Properties

Label 1792.1.bt.a.1133.1
Level $1792$
Weight $1$
Character 1792.1133
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 1133.1
Root \(-0.471397 + 0.881921i\) of defining polynomial
Character \(\chi\) \(=\) 1792.1133
Dual form 1792.1.bt.a.1637.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.995185 - 0.0980171i) q^{2} +(0.980785 - 0.195090i) q^{4} +(0.290285 - 0.956940i) q^{7} +(0.956940 - 0.290285i) q^{8} +(0.881921 + 0.471397i) q^{9} +O(q^{10})\) \(q+(0.995185 - 0.0980171i) q^{2} +(0.980785 - 0.195090i) q^{4} +(0.290285 - 0.956940i) q^{7} +(0.956940 - 0.290285i) q^{8} +(0.881921 + 0.471397i) q^{9} +(-1.46586 - 0.217440i) q^{11} +(0.195090 - 0.980785i) q^{14} +(0.923880 - 0.382683i) q^{16} +(0.923880 + 0.382683i) q^{18} +(-1.48012 - 0.0727135i) q^{22} +(-0.938254 - 0.0924099i) q^{23} +(0.634393 - 0.773010i) q^{25} +(0.0980171 - 0.995185i) q^{28} +(-0.509389 + 0.686831i) q^{29} +(0.881921 - 0.471397i) q^{32} +(0.956940 + 0.290285i) q^{36} +(0.0970732 + 1.97597i) q^{37} +(0.390327 + 1.55827i) q^{43} +(-1.48012 + 0.0727135i) q^{44} -0.942793 q^{46} +(-0.831470 - 0.555570i) q^{49} +(0.555570 - 0.831470i) q^{50} +(-1.02190 - 1.37787i) q^{53} -1.00000i q^{56} +(-0.439614 + 0.733452i) q^{58} +(0.707107 - 0.707107i) q^{63} +(0.831470 - 0.555570i) q^{64} +(0.416822 - 0.249834i) q^{67} +(-0.523788 - 0.979938i) q^{71} +(0.980785 + 0.195090i) q^{72} +(0.290285 + 1.95694i) q^{74} +(-0.633595 + 1.33962i) q^{77} +(-0.858923 + 1.28547i) q^{79} +(0.555570 + 0.831470i) q^{81} +(0.541185 + 1.51251i) q^{86} +(-1.46586 + 0.217440i) q^{88} +(-0.938254 + 0.0924099i) q^{92} +(-0.881921 - 0.471397i) q^{98} +(-1.19028 - 0.882768i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + O(q^{10}) \) \( 32q + O(q^{100}) \)

Character values

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

\(n\) \(1023\) \(1025\) \(1541\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{55}{64}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.995185 0.0980171i 0.995185 0.0980171i
\(3\) 0 0 −0.970031 0.242980i \(-0.921875\pi\)
0.970031 + 0.242980i \(0.0781250\pi\)
\(4\) 0.980785 0.195090i 0.980785 0.195090i
\(5\) 0 0 0.903989 0.427555i \(-0.140625\pi\)
−0.903989 + 0.427555i \(0.859375\pi\)
\(6\) 0 0
\(7\) 0.290285 0.956940i 0.290285 0.956940i
\(8\) 0.956940 0.290285i 0.956940 0.290285i
\(9\) 0.881921 + 0.471397i 0.881921 + 0.471397i
\(10\) 0 0
\(11\) −1.46586 0.217440i −1.46586 0.217440i −0.634393 0.773010i \(-0.718750\pi\)
−0.831470 + 0.555570i \(0.812500\pi\)
\(12\) 0 0
\(13\) 0 0 −0.336890 0.941544i \(-0.609375\pi\)
0.336890 + 0.941544i \(0.390625\pi\)
\(14\) 0.195090 0.980785i 0.195090 0.980785i
\(15\) 0 0
\(16\) 0.923880 0.382683i 0.923880 0.382683i
\(17\) 0 0 −0.980785 0.195090i \(-0.937500\pi\)
0.980785 + 0.195090i \(0.0625000\pi\)
\(18\) 0.923880 + 0.382683i 0.923880 + 0.382683i
\(19\) 0 0 0.740951 0.671559i \(-0.234375\pi\)
−0.740951 + 0.671559i \(0.765625\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −1.48012 0.0727135i −1.48012 0.0727135i
\(23\) −0.938254 0.0924099i −0.938254 0.0924099i −0.382683 0.923880i \(-0.625000\pi\)
−0.555570 + 0.831470i \(0.687500\pi\)
\(24\) 0 0
\(25\) 0.634393 0.773010i 0.634393 0.773010i
\(26\) 0 0
\(27\) 0 0
\(28\) 0.0980171 0.995185i 0.0980171 0.995185i
\(29\) −0.509389 + 0.686831i −0.509389 + 0.686831i −0.980785 0.195090i \(-0.937500\pi\)
0.471397 + 0.881921i \(0.343750\pi\)
\(30\) 0 0
\(31\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(32\) 0.881921 0.471397i 0.881921 0.471397i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0.956940 + 0.290285i 0.956940 + 0.290285i
\(37\) 0.0970732 + 1.97597i 0.0970732 + 1.97597i 0.195090 + 0.980785i \(0.437500\pi\)
−0.0980171 + 0.995185i \(0.531250\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 −0.634393 0.773010i \(-0.718750\pi\)
