Properties

Label 1792.1.bt.a.13.1
Level $1792$
Weight $1$
Character 1792.13
Analytic conductor $0.894$
Analytic rank $0$
Dimension $32$
Projective image $D_{64}$
CM discriminant -7
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1792 = 2^{8} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1792.bt (of order \(64\), degree \(32\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.894324502638\)
Analytic rank: \(0\)
Dimension: \(32\)
Coefficient field: \(\Q(\zeta_{64})\)
Defining polynomial: \(x^{32} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{64}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{64} - \cdots)\)

Embedding invariants

Embedding label 13.1
Root \(0.956940 - 0.290285i\) of defining polynomial
Character \(\chi\) \(=\) 1792.13
Dual form 1792.1.bt.a.965.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.634393 - 0.773010i) q^{2} +(-0.195090 - 0.980785i) q^{4} +(0.471397 + 0.881921i) q^{7} +(-0.881921 - 0.471397i) q^{8} +(-0.290285 - 0.956940i) q^{9} +O(q^{10})\) \(q+(0.634393 - 0.773010i) q^{2} +(-0.195090 - 0.980785i) q^{4} +(0.471397 + 0.881921i) q^{7} +(-0.881921 - 0.471397i) q^{8} +(-0.290285 - 0.956940i) q^{9} +(-0.457553 - 1.82665i) q^{11} +(0.980785 + 0.195090i) q^{14} +(-0.923880 + 0.382683i) q^{16} +(-0.923880 - 0.382683i) q^{18} +(-1.70229 - 0.805124i) q^{22} +(1.21415 + 1.47945i) q^{23} +(-0.0980171 - 0.995185i) q^{25} +(0.773010 - 0.634393i) q^{28} +(-0.761850 - 1.27107i) q^{29} +(-0.290285 + 0.956940i) q^{32} +(-0.881921 + 0.471397i) q^{36} +(0.207775 + 0.439303i) q^{37} +(1.37787 - 1.02190i) q^{43} +(-1.70229 + 0.805124i) q^{44} +1.91388 q^{46} +(-0.555570 + 0.831470i) q^{49} +(-0.831470 - 0.555570i) q^{50} +(0.150869 - 0.251710i) q^{53} -1.00000i q^{56} +(-1.46586 - 0.217440i) q^{58} +(0.707107 - 0.707107i) q^{63} +(0.555570 + 0.831470i) q^{64} +(0.235710 + 1.58903i) q^{67} +(-1.59133 - 0.482726i) q^{71} +(-0.195090 + 0.980785i) q^{72} +(0.471397 + 0.118079i) q^{74} +(1.39528 - 1.26460i) q^{77} +(1.65493 + 1.10579i) q^{79} +(-0.831470 + 0.555570i) q^{81} +(0.0841735 - 1.71339i) q^{86} +(-0.457553 + 1.82665i) q^{88} +(1.21415 - 1.47945i) q^{92} +(0.290285 + 0.956940i) q^{98} +(-1.61518 + 0.968101i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + O(q^{10}) \) \( 32q + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times\).

\(n\) \(1023\) \(1025\) \(1541\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{47}{64}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.634393 0.773010i 0.634393 0.773010i
\(3\) 0 0 0.595699 0.803208i \(-0.296875\pi\)
−0.595699 + 0.803208i \(0.703125\pi\)
\(4\) −0.195090 0.980785i −0.195090 0.980785i
\(5\) 0 0 0.671559 0.740951i \(-0.265625\pi\)
−0.671559 + 0.740951i \(0.734375\pi\)
\(6\) 0 0
\(7\) 0.471397 + 0.881921i 0.471397 + 0.881921i
\(8\) −0.881921 0.471397i −0.881921 0.471397i
\(9\) −0.290285 0.956940i −0.290285 0.956940i
\(10\) 0 0
\(11\) −0.457553 1.82665i −0.457553 1.82665i −0.555570 0.831470i \(-0.687500\pi\)
0.0980171 0.995185i \(-0.468750\pi\)
\(12\) 0 0
\(13\) 0 0 0.0490677 0.998795i \(-0.484375\pi\)
−0.0490677 + 0.998795i \(0.515625\pi\)
\(14\) 0.980785 + 0.195090i 0.980785 + 0.195090i
\(15\) 0 0
\(16\) −0.923880 + 0.382683i −0.923880 + 0.382683i
\(17\) 0 0 0.195090 0.980785i \(-0.437500\pi\)
−0.195090 + 0.980785i \(0.562500\pi\)
\(18\) −0.923880 0.382683i −0.923880 0.382683i
\(19\) 0 0 0.941544 0.336890i \(-0.109375\pi\)
−0.941544 + 0.336890i \(0.890625\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −1.70229 0.805124i −1.70229 0.805124i
\(23\) 1.21415 + 1.47945i 1.21415 + 1.47945i 0.831470 + 0.555570i \(0.187500\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(24\) 0 0
\(25\) −0.0980171 0.995185i −0.0980171 0.995185i
\(26\) 0 0
\(27\) 0 0
\(28\) 0.773010 0.634393i 0.773010 0.634393i
\(29\) −0.761850 1.27107i −0.761850 1.27107i −0.956940 0.290285i \(-0.906250\pi\)
