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(150\) 0 0
\(151\) 1.03137 0.749337i 1.03137 0.749337i 0.0627905 0.998027i \(-0.480000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(152\) −1.07927 + 3.32166i −1.07927 + 3.32166i
\(153\) 0 0
\(154\) 0 0
\(155\) −0.725978 −0.725978
\(156\) 0 0
\(157\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(158\) −1.41789 1.03016i −1.41789 1.03016i
\(159\) 0 0
\(160\) 0.155737 + 0.479308i 0.155737 + 0.479308i
\(161\) 0 0
\(162\) −1.41789 + 1.03016i −1.41789 + 1.03016i
\(163\) 0.450527 1.38658i 0.450527 1.38658i −0.425779 0.904827i \(-0.640000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 1.08317 1.08317
\(167\) −0.115808 + 0.356420i −0.115808 + 0.356420i −0.992115 0.125333i \(-0.960000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(168\) 0 0
\(169\) 0.222357 + 0.161552i 0.222357 + 0.161552i
\(170\) 0 0
\(171\) −0.574633 1.76854i −0.574633 1.76854i
\(172\) 0 0
\(173\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.889411 + 0.835213i 0.889411 + 0.835213i
\(177\) 0 0
\(178\) −1.07463 + 3.30738i −1.07463 + 3.30738i
\(179\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(180\) −3.24670 2.35886i −3.24670 2.35886i
\(181\) −0.263146 0.809880i −0.263146 0.809880i −0.992115 0.125333i \(-0.960000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 2.82557 2.05290i 2.82557 2.05290i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 5.10763 3.71091i 5.10763 3.71091i
\(191\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(192\) 0 0
\(193\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(194\) −0.178061 0.129369i −0.178061 0.129369i
\(195\) 0 0
\(196\) 0.640176 1.97026i 0.640176 1.97026i
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) −1.73879 0.219661i −1.73879 0.219661i
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 1.59760 4.91691i 1.59760 4.91691i
\(201\) 0 0
\(202\) 2.81343 + 2.04407i 2.81343 + 2.04407i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −0.574633 + 1.76854i −0.574633 + 1.76854i
\(208\) −1.03898 −1.03898
\(209\) 0.791759 1.68257i 0.791759 1.68257i
\(210\) 0 0
\(211\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) −0.751987 3.94205i −0.751987 3.94205i
\(221\) 0 0
\(222\) 0 0
\(223\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(224\) 0 0
\(225\) 0.850604 + 2.61789i 0.850604 + 2.61789i
\(226\) 0 0
\(227\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(228\) 0 0
\(229\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(230\) −6.31337 −6.31337
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(234\) 1.20742 0.877242i 1.20742 0.877242i
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −1.56720 + 1.13864i −1.56720 + 1.13864i −0.637424 + 0.770513i \(0.720000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(240\) 0 0
\(241\) 1.45794 1.45794 0.728969 0.684547i \(-0.240000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(242\) −1.11716 1.35041i −1.11716 1.35041i
\(243\) 0 0
\(244\) 0 0
\(245\) −1.56720 + 1.13864i −1.56720 + 1.13864i
\(246\) 0 0
\(247\) 0.489334 + 1.50602i 0.489334 + 1.50602i
\(248\) −0.217510 0.669427i −0.217510 0.669427i
\(249\) 0 0
\(250\) −4.81390 + 3.49750i −4.81390 + 3.49750i
\(251\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(252\) 0 0
\(253\) −1.62954 + 0.895846i −1.62954 + 0.895846i
\(254\) 0 0
\(255\) 0 0
\(256\) 1.64957 1.19848i 1.64957 1.19848i
\(257\) 0.688925 + 0.500534i 0.688925 + 0.500534i 0.876307 0.481754i \(-0.160000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 2.76475 + 2.00871i 2.76475 + 2.00871i
\(261\) 0 0
\(262\) 0.580394 1.78627i 0.580394 1.78627i