0.634393 + 0.773010i \(0.281250\pi\)
\(42\) 0 0
\(43\) 0.390327 + 1.55827i 0.390327 + 1.55827i 0.773010 + 0.634393i \(0.218750\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(44\) −1.48012 + 0.0727135i −1.48012 + 0.0727135i
\(45\) 0 0
\(46\) −0.942793 −0.942793
\(47\) 0 0 0.831470 0.555570i \(-0.187500\pi\)
−0.831470 + 0.555570i \(0.812500\pi\)
\(48\) 0 0
\(49\) −0.831470 0.555570i −0.831470 0.555570i
\(50\) 0.555570 0.831470i 0.555570 0.831470i
\(51\) 0 0
\(52\) 0 0
\(53\) −1.02190 1.37787i −1.02190 1.37787i −0.923880 0.382683i \(-0.875000\pi\)
−0.0980171 0.995185i \(-0.531250\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 1.00000i 1.00000i
\(57\) 0 0
\(58\) −0.439614 + 0.733452i −0.439614 + 0.733452i
\(59\) 0 0 0.336890 0.941544i \(-0.390625\pi\)
−0.336890 + 0.941544i \(0.609375\pi\)
\(60\) 0 0
\(61\) 0 0 −0.514103 0.857729i \(-0.671875\pi\)
0.514103 + 0.857729i \(0.328125\pi\)
\(62\) 0 0
\(63\) 0.707107 0.707107i 0.707107 0.707107i
\(64\) 0.831470 0.555570i 0.831470 0.555570i
\(65\) 0 0
\(66\) 0 0
\(67\) 0.416822 0.249834i 0.416822 0.249834i −0.290285 0.956940i \(-0.593750\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −0.523788 0.979938i −0.523788 0.979938i −0.995185 0.0980171i \(-0.968750\pi\)
0.471397 0.881921i \(-0.343750\pi\)
\(72\) 0.980785 + 0.195090i 0.980785 + 0.195090i
\(73\) 0 0 −0.290285 0.956940i \(-0.593750\pi\)
0.290285 + 0.956940i \(0.406250\pi\)
\(74\) 0.290285 + 1.95694i 0.290285 + 1.95694i
\(75\) 0 0
\(76\) 0 0
\(77\) −0.633595 + 1.33962i −0.633595 + 1.33962i
\(78\) 0 0
\(79\) −0.858923 + 1.28547i −0.858923 + 1.28547i 0.0980171 + 0.995185i \(0.468750\pi\)
−0.956940 + 0.290285i \(0.906250\pi\)
\(80\) 0 0
\(81\) 0.555570 + 0.831470i 0.555570 + 0.831470i
\(82\) 0 0
\(83\) 0 0 0.0490677 0.998795i \(-0.484375\pi\)
−0.0490677 + 0.998795i \(0.515625\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0.541185 + 1.51251i 0.541185 + 1.51251i
\(87\) 0 0
\(88\) −1.46586 + 0.217440i −1.46586 + 0.217440i
\(89\) 0 0 0.995185 0.0980171i \(-0.0312500\pi\)
−0.995185 + 0.0980171i \(0.968750\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −0.938254 + 0.0924099i −0.938254 + 0.0924099i
\(93\) 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 \(0.375000\pi\)
\(98\) −0.881921 0.471397i −0.881921 0.471397i
\(99\) −1.19028 0.882768i −1.19028 0.882768i
\(100\) 0.471397 0.881921i 0.471397 0.881921i
\(101\) 0 0 0.671559 0.740951i \(-0.265625\pi\)
−0.671559 + 0.740951i \(0.734375\pi\)
\(102\) 0 0
\(103\) 0 0 −0.773010 0.634393i \(-0.781250\pi\)
0.773010 + 0.634393i \(0.218750\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −1.15203 1.27107i −1.15203 1.27107i
\(107\) 0.881921 + 0.528603i 0.881921 + 0.528603i 0.881921 0.471397i \(-0.156250\pi\)
1.00000i \(0.5\pi\)
\(108\) 0 0
\(109\) 0.0659037 + 0.0727135i 0.0659037 + 0.0727135i 0.773010 0.634393i \(-0.218750\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −0.0980171 0.995185i −0.0980171 0.995185i
\(113\) 0.113263 + 0.569414i 0.113263 + 0.569414i 0.995185 + 0.0980171i \(0.0312500\pi\)
−0.881921 + 0.471397i \(0.843750\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −0.365607 + 0.773010i −0.365607 + 0.773010i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 1.14453 + 0.347190i 1.14453 + 0.347190i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0.634393 0.773010i 0.634393 0.773010i
\(127\) 0.390181i 0.390181i 0.980785 + 0.195090i \(0.0625000\pi\)
−0.980785 + 0.195090i \(0.937500\pi\)
\(128\) 0.773010 0.634393i 0.773010 0.634393i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 0.242980 0.970031i \(-0.421875\pi\)
−0.242980 + 0.970031i \(0.578125\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0.390327 0.289486i 0.390327 0.289486i