0.195090 0.980785i \(-0.437500\pi\)
\(30\) 0 0
\(31\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(32\) −0.290285 + 0.956940i −0.290285 + 0.956940i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) −0.881921 + 0.471397i −0.881921 + 0.471397i
\(37\) 0.207775 + 0.439303i 0.207775 + 0.439303i 0.980785 0.195090i \(-0.0625000\pi\)
−0.773010 + 0.634393i \(0.781250\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 0.0980171 0.995185i \(-0.468750\pi\)
−0.0980171 + 0.995185i \(0.531250\pi\)
\(42\) 0 0
\(43\) 1.37787 1.02190i 1.37787 1.02190i 0.382683 0.923880i \(-0.375000\pi\)
0.995185 0.0980171i \(-0.0312500\pi\)
\(44\) −1.70229 + 0.805124i −1.70229 + 0.805124i
\(45\) 0 0
\(46\) 1.91388 1.91388
\(47\) 0 0 −0.555570 0.831470i \(-0.687500\pi\)
0.555570 + 0.831470i \(0.312500\pi\)
\(48\) 0 0
\(49\) −0.555570 + 0.831470i −0.555570 + 0.831470i
\(50\) −0.831470 0.555570i −0.831470 0.555570i
\(51\) 0 0
\(52\) 0 0
\(53\) 0.150869 0.251710i 0.150869 0.251710i −0.773010 0.634393i \(-0.781250\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 1.00000i 1.00000i
\(57\) 0 0
\(58\) −1.46586 0.217440i −1.46586 0.217440i
\(59\) 0 0 −0.0490677 0.998795i \(-0.515625\pi\)
0.0490677 + 0.998795i \(0.484375\pi\)
\(60\) 0 0
\(61\) 0 0 0.989177 0.146730i \(-0.0468750\pi\)
−0.989177 + 0.146730i \(0.953125\pi\)
\(62\) 0 0
\(63\) 0.707107 0.707107i 0.707107 0.707107i
\(64\) 0.555570 + 0.831470i 0.555570 + 0.831470i
\(65\) 0 0
\(66\) 0 0
\(67\) 0.235710 + 1.58903i 0.235710 + 1.58903i 0.707107 + 0.707107i \(0.250000\pi\)
−0.471397 + 0.881921i \(0.656250\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −1.59133 0.482726i −1.59133 0.482726i −0.634393 0.773010i \(-0.718750\pi\)
−0.956940 + 0.290285i \(0.906250\pi\)
\(72\) −0.195090 + 0.980785i −0.195090 + 0.980785i
\(73\) 0 0 0.471397 0.881921i \(-0.343750\pi\)
−0.471397 + 0.881921i \(0.656250\pi\)
\(74\) 0.471397 + 0.118079i 0.471397 + 0.118079i
\(75\) 0 0
\(76\) 0 0
\(77\) 1.39528 1.26460i 1.39528 1.26460i
\(78\) 0 0
\(79\) 1.65493 + 1.10579i 1.65493 + 1.10579i 0.881921 + 0.471397i \(0.156250\pi\)
0.773010 + 0.634393i \(0.218750\pi\)
\(80\) 0 0
\(81\) −0.831470 + 0.555570i −0.831470 + 0.555570i
\(82\) 0 0
\(83\) 0 0 0.427555 0.903989i \(-0.359375\pi\)
−0.427555 + 0.903989i \(0.640625\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0.0841735 1.71339i 0.0841735 1.71339i
\(87\) 0 0
\(88\) −0.457553 + 1.82665i −0.457553 + 1.82665i
\(89\) 0 0 0.634393 0.773010i \(-0.281250\pi\)
−0.634393 + 0.773010i \(0.718750\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 1.21415 1.47945i 1.21415 1.47945i
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(98\) 0.290285 + 0.956940i 0.290285 + 0.956940i
\(99\) −1.61518 + 0.968101i −1.61518 + 0.968101i
\(100\) −0.956940 + 0.290285i −0.956940 + 0.290285i
\(101\) 0 0 0.336890 0.941544i \(-0.390625\pi\)
−0.336890 + 0.941544i \(0.609375\pi\)
\(102\) 0 0
\(103\) 0 0 0.995185 0.0980171i \(-0.0312500\pi\)
−0.995185 + 0.0980171i \(0.968750\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −0.0988640 0.276306i −0.0988640 0.276306i
\(107\) −0.290285 + 1.95694i −0.290285 + 1.95694i 1.00000i \(0.5\pi\)
−0.290285 + 0.956940i \(0.593750\pi\)
\(108\) 0 0
\(109\) 0.288078 + 0.805124i 0.288078 + 0.805124i 0.995185 + 0.0980171i \(0.0312500\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −0.773010 0.634393i −0.773010 0.634393i
\(113\) 0.924678 0.183930i 0.924678 0.183930i 0.290285 0.956940i \(-0.406250\pi\)
0.634393 + 0.773010i \(0.281250\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −1.09802 + 0.995185i −1.09802 + 0.995185i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −2.24539 + 1.20019i −2.24539 + 1.20019i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) −0.0980171 0.995185i −0.0980171 0.995185i
\(127\) 1.96157i 1.96157i 0.195090 + 0.980785i \(0.437500\pi\)
