Properties

Label 1792.1.bt.a.349.1
Level $1792$
Weight $1$
Character 1792.349
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 349.1
Root \(0.0980171 - 0.995185i\) of defining polynomial
Character \(\chi\) \(=\) 1792.349
Dual form 1792.1.bt.a.1525.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.290285 + 0.956940i) q^{2} +(-0.831470 - 0.555570i) q^{4} +(0.634393 - 0.773010i) q^{7} +(0.773010 - 0.634393i) q^{8} +(-0.995185 - 0.0980171i) q^{9} +O(q^{10})\) \(q+(-0.290285 + 0.956940i) q^{2} +(-0.831470 - 0.555570i) q^{4} +(0.634393 - 0.773010i) q^{7} +(0.773010 - 0.634393i) q^{8} +(-0.995185 - 0.0980171i) q^{9} +(0.276306 + 0.0988640i) q^{11} +(0.555570 + 0.831470i) q^{14} +(0.382683 + 0.923880i) q^{16} +(0.382683 - 0.923880i) q^{18} +(-0.174814 + 0.235710i) q^{22} +(-0.0569057 - 0.187593i) q^{23} +(-0.471397 - 0.881921i) q^{25} +(-0.956940 + 0.290285i) q^{28} +(0.733452 - 1.55075i) q^{29} +(-0.995185 + 0.0980171i) q^{32} +(0.773010 + 0.634393i) q^{36} +(1.51251 - 1.12175i) q^{37} +(1.80580 - 0.0887133i) q^{43} +(-0.174814 - 0.235710i) q^{44} +0.196034 q^{46} +(-0.195090 - 0.980785i) q^{49} +(0.980785 - 0.195090i) q^{50} +(0.574257 + 1.21416i) q^{53} -1.00000i q^{56} +(1.27107 + 1.15203i) q^{58} +(-0.707107 + 0.707107i) q^{63} +(0.195090 - 0.980785i) q^{64} +(-1.34150 - 1.48012i) q^{67} +(0.192268 + 1.95213i) q^{71} +(-0.831470 + 0.555570i) q^{72} +(0.634393 + 1.77301i) q^{74} +(0.251710 - 0.150869i) q^{77} +(-1.72995 + 0.344109i) q^{79} +(0.980785 + 0.195090i) q^{81} +(-0.439303 + 1.75380i) q^{86} +(0.276306 - 0.0988640i) q^{88} +(-0.0569057 + 0.187593i) q^{92} +(0.995185 + 0.0980171i) q^{98} +(-0.265286 - 0.125471i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + O(q^{10}) \) \( 32q + O(q^{100}) \)