\(135\) 0 0
\(136\) 0 0
\(137\) −0.598102 + 1.11897i −0.598102 + 1.11897i 0.382683 + 0.923880i \(0.375000\pi\)
−0.980785 + 0.195090i \(0.937500\pi\)
\(138\) 0 0
\(139\) 0 0 0.146730 0.989177i \(-0.453125\pi\)
−0.146730 + 0.989177i \(0.546875\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −0.617317 0.923880i −0.617317 0.923880i
\(143\) 0 0
\(144\) 0.995185 + 0.0980171i 0.995185 + 0.0980171i
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0.480701 + 1.91906i 0.480701 + 1.91906i
\(149\) −1.66405 0.997391i −1.66405 0.997391i −0.956940 0.290285i \(-0.906250\pi\)
−0.707107 0.707107i \(-0.750000\pi\)
\(150\) 0 0
\(151\) 0.195090 1.98079i 0.195090 1.98079i 1.00000i \(-0.5\pi\)
0.195090 0.980785i \(-0.437500\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) −0.499238 + 1.39528i −0.499238 + 1.39528i
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 −0.803208 0.595699i \(-0.796875\pi\)
0.803208 + 0.595699i \(0.203125\pi\)
\(158\) −0.728789 + 1.36347i −0.728789 + 1.36347i
\(159\) 0 0
\(160\) 0 0
\(161\) −0.360791 + 0.871028i −0.360791 + 0.871028i
\(162\) 0.634393 + 0.773010i 0.634393 + 0.773010i
\(163\) −0.666487 + 0.0988640i −0.666487 + 0.0988640i −0.471397 0.881921i \(-0.656250\pi\)
−0.195090 + 0.980785i \(0.562500\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 0.995185 0.0980171i \(-0.0312500\pi\)
−0.995185 + 0.0980171i \(0.968750\pi\)
\(168\) 0 0
\(169\) −0.773010 + 0.634393i −0.773010 + 0.634393i
\(170\) 0 0
\(171\) 0 0
\(172\) 0.686831 + 1.45218i 0.686831 + 1.45218i
\(173\) 0 0 0.0490677 0.998795i \(-0.484375\pi\)
−0.0490677 + 0.998795i \(0.515625\pi\)
\(174\) 0 0
\(175\) −0.555570 0.831470i −0.555570 0.831470i
\(176\) −1.43749 + 0.360073i −1.43749 + 0.360073i
\(177\) 0 0
\(178\) 0 0
\(179\) −0.125471 + 0.265286i −0.125471 + 0.265286i −0.956940 0.290285i \(-0.906250\pi\)
0.831470 + 0.555570i \(0.187500\pi\)
\(180\) 0 0
\(181\) 0 0 0.803208 0.595699i \(-0.203125\pi\)
−0.803208 + 0.595699i \(0.796875\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −0.924678 + 0.183930i −0.924678 + 0.183930i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0.138617 + 0.138617i 0.138617 + 0.138617i 0.773010 0.634393i \(-0.218750\pi\)
−0.634393 + 0.773010i \(0.718750\pi\)
\(192\) 0 0
\(193\) −1.24723 + 1.24723i −1.24723 + 1.24723i −0.290285 + 0.956940i \(0.593750\pi\)
−0.956940 + 0.290285i \(0.906250\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −0.923880 0.382683i −0.923880 0.382683i
\(197\) 0.401370 1.12175i 0.401370 1.12175i −0.555570 0.831470i \(-0.687500\pi\)
0.956940 0.290285i \(-0.0937500\pi\)
\(198\) −1.27107 0.761850i −1.27107 0.761850i
\(199\) 0 0 0.881921 0.471397i \(-0.156250\pi\)
−0.881921 + 0.471397i \(0.843750\pi\)
\(200\) 0.382683 0.923880i 0.382683 0.923880i
\(201\) 0 0
\(202\) 0 0
\(203\) 0.509389 + 0.686831i 0.509389 + 0.686831i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −0.783904 0.523788i −0.783904 0.523788i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −1.80580 0.0887133i −1.80580 0.0887133i −0.881921 0.471397i \(-0.843750\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(212\) −1.27107 1.15203i −1.27107 1.15203i
\(213\) 0 0
\(214\) 0.929487 + 0.439614i 0.929487 + 0.439614i
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0.0727135 + 0.0659037i 0.0727135 + 0.0659037i
\(219\) 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 \(0.125000\pi\)
\(224\) −0.195090 0.980785i −0.195090 0.980785i
\(225\) 0.923880 0.382683i 0.923880 0.382683i
\(226\) 0.168530 + 0.555570i 0.168530 + 0.555570i
\(227\) 0 0 0.595699 0.803208i \(-0.296875\pi\)
−0.595699 + 0.803208i \(0.703125\pi\)
\(228\) 0 0
\(229\) 0 0 −0.740951 0.671559i \(-0.765625\pi\)
0.740951 + 0.671559i \(0.234375\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −0.288078 + 0.805124i −0.288078 + 0.805124i