\(263\) 1.45794 1.45794 0.728969 0.684547i \(-0.240000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 2.13665 + 1.55237i 2.13665 + 1.55237i
\(269\) −0.393950 1.21245i −0.393950 1.21245i −0.929776 0.368125i \(-0.880000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(270\) 0 0
\(271\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.17201 + 2.49064i −1.17201 + 2.49064i
\(276\) 0 0
\(277\) 0.598617 1.84235i 0.598617 1.84235i 0.0627905 0.998027i \(-0.480000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(278\) 0 0
\(279\) 0.303189 + 0.220280i 0.303189 + 0.220280i
\(280\) 0 0
\(281\) 0.598617 + 1.84235i 0.598617 + 1.84235i 0.535827 + 0.844328i \(0.320000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(282\) 0 0
\(283\) 0.303189 0.220280i 0.303189 0.220280i −0.425779 0.904827i \(-0.640000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 1.48068 + 0.187054i 1.48068 + 0.187054i
\(287\) 0 0
\(288\) 0.0803940 0.247427i 0.0803940 0.247427i
\(289\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(290\) 0 0
\(291\) 0 0
\(292\) 0.686047 + 2.11144i 0.686047 + 2.11144i
\(293\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0.489334 1.50602i 0.489334 1.50602i
\(300\) 0 0
\(301\) 0 0
\(302\) −0.690441 2.12496i −0.690441 2.12496i
\(303\) 0 0
\(304\) 1.83552 + 1.33359i 1.83552 + 1.33359i
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −0.393180 + 1.21008i −0.393180 + 1.21008i
\(311\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(312\) 0 0
\(313\) −0.115808 0.356420i −0.115808 0.356420i 0.876307 0.481754i \(-0.160000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −1.67600 + 1.21769i −1.67600 + 1.21769i
\(317\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −1.48026 −1.48026
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0.640176 + 1.97026i 0.640176 + 1.97026i
\(325\) −0.724339 2.22929i −0.724339 2.22929i
\(326\) −2.06720 1.50191i −2.06720 1.50191i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0.395651 1.21769i 0.395651 1.21769i
\(333\) 0 0
\(334\) 0.531374 + 0.386066i 0.531374 + 0.386066i
\(335\) −0.763146 2.34872i −0.763146 2.34872i
\(336\) 0 0
\(337\) −0.101597 0.0738147i −0.101597 0.0738147i 0.535827 0.844328i \(-0.320000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(338\) 0.389705 0.283137i 0.389705 0.283137i
\(339\) 0 0
\(340\) 0 0
\(341\) 0.0702235 + 0.368125i 0.0702235 + 0.368125i
\(342\) −3.25908 −3.25908
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −0.393950 1.21245i −0.393950 1.21245i −0.929776 0.368125i \(-0.880000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(348\) 0 0
\(349\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0.227980 0.125333i 0.227980 0.125333i
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 3.32557 + 2.41617i 3.32557 + 2.41617i
\(357\) 0 0
\(358\) 0.334719 + 1.03016i 0.334719 + 1.03016i
\(359\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(360\) −2.94351 + 2.13858i −2.94351 + 2.13858i
\(361\) 0.759544 2.33764i 0.759544 2.33764i
\(362\) −1.49245 −1.49245
\(363\) 0 0
\(364\) 0 0
\(365\) 0.641510 1.97437i 0.641510 1.97437i
\(366\) 0 0
\(367\) 1.60528 + 1.16630i 1.60528 + 1.16630i 0.876307 + 0.481754i \(0.160000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(368\) −0.701107 2.15779i −0.701107 2.15779i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(380\) −2.30608 7.09739i −2.30608 7.09739i
\(381\) 0 0
\(382\) 0 0
\(383\) 0.541587 1.66683i 0.541587 1.66683i −0.187381 0.982287i \(-0.560000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) −0.210474 + 0.152918i −0.210474 + 0.152918i
\(389\) 0.303189 + 0.220280i 0.303189 + 0.220280i 0.728969 0.684547i \(-0.240000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −1.51949 1.10397i −1.51949 1.10397i