−0.195090 + 0.980785i \(0.562500\pi\)
\(128\) 0.995185 + 0.0980171i 0.995185 + 0.0980171i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 −0.803208 0.595699i \(-0.796875\pi\)
0.803208 + 0.595699i \(0.203125\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 1.37787 + 0.825862i 1.37787 + 0.825862i
\(135\) 0 0
\(136\) 0 0
\(137\) −0.187593 + 0.0569057i −0.187593 + 0.0569057i −0.382683 0.923880i \(-0.625000\pi\)
0.195090 + 0.980785i \(0.437500\pi\)
\(138\) 0 0
\(139\) 0 0 0.970031 0.242980i \(-0.0781250\pi\)
−0.970031 + 0.242980i \(0.921875\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −1.38268 + 0.923880i −1.38268 + 0.923880i
\(143\) 0 0
\(144\) 0.634393 + 0.773010i 0.634393 + 0.773010i
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0.390327 0.289486i 0.390327 0.289486i
\(149\) 0.174814 1.17850i 0.174814 1.17850i −0.707107 0.707107i \(-0.750000\pi\)
0.881921 0.471397i \(-0.156250\pi\)
\(150\) 0 0
\(151\) 0.980785 0.804910i 0.980785 0.804910i 1.00000i \(-0.5\pi\)
0.980785 + 0.195090i \(0.0625000\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) −0.0923988 1.88082i −0.0923988 1.88082i
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.857729 0.514103i \(-0.171875\pi\)
−0.857729 + 0.514103i \(0.828125\pi\)
\(158\) 1.90466 0.577774i 1.90466 0.577774i
\(159\) 0 0
\(160\) 0 0
\(161\) −0.732410 + 1.76820i −0.732410 + 1.76820i
\(162\) −0.0980171 + 0.995185i −0.0980171 + 0.995185i
\(163\) −0.0238449 + 0.0951944i −0.0238449 + 0.0951944i −0.980785 0.195090i \(-0.937500\pi\)
0.956940 + 0.290285i \(0.0937500\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 0.634393 0.773010i \(-0.281250\pi\)
−0.634393 + 0.773010i \(0.718750\pi\)
\(168\) 0 0
\(169\) −0.995185 0.0980171i −0.995185 0.0980171i
\(170\) 0 0
\(171\) 0 0
\(172\) −1.27107 1.15203i −1.27107 1.15203i
\(173\) 0 0 0.427555 0.903989i \(-0.359375\pi\)
−0.427555 + 0.903989i \(0.640625\pi\)
\(174\) 0 0
\(175\) 0.831470 0.555570i 0.831470 0.555570i
\(176\) 1.12175 + 1.51251i 1.12175 + 1.51251i
\(177\) 0 0
\(178\) 0 0
\(179\) 1.43749 1.30287i 1.43749 1.30287i 0.555570 0.831470i \(-0.312500\pi\)
0.881921 0.471397i \(-0.156250\pi\)
\(180\) 0 0
\(181\) 0 0 −0.857729 0.514103i \(-0.828125\pi\)
0.857729 + 0.514103i \(0.171875\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −0.373380 1.87711i −0.373380 1.87711i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 1.09320 + 1.09320i 1.09320 + 1.09320i 0.995185 + 0.0980171i \(0.0312500\pi\)
0.0980171 + 0.995185i \(0.468750\pi\)
\(192\) 0 0
\(193\) 0.410525 0.410525i 0.410525 0.410525i −0.471397 0.881921i \(-0.656250\pi\)
0.881921 + 0.471397i \(0.156250\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0.923880 + 0.382683i 0.923880 + 0.382683i
\(197\) −0.0504517 1.02697i −0.0504517 1.02697i −0.881921 0.471397i \(-0.843750\pi\)
0.831470 0.555570i \(-0.187500\pi\)
\(198\) −0.276306 + 1.86271i −0.276306 + 1.86271i
\(199\) 0 0 0.290285 0.956940i \(-0.406250\pi\)
−0.290285 + 0.956940i \(0.593750\pi\)
\(200\) −0.382683 + 0.923880i −0.382683 + 0.923880i
\(201\) 0 0
\(202\) 0 0
\(203\) 0.761850 1.27107i 0.761850 1.27107i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 1.06330 1.59133i 1.06330 1.59133i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 1.21416 + 0.574257i 1.21416 + 0.574257i 0.923880 0.382683i \(-0.125000\pi\)
0.290285 + 0.956940i \(0.406250\pi\)
\(212\) −0.276306 0.0988640i −0.276306 0.0988640i
\(213\) 0 0
\(214\) 1.32858 + 1.46586i 1.32858 + 1.46586i
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0.805124 + 0.288078i 0.805124 + 0.288078i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(224\) −0.980785 + 0.195090i −0.980785 + 0.195090i
\(225\) −0.923880 + 0.382683i −0.923880 + 0.382683i
\(226\) 0.444430 0.831470i 0.444430 0.831470i
\(227\) 0 0 −0.514103 0.857729i \(-0.671875\pi\)