\(233\) 1.53858 + 0.151537i 1.53858 + 0.151537i 0.831470 0.555570i \(-0.187500\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −1.92388 0.382683i −1.92388 0.382683i −0.923880 0.382683i \(-0.875000\pi\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) 0 0 0.980785 0.195090i \(-0.0625000\pi\)
−0.980785 + 0.195090i \(0.937500\pi\)
\(242\) 1.17305 + 0.233335i 1.17305 + 0.233335i
\(243\) 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 0.903989 0.427555i \(-0.140625\pi\)
−0.903989 + 0.427555i \(0.859375\pi\)
\(252\) 0.555570 0.831470i 0.555570 0.831470i
\(253\) 1.35526 + 0.339474i 1.35526 + 0.339474i
\(254\) 0.0382444 + 0.388302i 0.0382444 + 0.388302i
\(255\) 0 0
\(256\) 0.707107 0.707107i 0.707107 0.707107i
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) 1.91906 + 0.480701i 1.91906 + 0.480701i
\(260\) 0 0
\(261\) −0.773010 + 0.365607i −0.773010 + 0.365607i
\(262\) 0 0
\(263\) 0.222174 0.732410i 0.222174 0.732410i −0.773010 0.634393i \(-0.781250\pi\)
0.995185 0.0980171i \(-0.0312500\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0.360073 0.326351i 0.360073 0.326351i
\(269\) 0 0 −0.336890 0.941544i \(-0.609375\pi\)
0.336890 + 0.941544i \(0.390625\pi\)
\(270\) 0 0
\(271\) 0 0 0.980785 0.195090i \(-0.0625000\pi\)
−0.980785 + 0.195090i \(0.937500\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) −0.485544 + 1.17221i −0.485544 + 1.17221i
\(275\) −1.09802 + 0.995185i −1.09802 + 0.995185i
\(276\) 0 0
\(277\) 1.02697 1.71339i 1.02697 1.71339i 0.471397 0.881921i \(-0.343750\pi\)
0.555570 0.831470i \(-0.312500\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1.26268 1.53858i 1.26268 1.53858i 0.555570 0.831470i \(-0.312500\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(282\) 0 0
\(283\) 0 0 −0.740951 0.671559i \(-0.765625\pi\)
0.740951 + 0.671559i \(0.234375\pi\)
\(284\) −0.704900 0.858923i −0.704900 0.858923i
\(285\) 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 −0.0490677 0.998795i \(-0.515625\pi\)
0.0490677 + 0.998795i \(0.484375\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0.666487 + 1.86271i 0.666487 + 1.86271i
\(297\) 0 0
\(298\) −1.75380 0.829484i −1.75380 0.829484i
\(299\) 0 0
\(300\) 0 0
\(301\) 1.60448 + 0.0788231i 1.60448 + 0.0788231i
\(302\) 1.99037i 1.99037i
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 −0.903989 0.427555i \(-0.859375\pi\)
0.903989 + 0.427555i \(0.140625\pi\)
\(308\) −0.360073 + 1.43749i −0.360073 + 1.43749i
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.956940 0.290285i \(-0.0937500\pi\)
−0.956940 + 0.290285i \(0.906250\pi\)
\(312\) 0 0
\(313\) 0 0 0.881921 0.471397i \(-0.156250\pi\)
−0.881921 + 0.471397i \(0.843750\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −0.591637 + 1.42834i −0.591637 + 1.42834i
\(317\) 0.346392 + 0.577920i 0.346392 + 0.577920i 0.980785 0.195090i \(-0.0625000\pi\)
−0.634393 + 0.773010i \(0.718750\pi\)
\(318\) 0 0
\(319\) 0.896038 0.896038i 0.896038 0.896038i
\(320\) 0 0
\(321\) 0 0
\(322\) −0.273678 + 0.902197i −0.273678 + 0.902197i
\(323\) 0 0
\(324\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(325\) 0 0
\(326\) −0.653587 + 0.163715i −0.653587 + 0.163715i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 1.51251 1.12175i 1.51251 1.12175i 0.555570 0.831470i \(-0.312500\pi\)
0.956940 0.290285i \(-0.0937500\pi\)
\(332\) 0 0
\(333\) −0.845855 + 1.78841i −0.845855 + 1.78841i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −1.06330 1.59133i −1.06330 1.59133i −0.773010 0.634393i \(-0.781250\pi\)
−0.290285 0.956940i \(-0.593750\pi\)
\(338\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −0.773010 + 0.634393i −0.773010 + 0.634393i
\(344\) 0.825862 + 1.37787i 0.825862 + 1.37787i