\(393\) 0 0
\(394\) 0 0
\(395\) 1.93717 1.93717
\(396\) −0.882067 + 1.87449i −0.882067 + 1.87449i
\(397\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −2.71704 1.97405i −2.71704 1.97405i
\(401\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(402\) 0 0
\(403\) −0.258183 0.187581i −0.258183 0.187581i
\(404\) 3.32557 2.41617i 3.32557 2.41617i
\(405\) 0.598617 1.84235i 0.598617 1.84235i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 2.63665 + 1.91564i 2.63665 + 1.91564i
\(415\) −0.968583 + 0.703717i −0.968583 + 0.703717i
\(416\) −0.0684602 + 0.210699i −0.0684602 + 0.210699i
\(417\) 0 0
\(418\) −2.37577 2.23099i −2.37577 2.23099i
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) −0.101597 + 0.0738147i −0.101597 + 0.0738147i −0.637424 0.770513i \(-0.720000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0.331159 1.01920i 0.331159 1.01920i −0.637424 0.770513i \(-0.720000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(432\) 0 0
\(433\) 1.50441 + 1.09302i 1.50441 + 1.09302i 0.968583 + 0.248690i \(0.0800000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −2.79753 + 2.03252i −2.79753 + 2.03252i
\(438\) 0 0
\(439\) 0.125581 0.125581 0.0627905 0.998027i \(-0.480000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(440\) −3.60969 0.456009i −3.60969 0.456009i
\(441\) 1.00000 1.00000
\(442\) 0 0
\(443\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(444\) 0 0
\(445\) −1.18779 3.65565i −1.18779 3.65565i
\(446\) 0.334719 + 1.03016i 0.334719 + 1.03016i
\(447\) 0 0
\(448\) 0 0
\(449\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(450\) 4.82427 4.82427
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −0.613161 1.88711i −0.613161 1.88711i −0.425779 0.904827i \(-0.640000\pi\)
−0.187381 0.982287i \(-0.560000\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) −2.30608 + 7.09739i −2.30608 + 7.09739i
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0.541587 + 1.66683i 0.541587 + 1.66683i 0.728969 + 0.684547i \(0.240000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(468\) −0.545148 1.67779i −0.545148 1.67779i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −1.58174 + 4.86811i −1.58174 + 4.86811i
\(476\) 0 0
\(477\) 0 0
\(478\) 1.04914 + 3.22894i 1.04914 + 3.22894i
\(479\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0.789600 2.43014i 0.789600 2.43014i
\(483\) 0 0
\(484\) −1.92617 + 0.762627i −1.92617 + 0.762627i
\(485\) 0.243271 0.243271
\(486\) 0 0
\(487\) 0.688925 0.500534i 0.688925 0.500534i −0.187381 0.982287i \(-0.560000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 1.04914 + 3.22894i 1.04914 + 3.22894i
\(491\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 2.77530 2.77530
\(495\) 1.69755 0.933237i 1.69755 0.933237i
\(496\) −0.457246 −0.457246
\(497\) 0 0
\(498\) 0 0
\(499\) −1.41789 1.03016i −1.41789 1.03016i −0.992115 0.125333i \(-0.960000\pi\)
−0.425779 0.904827i \(-0.640000\pi\)
\(500\) 2.17346 + 6.68924i 2.17346 + 6.68924i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(504\) 0 0
\(505\) −3.84378 −3.84378
\(506\) 0.610690 + 3.20135i 0.610690 + 3.20135i
\(507\) 0 0
\(508\) 0 0
\(509\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.610048 1.87753i −0.610048 1.87753i
\(513\) 0 0
\(514\) 1.20742 0.877242i 1.20742 0.877242i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 2.50657 1.82113i 2.50657 1.82113i
\(521\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(522\) 0 0
\(523\) −0.613161 1.88711i −0.613161 1.88711i −0.425779 0.904827i \(-0.640000\pi\)
−0.187381 0.982287i \(-0.560000\pi\)
\(524\) −1.79609 1.30494i −1.79609 1.30494i
\(525\) 0 0