0.514103 + 0.857729i \(0.328125\pi\)
\(228\) 0 0
\(229\) 0 0 −0.941544 0.336890i \(-0.890625\pi\)
0.941544 + 0.336890i \(0.109375\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0.0727135 + 1.48012i 0.0727135 + 1.48012i
\(233\) 1.26268 + 1.53858i 1.26268 + 1.53858i 0.707107 + 0.707107i \(0.250000\pi\)
0.555570 + 0.831470i \(0.312500\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −0.0761205 + 0.382683i −0.0761205 + 0.382683i 0.923880 + 0.382683i \(0.125000\pi\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) 0 0 −0.195090 0.980785i \(-0.562500\pi\)
0.195090 + 0.980785i \(0.437500\pi\)
\(242\) −0.496704 + 2.49710i −0.496704 + 2.49710i
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 0.671559 0.740951i \(-0.265625\pi\)
−0.671559 + 0.740951i \(0.734375\pi\)
\(252\) −0.831470 0.555570i −0.831470 0.555570i
\(253\) 2.14690 2.89476i 2.14690 2.89476i
\(254\) 1.51631 + 1.24441i 1.51631 + 1.24441i
\(255\) 0 0
\(256\) 0.707107 0.707107i 0.707107 0.707107i
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) −0.289486 + 0.390327i −0.289486 + 0.390327i
\(260\) 0 0
\(261\) −0.995185 + 1.09802i −0.995185 + 1.09802i
\(262\) 0 0
\(263\) −0.360791 0.674993i −0.360791 0.674993i 0.634393 0.773010i \(-0.281250\pi\)
−0.995185 + 0.0980171i \(0.968750\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 1.51251 0.541185i 1.51251 0.541185i
\(269\) 0 0 0.0490677 0.998795i \(-0.484375\pi\)
−0.0490677 + 0.998795i \(0.515625\pi\)
\(270\) 0 0
\(271\) 0 0 −0.195090 0.980785i \(-0.562500\pi\)
0.195090 + 0.980785i \(0.437500\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) −0.0750191 + 0.181112i −0.0750191 + 0.181112i
\(275\) −1.77301 + 0.634393i −1.77301 + 0.634393i
\(276\) 0 0
\(277\) −1.78841 0.265286i −1.78841 0.265286i −0.831470 0.555570i \(-0.812500\pi\)
−0.956940 + 0.290285i \(0.906250\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −0.124363 1.26268i −0.124363 1.26268i −0.831470 0.555570i \(-0.812500\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(282\) 0 0
\(283\) 0 0 −0.941544 0.336890i \(-0.890625\pi\)
0.941544 + 0.336890i \(0.109375\pi\)
\(284\) −0.162997 + 1.65493i −0.162997 + 1.65493i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 1.00000 1.00000
\(289\) −0.923880 0.382683i −0.923880 0.382683i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 −0.427555 0.903989i \(-0.640625\pi\)
0.427555 + 0.903989i \(0.359375\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0.0238449 0.485375i 0.0238449 0.485375i
\(297\) 0 0
\(298\) −0.800094 0.882768i −0.800094 0.882768i
\(299\) 0 0
\(300\) 0 0
\(301\) 1.55075 + 0.733452i 1.55075 + 0.733452i
\(302\) 1.26879i 1.26879i
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 −0.671559 0.740951i \(-0.734375\pi\)
0.671559 + 0.740951i \(0.265625\pi\)
\(308\) −1.51251 1.12175i −1.51251 1.12175i
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 −0.881921 0.471397i \(-0.843750\pi\)
0.881921 + 0.471397i \(0.156250\pi\)
\(312\) 0 0
\(313\) 0 0 0.290285 0.956940i \(-0.406250\pi\)
−0.290285 + 0.956940i \(0.593750\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0.761681 1.83886i 0.761681 1.83886i
\(317\) −0.0970732 + 0.0143994i −0.0970732 + 0.0143994i −0.195090 0.980785i \(-0.562500\pi\)
0.0980171 + 0.995185i \(0.468750\pi\)
\(318\) 0 0
\(319\) −1.97322 + 1.97322i −1.97322 + 1.97322i
\(320\) 0 0
\(321\) 0 0
\(322\) 0.902197 + 1.68789i 0.902197 + 1.68789i
\(323\) 0 0
\(324\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(325\) 0 0
\(326\) 0.0584592 + 0.0788231i 0.0584592 + 0.0788231i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −1.71339 1.02697i −1.71339 1.02697i −0.881921 0.471397i \(-0.843750\pi\)
−0.831470 0.555570i \(-0.812500\pi\)
\(332\) 0 0
\(333\) 0.360073 0.326351i 0.360073 0.326351i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −1.46658 + 0.979938i −1.46658 + 0.979938i −0.471397 + 0.881921i \(0.656250\pi\)