\(345\) 0 0
\(346\) 0 0
\(347\) 1.88082 0.0923988i 1.88082 0.0923988i 0.923880 0.382683i \(-0.125000\pi\)
0.956940 + 0.290285i \(0.0937500\pi\)
\(348\) 0 0
\(349\) 0 0 0.989177 0.146730i \(-0.0468750\pi\)
−0.989177 + 0.146730i \(0.953125\pi\)
\(350\) −0.634393 0.773010i −0.634393 0.773010i
\(351\) 0 0
\(352\) −1.39528 + 0.499238i −1.39528 + 0.499238i
\(353\) 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
\(358\) −0.0988640 + 0.276306i −0.0988640 + 0.276306i
\(359\) 1.47945 + 1.21415i 1.47945 + 1.21415i 0.923880 + 0.382683i \(0.125000\pi\)
0.555570 + 0.831470i \(0.312500\pi\)
\(360\) 0 0
\(361\) 0.0980171 0.995185i 0.0980171 0.995185i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 0.195090 0.980785i \(-0.437500\pi\)
−0.195090 + 0.980785i \(0.562500\pi\)
\(368\) −0.902197 + 0.273678i −0.902197 + 0.273678i
\(369\) 0 0
\(370\) 0 0
\(371\) −1.61518 + 0.577920i −1.61518 + 0.577920i
\(372\) 0 0
\(373\) −0.197076 + 1.32858i −0.197076 + 1.32858i 0.634393 + 0.773010i \(0.281250\pi\)
−0.831470 + 0.555570i \(0.812500\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −0.733452 1.55075i −0.733452 1.55075i −0.831470 0.555570i \(-0.812500\pi\)
0.0980171 0.995185i \(-0.468750\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0.151537 + 0.124363i 0.151537 + 0.124363i
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −1.11897 + 1.36347i −1.11897 + 1.36347i
\(387\) −0.390327 + 1.55827i −0.390327 + 1.55827i
\(388\) 0 0
\(389\) −0.686831 1.45218i −0.686831 1.45218i −0.881921 0.471397i \(-0.843750\pi\)
0.195090 0.980785i \(-0.437500\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.956940 0.290285i −0.956940 0.290285i
\(393\) 0 0
\(394\) 0.289486 1.15569i 0.289486 1.15569i
\(395\) 0 0
\(396\) −1.33962 0.633595i −1.33962 0.633595i
\(397\) 0 0 0.941544 0.336890i \(-0.109375\pi\)
−0.941544 + 0.336890i \(0.890625\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.290285 0.956940i 0.290285 0.956940i
\(401\) −0.373380 + 1.87711i −0.373380 + 1.87711i 0.0980171 + 0.995185i \(0.468750\pi\)
−0.471397 + 0.881921i \(0.656250\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0.574257 + 0.633595i 0.574257 + 0.633595i
\(407\) 0.287359 2.91761i 0.287359 2.91761i
\(408\) 0 0
\(409\) 0 0 −0.773010 0.634393i \(-0.781250\pi\)
0.773010 + 0.634393i \(0.218750\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) −0.831470 0.444430i −0.831470 0.444430i
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 0.989177 0.146730i \(-0.0468750\pi\)
−0.989177 + 0.146730i \(0.953125\pi\)
\(420\) 0 0
\(421\) 0.672968 0.0330608i 0.672968 0.0330608i 0.290285 0.956940i \(-0.406250\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(422\) −1.80580 + 0.0887133i −1.80580 + 0.0887133i
\(423\) 0 0
\(424\) −1.37787 1.02190i −1.37787 1.02190i
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0.968101 + 0.346392i 0.968101 + 0.346392i
\(429\) 0 0
\(430\) 0 0
\(431\) 1.02656 + 1.53636i 1.02656 + 1.53636i 0.831470 + 0.555570i \(0.187500\pi\)
0.195090 + 0.980785i \(0.437500\pi\)
\(432\) 0 0
\(433\) 0 0 0.555570 0.831470i \(-0.312500\pi\)
−0.555570 + 0.831470i \(0.687500\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0.0788231 + 0.0584592i 0.0788231 + 0.0584592i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 −0.290285 0.956940i \(-0.593750\pi\)
0.290285 + 0.956940i \(0.406250\pi\)
\(440\) 0 0
\(441\) −0.471397 0.881921i −0.471397 0.881921i
\(442\) 0 0
\(443\) 1.86271 + 0.666487i 1.86271 + 0.666487i 0.980785 + 0.195090i \(0.0625000\pi\)
0.881921 + 0.471397i \(0.156250\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) −0.290285 0.956940i −0.290285 0.956940i
\(449\) 1.17588 1.17588i 1.17588 1.17588i 0.195090 0.980785i \(-0.437500\pi\)
0.980785 0.195090i \(-0.0625000\pi\)