\(526\) 0.789600 2.43014i 0.789600 2.43014i
\(527\) 0 0
\(528\) 0 0
\(529\) 2.45794 2.45794
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 1.93712 1.40740i 1.93712 1.40740i
\(537\) 0 0
\(538\) −2.23432 −2.23432
\(539\) 0.728969 + 0.684547i 0.728969 + 0.684547i
\(540\) 0 0
\(541\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −1.17950 + 0.856954i −1.17950 + 0.856954i −0.992115 0.125333i \(-0.960000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 3.51674 + 3.30244i 3.51674 + 3.30244i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) −2.74670 1.99559i −2.74670 1.99559i
\(555\) 0 0
\(556\) 0 0
\(557\) 1.50441 + 1.09302i 1.50441 + 1.09302i 0.968583 + 0.248690i \(0.0800000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(558\) 0.531374 0.386066i 0.531374 0.386066i
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 3.39510 3.39510
\(563\) 0.618034 1.90211i 0.618034 1.90211i 0.309017 0.951057i \(-0.400000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −0.202967 0.624667i −0.202967 0.624667i
\(567\) 0 0
\(568\) 0 0
\(569\) −0.101597 + 0.0738147i −0.101597 + 0.0738147i −0.637424 0.770513i \(-0.720000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(570\) 0 0
\(571\) −0.374763 −0.374763 −0.187381 0.982287i \(-0.560000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(572\) 0.751132 1.59624i 0.751132 1.59624i
\(573\) 0 0
\(574\) 0 0
\(575\) 4.14106 3.00866i 4.14106 3.00866i
\(576\) 0.618198 + 0.449147i 0.618198 + 0.449147i
\(577\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(578\) 0.541587 + 1.66683i 0.541587 + 1.66683i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 2.01277 2.01277
\(585\) −0.509758 + 1.56887i −0.509758 + 1.56887i
\(586\) 0 0
\(587\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(588\) 0 0
\(589\) 0.215351 + 0.662783i 0.215351 + 0.662783i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1.93717 1.93717 0.968583 0.248690i \(-0.0800000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) −2.24526 1.63128i −2.24526 1.63128i
\(599\) 0.331159 + 1.01920i 0.331159 + 1.01920i 0.968583 + 0.248690i \(0.0800000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(600\) 0 0
\(601\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(602\) 0 0
\(603\) −0.393950 + 1.21245i −0.393950 + 1.21245i
\(604\) −2.64104 −2.64104
\(605\) 1.87631 + 0.481754i 1.87631 + 0.481754i
\(606\) 0 0
\(607\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(608\) 0.391388 0.284360i 0.391388 0.284360i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −0.851559 −0.851559 −0.425779 0.904827i \(-0.640000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(618\) 0 0
\(619\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(620\) 1.21674 + 0.884014i 1.21674 + 0.884014i
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 1.18176 3.63709i 1.18176 3.63709i
\(626\) −0.656814 −0.656814
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(632\) 0.580394 + 1.78627i 0.580394 + 1.78627i
\(633\) 0 0
\(634\) 2.29420 + 1.66683i 2.29420 + 1.66683i
\(635\) 0 0
\(636\) 0 0
\(637\) −0.851559 −0.851559
\(638\) 0 0
\(639\) 0 0
\(640\) −0.957424 + 2.94665i −0.957424 + 2.94665i
\(641\) 1.50441 1.09302i 1.50441 1.09302i 0.535827 0.844328i \(-0.320000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(642\) 0 0
\(643\) 0.331159 + 1.01920i 0.331159 + 1.01920i 0.968583 + 0.248690i \(0.0800000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(648\) 1.87819 1.87819
\(649\) 0 0
\(650\) −4.10815 −4.10815
\(651\) 0 0
\(652\) −2.44351 + 1.77531i −2.44351 + 1.77531i
\(653\) 1.60528 + 1.16630i 1.60528 + 1.16630i 0.876307 + 0.481754i \(0.160000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(654\) 0 0