−0.995185 + 0.0980171i \(0.968750\pi\)
\(338\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −0.995185 0.0980171i −0.995185 0.0980171i
\(344\) −1.69689 + 0.251710i −1.69689 + 0.251710i
\(345\) 0 0
\(346\) 0 0
\(347\) −1.80580 + 0.854080i −1.80580 + 0.854080i −0.881921 + 0.471397i \(0.843750\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(348\) 0 0
\(349\) 0 0 0.242980 0.970031i \(-0.421875\pi\)
−0.242980 + 0.970031i \(0.578125\pi\)
\(350\) 0.0980171 0.995185i 0.0980171 0.995185i
\(351\) 0 0
\(352\) 1.88082 + 0.0923988i 1.88082 + 0.0923988i
\(353\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) −0.0951944 1.93773i −0.0951944 1.93773i
\(359\) −1.75535 + 0.172887i −1.75535 + 0.172887i −0.923880 0.382683i \(-0.875000\pi\)
−0.831470 + 0.555570i \(0.812500\pi\)
\(360\) 0 0
\(361\) 0.773010 0.634393i 0.773010 0.634393i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 −0.980785 0.195090i \(-0.937500\pi\)
0.980785 + 0.195090i \(0.0625000\pi\)
\(368\) −1.68789 0.902197i −1.68789 0.902197i
\(369\) 0 0
\(370\) 0 0
\(371\) 0.293107 + 0.0143994i 0.293107 + 0.0143994i
\(372\) 0 0
\(373\) −0.653587 + 0.163715i −0.653587 + 0.163715i −0.555570 0.831470i \(-0.687500\pi\)
−0.0980171 + 0.995185i \(0.531250\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0.217440 + 0.197076i 0.217440 + 0.197076i 0.773010 0.634393i \(-0.218750\pi\)
−0.555570 + 0.831470i \(0.687500\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 1.53858 0.151537i 1.53858 0.151537i
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −0.0569057 0.577774i −0.0569057 0.577774i
\(387\) −1.37787 1.02190i −1.37787 1.02190i
\(388\) 0 0
\(389\) 1.27107 + 1.15203i 1.27107 + 1.15203i 0.980785 + 0.195090i \(0.0625000\pi\)
0.290285 + 0.956940i \(0.406250\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.881921 0.471397i 0.881921 0.471397i
\(393\) 0 0
\(394\) −0.825862 0.612501i −0.825862 0.612501i
\(395\) 0 0
\(396\) 1.26460 + 1.39528i 1.26460 + 1.39528i
\(397\) 0 0 −0.998795 0.0490677i \(-0.984375\pi\)
0.998795 + 0.0490677i \(0.0156250\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.471397 + 0.881921i 0.471397 + 0.881921i
\(401\) 1.72995 + 0.344109i 1.72995 + 0.344109i 0.956940 0.290285i \(-0.0937500\pi\)
0.773010 + 0.634393i \(0.218750\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) −0.499238 1.39528i −0.499238 1.39528i
\(407\) 0.707387 0.580537i 0.707387 0.580537i
\(408\) 0 0
\(409\) 0 0 0.995185 0.0980171i \(-0.0312500\pi\)
−0.995185 + 0.0980171i \(0.968750\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) −0.555570 1.83147i −0.555570 1.83147i
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 0.242980 0.970031i \(-0.421875\pi\)
−0.242980 + 0.970031i \(0.578125\pi\)
\(420\) 0 0
\(421\) 0.0887133 0.0419583i 0.0887133 0.0419583i −0.382683 0.923880i \(-0.625000\pi\)
0.471397 + 0.881921i \(0.343750\pi\)
\(422\) 1.21416 0.574257i 1.21416 0.574257i
\(423\) 0 0
\(424\) −0.251710 + 0.150869i −0.251710 + 0.150869i
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 1.97597 0.0970732i 1.97597 0.0970732i
\(429\) 0 0
\(430\) 0 0
\(431\) 1.53636 1.02656i 1.53636 1.02656i 0.555570 0.831470i \(-0.312500\pi\)
0.980785 0.195090i \(-0.0625000\pi\)
\(432\) 0 0
\(433\) 0 0 −0.831470 0.555570i \(-0.812500\pi\)
0.831470 + 0.555570i \(0.187500\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0.733452 0.439614i 0.733452 0.439614i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 0.471397 0.881921i \(-0.343750\pi\)
−0.471397 + 0.881921i \(0.656250\pi\)
\(440\) 0 0
\(441\) 0.956940 + 0.290285i 0.956940 + 0.290285i
\(442\) 0 0
\(443\) −0.485375 + 0.0238449i −0.485375 + 0.0238449i −0.290285 0.956940i \(-0.593750\pi\)
−0.195090 + 0.980785i \(0.562500\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) −0.471397 + 0.881921i −0.471397 + 0.881921i