\(450\) 0.881921 0.471397i 0.881921 0.471397i
\(451\) 0 0
\(452\) 0.222174 + 0.536376i 0.222174 + 0.536376i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 1.87711 0.569414i 1.87711 0.569414i 0.881921 0.471397i \(-0.156250\pi\)
0.995185 0.0980171i \(-0.0312500\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 −0.903989 0.427555i \(-0.859375\pi\)
0.903989 + 0.427555i \(0.140625\pi\)
\(462\) 0 0
\(463\) 1.59133 + 1.06330i 1.59133 + 1.06330i 0.956940 + 0.290285i \(0.0937500\pi\)
0.634393 + 0.773010i \(0.281250\pi\)
\(464\) −0.207775 + 0.829484i −0.207775 + 0.829484i
\(465\) 0 0
\(466\) 1.54602 1.54602
\(467\) 0 0 −0.998795 0.0490677i \(-0.984375\pi\)
0.998795 + 0.0490677i \(0.0156250\pi\)
\(468\) 0 0
\(469\) −0.118079 0.471397i −0.118079 0.471397i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −0.233335 2.36909i −0.233335 2.36909i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −0.251710 1.69689i −0.251710 1.69689i
\(478\) −1.95213 0.192268i −1.95213 0.192268i
\(479\) 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
\(484\) 1.19028 + 0.117232i 1.19028 + 0.117232i
\(485\) 0 0
\(486\) 0 0
\(487\) 0.804910 0.980785i 0.804910 0.980785i −0.195090 0.980785i \(-0.562500\pi\)
1.00000 \(0\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −0.997391 + 1.66405i −0.997391 + 1.66405i −0.290285 + 0.956940i \(0.593750\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1.08979 + 0.216773i −1.08979 + 0.216773i
\(498\) 0 0
\(499\) −0.653587 1.82665i −0.653587 1.82665i −0.555570 0.831470i \(-0.687500\pi\)
−0.0980171 0.995185i \(-0.531250\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 −0.881921 0.471397i \(-0.843750\pi\)
0.881921 + 0.471397i \(0.156250\pi\)
\(504\) 0.471397 0.881921i 0.471397 0.881921i
\(505\) 0 0
\(506\) 1.38201 + 0.205001i 1.38201 + 0.205001i
\(507\) 0 0
\(508\) 0.0761205 + 0.382683i 0.0761205 + 0.382683i
\(509\) 0 0 −0.970031 0.242980i \(-0.921875\pi\)
0.970031 + 0.242980i \(0.0781250\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.634393 0.773010i 0.634393 0.773010i
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 1.95694 + 0.290285i 1.95694 + 0.290285i
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 −0.881921 0.471397i \(-0.843750\pi\)
0.881921 + 0.471397i \(0.156250\pi\)
\(522\) −0.733452 + 0.439614i −0.733452 + 0.439614i
\(523\) 0 0 −0.989177 0.146730i \(-0.953125\pi\)
0.989177 + 0.146730i \(0.0468750\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0.149316 0.750661i 0.149316 0.750661i
\(527\) 0 0
\(528\) 0 0
\(529\) −0.109005 0.0216824i −0.109005 0.0216824i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0.326351 0.360073i 0.326351 0.360073i
\(537\) 0 0
\(538\) 0 0
\(539\) 1.09802 + 0.995185i 1.09802 + 0.995185i
\(540\) 0 0
\(541\) 0.612501 0.825862i 0.612501 0.825862i −0.382683 0.923880i \(-0.625000\pi\)
0.995185 + 0.0980171i \(0.0312500\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0.265286 + 1.78841i 0.265286 + 1.78841i 0.555570 + 0.831470i \(0.312500\pi\)
−0.290285 + 0.956940i \(0.593750\pi\)
\(548\) −0.368309 + 1.21415i −0.368309 + 1.21415i
\(549\) 0 0
\(550\) −0.995185 + 1.09802i −0.995185 + 1.09802i
\(551\) 0 0
\(552\) 0 0
\(553\) 0.980785 + 1.19509i 0.980785 + 1.19509i
\(554\) 0.854080 1.80580i 0.854080 1.80580i
\(555\) 0 0
\(556\) 0 0
\(557\) −1.99518 0.0980171i −1.99518 0.0980171i −0.995185 0.0980171i \(-0.968750\pi\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 1.10579 1.65493i 1.10579 1.65493i
\(563\) 0 0 −0.903989 0.427555i \(-0.859375\pi\)
0.903989 + 0.427555i \(0.140625\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0.956940 0.290285i 0.956940 0.290285i
\(568\) −0.785695 0.785695i −0.785695 0.785695i
\(569\) −0.344109 + 0.183930i −0.344109 + 0.183930i −0.634393 0.773010i \(-0.718750\pi\)