\(655\) 0.641510 + 1.97437i 0.641510 + 1.97437i
\(656\) 0 0
\(657\) −0.866986 + 0.629902i −0.866986 + 0.629902i
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) −0.939097 0.682294i −0.939097 0.682294i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0.628103 0.456344i 0.628103 0.456344i
\(669\) 0 0
\(670\) −4.32824 −4.32824
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(674\) −0.178061 + 0.129369i −0.178061 + 0.129369i
\(675\) 0 0
\(676\) −0.175951 0.541522i −0.175951 0.541522i
\(677\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0.651635 + 0.0823206i 0.651635 + 0.0823206i
\(683\) 1.07165 1.07165 0.535827 0.844328i \(-0.320000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(684\) −1.19044 + 3.66380i −1.19044 + 3.66380i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −2.23432 −2.23432
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0.143185 + 0.750599i 0.143185 + 0.750599i
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(710\) 0 0
\(711\) −0.809017 0.587785i −0.809017 0.587785i
\(712\) 3.01502 2.19054i 3.01502 2.19054i
\(713\) 0.215351 0.662783i 0.215351 0.662783i
\(714\) 0 0
\(715\) −1.44556 + 0.794706i −1.44556 + 0.794706i
\(716\) 1.28035 1.28035
\(717\) 0 0
\(718\) 0 0
\(719\) −1.17950 0.856954i −1.17950 0.856954i −0.187381 0.982287i \(-0.560000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(720\) 0.730370 + 2.24785i 0.730370 + 2.24785i
\(721\) 0 0
\(722\) −3.48509 2.53207i −3.48509 2.53207i
\(723\) 0 0
\(724\) −0.545148 + 1.67779i −0.545148 + 1.67779i
\(725\) 0 0
\(726\) 0 0
\(727\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(728\) 0 0
\(729\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(730\) −2.94351 2.13858i −2.94351 2.13858i
\(731\) 0 0
\(732\) 0 0
\(733\) 1.03137 + 0.749337i 1.03137 + 0.749337i 0.968583 0.248690i \(-0.0800000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(734\) 2.81343 2.04407i 2.81343 2.04407i
\(735\) 0 0
\(736\) −0.483782 −0.483782
\(737\) −1.11716 + 0.614163i −1.11716 + 0.614163i
\(738\) 0 0
\(739\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −0.263146 0.809880i −0.263146 0.809880i −0.992115 0.125333i \(-0.960000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0.618034 0.618034
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −1.41789 + 1.03016i −1.41789 + 1.03016i −0.425779 + 0.904827i \(0.640000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 1.99794 + 1.45159i 1.99794 + 1.45159i
\(756\) 0 0
\(757\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) −6.76575 −6.76575
\(761\) −0.574633 + 1.76854i −0.574633 + 1.76854i 0.0627905 + 0.998027i \(0.480000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) −2.48502 1.80547i −2.48502 1.80547i
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −0.866986 + 0.629902i −0.866986 + 0.629902i −0.929776 0.368125i \(-0.880000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(774\) 0 0
\(775\) −0.318775 0.981088i −0.318775 0.981088i
\(776\) 0.0728865 + 0.224322i 0.0728865 + 0.224322i
\(777\) 0 0
\(778\) 0.531374 0.386066i 0.531374 0.386066i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −0.987078 + 0.717154i −0.987078 + 0.717154i
\(785\) 0 0
\(786\) 0 0
\(787\) 0.0388067 + 0.119435i 0.0388067 + 0.119435i 0.968583 0.248690i \(-0.0800000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 1.04914 3.22894i 1.04914 3.22894i
\(791\) 0 0
\(792\) 1.36914 + 1.28571i 1.36914 + 1.28571i
\(793\) 0 0
\(794\) 0.334719 1.03016i 0.334719 1.03016i
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −0.579354 + 0.420925i −0.579354 + 0.420925i
\(801\) −0.613161 + 1.88711i −0.613161 + 1.88711i
\(802\) 0 0
\(803\) −1.06320