\(449\) 0.785695 0.785695i 0.785695 0.785695i −0.195090 0.980785i \(-0.562500\pi\)
0.980785 + 0.195090i \(0.0625000\pi\)
\(450\) −0.290285 + 0.956940i −0.290285 + 0.956940i
\(451\) 0 0
\(452\) −0.360791 0.871028i −0.360791 0.871028i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0.344109 + 0.183930i 0.344109 + 0.183930i 0.634393 0.773010i \(-0.281250\pi\)
−0.290285 + 0.956940i \(0.593750\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 −0.671559 0.740951i \(-0.734375\pi\)
0.671559 + 0.740951i \(0.265625\pi\)
\(462\) 0 0
\(463\) −0.979938 + 1.46658i −0.979938 + 1.46658i −0.0980171 + 0.995185i \(0.531250\pi\)
−0.881921 + 0.471397i \(0.843750\pi\)
\(464\) 1.19028 + 0.882768i 1.19028 + 0.882768i
\(465\) 0 0
\(466\) 1.99037 1.99037
\(467\) 0 0 −0.903989 0.427555i \(-0.859375\pi\)
0.903989 + 0.427555i \(0.140625\pi\)
\(468\) 0 0
\(469\) −1.29028 + 0.956940i −1.29028 + 0.956940i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −2.49710 2.04932i −2.49710 2.04932i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −0.284666 0.0713052i −0.284666 0.0713052i
\(478\) 0.247528 + 0.301614i 0.247528 + 0.301614i
\(479\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 1.61518 + 1.96810i 1.61518 + 1.96810i
\(485\) 0 0
\(486\) 0 0
\(487\) 0.0192147 + 0.195090i 0.0192147 + 0.195090i 1.00000 \(0\)
−0.980785 + 0.195090i \(0.937500\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −1.17850 0.174814i −1.17850 0.174814i −0.471397 0.881921i \(-0.656250\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −0.324423 1.63099i −0.324423 1.63099i
\(498\) 0 0
\(499\) 0.0584592 1.18996i 0.0584592 1.18996i −0.773010 0.634393i \(-0.781250\pi\)
0.831470 0.555570i \(-0.187500\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 −0.290285 0.956940i \(-0.593750\pi\)
0.290285 + 0.956940i \(0.406250\pi\)
\(504\) −0.956940 + 0.290285i −0.956940 + 0.290285i
\(505\) 0 0
\(506\) −0.875702 3.49600i −0.875702 3.49600i
\(507\) 0 0
\(508\) 1.92388 0.382683i 1.92388 0.382683i
\(509\) 0 0 0.595699 0.803208i \(-0.296875\pi\)
−0.595699 + 0.803208i \(0.703125\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.0980171 0.995185i −0.0980171 0.995185i
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0.118079 + 0.471397i 0.118079 + 0.471397i
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 −0.290285 0.956940i \(-0.593750\pi\)
0.290285 + 0.956940i \(0.406250\pi\)
\(522\) 0.217440 + 1.46586i 0.217440 + 1.46586i
\(523\) 0 0 −0.242980 0.970031i \(-0.578125\pi\)
0.242980 + 0.970031i \(0.421875\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) −0.750661 0.149316i −0.750661 0.149316i
\(527\) 0 0
\(528\) 0 0
\(529\) −0.519514 + 2.61177i −0.519514 + 2.61177i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0.541185 1.51251i 0.541185 1.51251i
\(537\) 0 0
\(538\) 0 0
\(539\) 1.77301 + 0.634393i 1.77301 + 0.634393i
\(540\) 0 0
\(541\) 1.01708 + 1.69689i 1.01708 + 1.69689i 0.634393 + 0.773010i \(0.281250\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −1.30287 0.326351i −1.30287 0.326351i −0.471397 0.881921i \(-0.656250\pi\)
−0.831470 + 0.555570i \(0.812500\pi\)
\(548\) 0.0924099 + 0.172887i 0.0924099 + 0.172887i
\(549\) 0 0
\(550\) −0.634393 + 1.77301i −0.634393 + 1.77301i
\(551\) 0 0
\(552\) 0 0
\(553\) −0.195090 + 1.98079i −0.195090 + 1.98079i
\(554\) −1.33962 + 1.21416i −1.33962 + 1.21416i
\(555\) 0 0
\(556\) 0 0
\(557\) −1.63439 0.773010i −1.63439 0.773010i −0.634393 0.773010i \(-0.718750\pi\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −1.05496 0.704900i −1.05496 0.704900i
\(563\) 0 0 −0.671559 0.740951i \(-0.734375\pi\)
0.671559 + 0.740951i \(0.265625\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −0.881921 0.471397i −0.881921 0.471397i
\(568\) 1.17588 + 1.17588i 1.17588 + 1.17588i
\(569\) 0.569414 1.87711i 0.569414 1.87711i 0.0980171 0.995185i \(-0.468750\pi\)