0.290285 + 0.956940i \(0.406250\pi\)
\(570\) 0 0
\(571\) 0.288078 0.805124i 0.288078 0.805124i −0.707107 0.707107i \(-0.750000\pi\)
0.995185 0.0980171i \(-0.0312500\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −0.666656 + 0.666656i −0.666656 + 0.666656i
\(576\) 0.995185 0.0980171i 0.995185 0.0980171i
\(577\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(578\) 0.956940 + 0.290285i 0.956940 + 0.290285i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 1.19836 + 2.24197i 1.19836 + 2.24197i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 0.803208 0.595699i \(-0.203125\pi\)
−0.803208 + 0.595699i \(0.796875\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0.845855 + 1.78841i 0.845855 + 1.78841i
\(593\) 0 0 −0.555570 0.831470i \(-0.687500\pi\)
0.555570 + 0.831470i \(0.312500\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −1.82665 0.653587i −1.82665 0.653587i
\(597\) 0 0
\(598\) 0 0
\(599\) 0.591637 0.485544i 0.591637 0.485544i −0.290285 0.956940i \(-0.593750\pi\)
0.881921 + 0.471397i \(0.156250\pi\)
\(600\) 0 0
\(601\) 0 0 0.995185 0.0980171i \(-0.0312500\pi\)
−0.995185 + 0.0980171i \(0.968750\pi\)
\(602\) 1.60448 0.0788231i 1.60448 0.0788231i
\(603\) 0.485375 0.0238449i 0.485375 0.0238449i
\(604\) −0.195090 1.98079i −0.195090 1.98079i
\(605\) 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
\(613\) −1.26460 + 1.39528i −1.26460 + 1.39528i −0.382683 + 0.923880i \(0.625000\pi\)
−0.881921 + 0.471397i \(0.843750\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) −0.217440 + 1.46586i −0.217440 + 1.46586i
\(617\) 0.192268 1.95213i 0.192268 1.95213i −0.0980171 0.995185i \(-0.531250\pi\)
0.290285 0.956940i \(-0.406250\pi\)
\(618\) 0 0
\(619\) 0 0 −0.857729 0.514103i \(-0.828125\pi\)
0.857729 + 0.514103i \(0.171875\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.195090 0.980785i −0.195090 0.980785i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0.783904 1.46658i 0.783904 1.46658i −0.0980171 0.995185i \(-0.531250\pi\)
0.881921 0.471397i \(-0.156250\pi\)
\(632\) −0.448786 + 1.47945i −0.448786 + 1.47945i
\(633\) 0 0
\(634\) 0.401370 + 0.541185i 0.401370 + 0.541185i
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0.803897 0.979551i 0.803897 0.979551i
\(639\) 1.11114i 1.11114i
\(640\) 0 0
\(641\) 1.76384i 1.76384i −0.471397 0.881921i \(-0.656250\pi\)
0.471397 0.881921i \(-0.343750\pi\)
\(642\) 0 0
\(643\) 0 0 0.242980 0.970031i \(-0.421875\pi\)
−0.242980 + 0.970031i \(0.578125\pi\)
\(644\) −0.183930 + 0.924678i −0.183930 + 0.924678i
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 −0.956940 0.290285i \(-0.906250\pi\)
0.956940 + 0.290285i \(0.0937500\pi\)
\(648\) 0.773010 + 0.634393i 0.773010 + 0.634393i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −0.634393 + 0.226990i −0.634393 + 0.226990i
\(653\) −1.26460 + 0.452483i −1.26460 + 0.452483i −0.881921 0.471397i \(-0.843750\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0.0659037 + 0.0727135i 0.0659037 + 0.0727135i 0.773010 0.634393i \(-0.218750\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(660\) 0 0
\(661\) 0 0 −0.857729 0.514103i \(-0.828125\pi\)
0.857729 + 0.514103i \(0.171875\pi\)
\(662\) 1.39528 1.26460i 1.39528 1.26460i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) −0.666487 + 1.86271i −0.666487 + 1.86271i
\(667\) 0.541406 0.597349i 0.541406 0.597349i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −0.636379 + 1.53636i −0.636379 + 1.53636i 0.195090 + 0.980785i \(0.437500\pi\)
−0.831470 + 0.555570i \(0.812500\pi\)
\(674\) −1.21415 1.47945i −1.21415 1.47945i
\(675\) 0 0
\(676\) −0.634393 + 0.773010i −0.634393 + 0.773010i
\(677\) 0 0 0.998795 0.0490677i \(-0.0156250\pi\)
−0.998795 + 0.0490677i \(0.984375\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0.284666 0.0713052i 0.284666 0.0713052i −0.0980171 0.995185i \(-0.531250\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(687\) 0 0
\(688\) 0.956940 + 1.29028i 0.956940 + 1.29028i
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 0.427555 0.903989i \(-0.359375\pi\)
−0.427555 + 0.903989i \(0.640625\pi\)
\(692\) 0 0
\(693\) −1.19028 + 0.882768i −1.19028 + 0.882768i
\(694\) 1.86271 0.276306i 1.86271 0.276306i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −0.707107 0.707107i −0.707107 0.707107i
\(701\) 1.02190 0.612501i 1.02190 0.612501i 0.0980171 0.995185i \(-0.468750\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −1.33962 + 0.633595i −1.33962 + 0.633595i
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 0.452483 1.26460i 0.452483 1.26460i −0.471397 0.881921i \(-0.656250\pi\)
0.923880 0.382683i \(-0.125000\pi\)
\(710\) 0 0
\(711\) −1.36347 + 0.728789i −1.36347 + 0.728789i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −0.0713052 + 0.284666i −0.0713052 + 0.284666i
\(717\) 0 0
\(718\) 1.59133 + 1.06330i 1.59133 + 1.06330i
\(719\) 0 0 −0.831470 0.555570i \(-0.812500\pi\)
0.831470 + 0.555570i \(0.187500\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 1.00000i 1.00000i
\(723\) 0 0
\(724\) 0 0
\(725\) 0.207775 + 0.829484i 0.207775 + 0.829484i
\(726\) 0 0
\(727\) 0 0 −0.634393 0.773010i \(-0.718750\pi\)
0.634393 + 0.773010i \(0.281250\pi\)
\(728\) 0 0
\(729\) 0.0980171 + 0.995185i 0.0980171 + 0.995185i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 −0.146730 0.989177i \(-0.546875\pi\)
0.146730 + 0.989177i \(0.453125\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) −0.871028 + 0.360791i −0.871028 + 0.360791i
\(737\) −0.665328 + 0.275588i −0.665328 + 0.275588i
\(738\) 0 0
\(739\) 1.18996 1.60448i 1.18996 1.60448i 0.555570 0.831470i \(-0.312500\pi\)
0.634393 0.773010i \(-0.281250\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −1.55075 + 0.733452i −1.55075 + 0.733452i
\(743\) −0.124363 + 0.151537i −0.124363 + 0.151537i −0.831470 0.555570i \(-0.812500\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −0.0659037 + 1.34150i −0.0659037 + 1.34150i
\(747\) 0 0
\(748\) 0 0
\(749\) 0.761850 0.690501i 0.761850 0.690501i
\(750\) 0 0
\(751\) −1.63099 0.324423i −1.63099 0.324423i −0.707107 0.707107i \(-0.750000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −1.01708 0.150869i −1.01708 0.150869i −0.382683 0.923880i \(-0.625000\pi\)
−0.634393 + 0.773010i \(0.718750\pi\)
\(758\) −0.881921 1.47140i −0.881921 1.47140i
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 0.290285 0.956940i \(-0.406250\pi\)
−0.290285 + 0.956940i \(0.593750\pi\)
\(762\) 0 0
\(763\) 0.0887133 0.0419583i 0.0887133 0.0419583i
\(764\) 0.162997 + 0.108911i 0.162997 + 0.108911i
\(765\) 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
\(772\) −0.979938 + 1.46658i −0.979938 + 1.46658i
\(773\) 0 0 0.903989 0.427555i \(-0.140625\pi\)
−0.903989 + 0.427555i \(0.859375\pi\)
\(774\) −0.235710 + 1.58903i −0.235710 + 1.58903i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) −0.825862 1.37787i −0.825862 1.37787i
\(779\) 0 0
\(780\) 0 0
\(781\) 0.554723 + 1.55035i 0.554723 + 1.55035i
\(782\) 0 0
\(783\) 0 0
\(784\) −0.980785 0.195090i −0.980785 0.195090i
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 0.740951 0.671559i \(-0.234375\pi\)
−0.740951 + 0.671559i \(0.765625\pi\)
\(788\) 0.174814 1.17850i 0.174814 1.17850i
\(789\) 0 0
\(790\) 0 0
\(791\) 0.577774 + 0.0569057i 0.577774 + 0.0569057i
\(792\) −1.39528 0.499238i −1.39528 0.499238i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 0.595699 0.803208i \(-0.296875\pi\)
−0.595699 + 0.803208i \(0.703125\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0.195090 0.980785i 0.195090 0.980785i