0.471397 0.881921i \(-0.343750\pi\)
\(570\) 0 0
\(571\) −0.0727135 1.48012i −0.0727135 1.48012i −0.707107 0.707107i \(-0.750000\pi\)
0.634393 0.773010i \(-0.281250\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.35332 1.35332i 1.35332 1.35332i
\(576\) 0.634393 0.773010i 0.634393 0.773010i
\(577\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(578\) −0.881921 + 0.471397i −0.881921 + 0.471397i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −0.528818 0.160415i −0.528818 0.160415i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 −0.857729 0.514103i \(-0.828125\pi\)
0.857729 + 0.514103i \(0.171875\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −0.360073 0.326351i −0.360073 0.326351i
\(593\) 0 0 0.831470 0.555570i \(-0.187500\pi\)
−0.831470 + 0.555570i \(0.812500\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −1.18996 + 0.0584592i −1.18996 + 0.0584592i
\(597\) 0 0
\(598\) 0 0
\(599\) −0.761681 0.0750191i −0.761681 0.0750191i −0.290285 0.956940i \(-0.593750\pi\)
−0.471397 + 0.881921i \(0.656250\pi\)
\(600\) 0 0
\(601\) 0 0 0.634393 0.773010i \(-0.281250\pi\)
−0.634393 + 0.773010i \(0.718750\pi\)
\(602\) 1.55075 0.733452i 1.55075 0.733452i
\(603\) 1.45218 0.686831i 1.45218 0.686831i
\(604\) −0.980785 0.804910i −0.980785 0.804910i
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0.672968 1.88082i 0.672968 1.88082i 0.290285 0.956940i \(-0.406250\pi\)
0.382683 0.923880i \(-0.375000\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) −1.82665 + 0.457553i −1.82665 + 0.457553i
\(617\) −0.301614 + 0.247528i −0.301614 + 0.247528i −0.773010 0.634393i \(-0.781250\pi\)
0.471397 + 0.881921i \(0.343750\pi\)
\(618\) 0 0
\(619\) 0 0 0.146730 0.989177i \(-0.453125\pi\)
−0.146730 + 0.989177i \(0.546875\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.980785 + 0.195090i −0.980785 + 0.195090i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) −1.06330 + 0.322547i −1.06330 + 0.322547i −0.773010 0.634393i \(-0.781250\pi\)
−0.290285 + 0.956940i \(0.593750\pi\)
\(632\) −0.938254 1.75535i −0.938254 1.75535i
\(633\) 0 0
\(634\) −0.0504517 + 0.0841735i −0.0504517 + 0.0841735i
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0.273522 + 2.77712i 0.273522 + 2.77712i
\(639\) 1.66294i 1.66294i
\(640\) 0 0
\(641\) 0.580569i 0.580569i 0.956940 + 0.290285i \(0.0937500\pi\)
−0.956940 + 0.290285i \(0.906250\pi\)
\(642\) 0 0
\(643\) 0 0 −0.803208 0.595699i \(-0.796875\pi\)
0.803208 + 0.595699i \(0.203125\pi\)
\(644\) 1.87711 + 0.373380i 1.87711 + 0.373380i
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.881921 0.471397i \(-0.156250\pi\)
−0.881921 + 0.471397i \(0.843750\pi\)
\(648\) 0.995185 0.0980171i 0.995185 0.0980171i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0.0980171 + 0.00481527i 0.0980171 + 0.00481527i
\(653\) 0.672968 + 0.0330608i 0.672968 + 0.0330608i 0.382683 0.923880i \(-0.375000\pi\)
0.290285 + 0.956940i \(0.406250\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0.288078 + 0.805124i 0.288078 + 0.805124i 0.995185 + 0.0980171i \(0.0312500\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(660\) 0 0
\(661\) 0 0 0.146730 0.989177i \(-0.453125\pi\)
−0.146730 + 0.989177i \(0.546875\pi\)
\(662\) −1.88082 + 0.672968i −1.88082 + 0.672968i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) −0.0238449 0.485375i −0.0238449 0.485375i
\(667\) 0.955482 2.67039i 0.955482 2.67039i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0.425215 1.02656i 0.425215 1.02656i −0.555570 0.831470i \(-0.687500\pi\)
0.980785 0.195090i \(-0.0625000\pi\)
\(674\) −0.172887 + 1.75535i −0.172887 + 1.75535i
\(675\) 0 0
\(676\) 0.0980171 + 0.995185i 0.0980171 + 0.995185i
\(677\) 0 0 0.903989 0.427555i \(-0.140625\pi\)
−0.903989 + 0.427555i \(0.859375\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1.15569 1.55827i −1.15569 1.55827i −0.773010 0.634393i \(-0.781250\pi\)
−0.382683 0.923880i \(-0.625000\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(687\) 0 0
\(688\) −0.881921 + 1.47140i −0.881921 + 1.47140i
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 0.740951 0.671559i \(-0.234375\pi\)
−0.740951 + 0.671559i \(0.765625\pi\)
\(692\) 0 0
\(693\) −1.61518 0.968101i −1.61518 0.968101i
\(694\) −0.485375 + 1.93773i −0.485375 + 1.93773i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −0.707107 0.707107i −0.707107 0.707107i
\(701\) −0.150869 1.01708i −0.150869 1.01708i −0.923880 0.382683i \(-0.875000\pi\)
0.773010 0.634393i \(-0.218750\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 1.26460 1.39528i 1.26460 1.39528i
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 0.0330608 + 0.672968i 0.0330608 + 0.672968i 0.956940 + 0.290285i \(0.0937500\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(710\) 0 0
\(711\) 0.577774 1.90466i 0.577774 1.90466i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −1.55827 1.15569i −1.55827 1.15569i
\(717\) 0 0
\(718\) −0.979938 + 1.46658i −0.979938 + 1.46658i
\(719\) 0 0 0.555570 0.831470i \(-0.312500\pi\)
−0.555570 + 0.831470i \(0.687500\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 1.00000i 1.00000i
\(723\) 0 0
\(724\) 0 0
\(725\) −1.19028 + 0.882768i −1.19028 + 0.882768i
\(726\) 0 0
\(727\) 0 0 0.0980171 0.995185i \(-0.468750\pi\)
−0.0980171 + 0.995185i \(0.531250\pi\)
\(728\) 0 0
\(729\) 0.773010 + 0.634393i 0.773010 + 0.634393i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 −0.970031 0.242980i \(-0.921875\pi\)
0.970031 + 0.242980i \(0.0781250\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) −1.76820 + 0.732410i −1.76820 + 0.732410i
\(737\) 2.79476 1.15763i 2.79476 1.15763i
\(738\) 0 0
\(739\) −0.929487 1.55075i −0.929487 1.55075i −0.831470 0.555570i \(-0.812500\pi\)
−0.0980171 0.995185i \(-0.531250\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0.197076 0.217440i 0.197076 0.217440i
\(743\) 0.151537 + 1.53858i 0.151537 + 1.53858i 0.707107 + 0.707107i \(0.250000\pi\)
−0.555570 + 0.831470i \(0.687500\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −0.288078 + 0.609090i −0.288078 + 0.609090i
\(747\) 0 0
\(748\) 0 0
\(749\) −1.86271 + 0.666487i −1.86271 + 0.666487i
\(750\) 0 0
\(751\) 0.216773 1.08979i 0.216773 1.08979i −0.707107 0.707107i \(-0.750000\pi\)
0.923880 0.382683i \(-0.125000\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0.480701 + 1.91906i 0.480701 + 1.91906i 0.382683 + 0.923880i \(0.375000\pi\)
0.0980171 + 0.995185i \(0.468750\pi\)
\(758\) 0.290285 0.0430597i 0.290285 0.0430597i
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 −0.471397 0.881921i \(-0.656250\pi\)
0.471397 + 0.881921i \(0.343750\pi\)
\(762\) 0 0
\(763\) −0.574257 + 0.633595i −0.574257 + 0.633595i
\(764\) 0.858923 1.28547i 0.858923 1.28547i
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −0.482726 0.322547i −0.482726 0.322547i
\(773\) 0 0 0.671559 0.740951i \(-0.265625\pi\)
−0.671559 + 0.740951i \(0.734375\pi\)
\(774\) −1.66405 + 0.416822i −1.66405 + 0.416822i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 1.69689 0.251710i 1.69689 0.251710i
\(779\) 0 0
\(780\) 0 0
\(781\) −0.153654 + 3.12769i −0.153654 + 3.12769i
\(782\) 0 0
\(783\) 0 0
\(784\) 0.195090 0.980785i 0.195090 0.980785i
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 0.941544 0.336890i \(-0.109375\pi\)
−0.941544 + 0.336890i \(0.890625\pi\)
\(788\) −0.997391 + 0.249834i −0.997391 + 0.249834i
\(789\) 0 0
\(790\) 0 0
\(791\) 0.598102 + 0.728789i 0.598102 + 0.728789i
\(792\) 1.88082 0.0923988i 1.88082 0.0923988i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 −0.514103 0.857729i \(-0.671875\pi\)
0.514103 + 0.857729i \(0.328125\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0.980785 + 0.195090i 0.980785 + 0.195090i