Character values

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

\(n\) \(1023\) \(1025\) \(1541\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{43}{64}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.290285 + 0.956940i −0.290285 + 0.956940i
\(3\) 0 0 0.0490677 0.998795i \(-0.484375\pi\)
−0.0490677 + 0.998795i \(0.515625\pi\)
\(4\) −0.831470 0.555570i −0.831470 0.555570i
\(5\) 0 0 0.514103 0.857729i \(-0.328125\pi\)
−0.514103 + 0.857729i \(0.671875\pi\)
\(6\) 0 0
\(7\) 0.634393 0.773010i 0.634393 0.773010i
\(8\) 0.773010 0.634393i 0.773010 0.634393i
\(9\) −0.995185 0.0980171i −0.995185 0.0980171i
\(10\) 0 0
\(11\) 0.276306 + 0.0988640i 0.276306 + 0.0988640i 0.471397 0.881921i \(-0.343750\pi\)
−0.195090 + 0.980785i \(0.562500\pi\)
\(12\) 0 0
\(13\) 0 0 0.242980 0.970031i \(-0.421875\pi\)
−0.242980 + 0.970031i \(0.578125\pi\)
\(14\) 0.555570 + 0.831470i 0.555570 + 0.831470i
\(15\) 0 0
\(16\) 0.382683 + 0.923880i 0.382683 + 0.923880i
\(17\) 0 0 0.831470 0.555570i \(-0.187500\pi\)
−0.831470 + 0.555570i \(0.812500\pi\)
\(18\) 0.382683 0.923880i 0.382683 0.923880i
\(19\) 0 0 −0.146730 0.989177i \(-0.546875\pi\)
0.146730 + 0.989177i \(0.453125\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −0.174814 + 0.235710i −0.174814 + 0.235710i
\(23\) −0.0569057 0.187593i −0.0569057 0.187593i 0.923880 0.382683i \(-0.125000\pi\)
−0.980785 + 0.195090i \(0.937500\pi\)
\(24\) 0 0
\(25\) −0.471397 0.881921i −0.471397 0.881921i
\(26\) 0 0
\(27\) 0 0
\(28\) −0.956940 + 0.290285i −0.956940 + 0.290285i
\(29\) 0.733452 1.55075i 0.733452 1.55075i −0.0980171 0.995185i \(-0.531250\pi\)
0.831470 0.555570i \(-0.187500\pi\)
\(30\) 0 0
\(31\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(32\) −0.995185 + 0.0980171i −0.995185 + 0.0980171i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0.773010 + 0.634393i 0.773010 + 0.634393i
\(37\) 1.51251 1.12175i 1.51251 1.12175i 0.555570 0.831470i \(-0.312500\pi\)
0.956940 0.290285i \(-0.0937500\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 0.471397 0.881921i \(-0.343750\pi\)
−0.471397 + 0.881921i \(0.656250\pi\)
\(42\) 0 0
\(43\) 1.80580 0.0887133i 1.80580 0.0887133i 0.881921 0.471397i \(-0.156250\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(44\) −0.174814 0.235710i −0.174814 0.235710i
\(45\) 0 0
\(46\) 0.196034 0.196034
\(47\) 0 0 0.195090 0.980785i \(-0.437500\pi\)
−0.195090 + 0.980785i \(0.562500\pi\)
\(48\) 0 0
\(49\) −0.195090 0.980785i −0.195090 0.980785i
\(50\) 0.980785 0.195090i 0.980785 0.195090i
\(51\) 0 0
\(52\) 0 0
\(53\) 0.574257 + 1.21416i 0.574257 + 1.21416i 0.956940 + 0.290285i \(0.0937500\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 1.00000i 1.00000i
\(57\) 0 0
\(58\) 1.27107 + 1.15203i 1.27107 + 1.15203i
\(59\) 0 0 −0.242980 0.970031i \(-0.578125\pi\)
0.242980 + 0.970031i \(0.421875\pi\)
\(60\) 0 0
\(61\) 0 0 0.740951 0.671559i \(-0.234375\pi\)
−0.740951 + 0.671559i \(0.765625\pi\)
\(62\) 0 0
\(63\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(64\) 0.195090 0.980785i 0.195090 0.980785i
\(65\) 0 0
\(66\) 0 0
\(67\) −1.34150 1.48012i −1.34150 1.48012i −0.707107 0.707107i \(-0.750000\pi\)
−0.634393 0.773010i \(-0.718750\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0.192268 + 1.95213i 0.192268 + 1.95213i 0.290285 + 0.956940i \(0.406250\pi\)
−0.0980171 + 0.995185i \(0.531250\pi\)
\(72\) −0.831470 + 0.555570i −0.831470 + 0.555570i
\(73\) 0 0 −0.634393 0.773010i \(-0.718750\pi\)
0.634393 + 0.773010i \(0.281250\pi\)
\(74\) 0.634393 + 1.77301i 0.634393 + 1.77301i
\(75\) 0 0
\(76\) 0 0
\(77\) 0.251710 0.150869i 0.251710 0.150869i
\(78\) 0 0
\(79\) −1.72995 + 0.344109i −1.72995 + 0.344109i −0.956940 0.290285i \(-0.906250\pi\)
−0.773010 + 0.634393i \(0.781250\pi\)
\(80\) 0 0
\(81\) 0.980785 + 0.195090i 0.980785 + 0.195090i
\(82\) 0 0
\(83\) 0 0 −0.803208 0.595699i \(-0.796875\pi\)
0.803208 + 0.595699i \(0.203125\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −0.439303 + 1.75380i −0.439303 + 1.75380i
\(87\) 0 0
\(88\) 0.276306 0.0988640i 0.276306 0.0988640i
\(89\) 0 0 0.290285 0.956940i \(-0.406250\pi\)
−0.290285 + 0.956940i \(0.593750\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −0.0569057 + 0.187593i −0.0569057 + 0.187593i
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(98\) 0.995185 + 0.0980171i 0.995185 + 0.0980171i
\(99\) −0.265286 0.125471i −0.265286 0.125471i
\(100\) −0.0980171 + 0.995185i −0.0980171 + 0.995185i
\(101\) 0 0 −0.989177 0.146730i \(-0.953125\pi\)
0.989177 + 0.146730i \(0.0468750\pi\)
\(102\) 0 0
\(103\) 0 0 0.881921 0.471397i \(-0.156250\pi\)
−0.881921 + 0.471397i \(0.843750\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −1.32858 + 0.197076i −1.32858 + 0.197076i
\(107\) −0.995185 + 1.09802i −0.995185 + 1.09802i 1.00000i \(0.5\pi\)
−0.995185 + 0.0980171i \(0.968750\pi\)
\(108\) 0 0
\(109\) 1.58903 0.235710i 1.58903 0.235710i 0.707107 0.707107i \(-0.250000\pi\)
0.881921 + 0.471397i \(0.156250\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0.956940 + 0.290285i 0.956940 + 0.290285i
\(113\) 0.704900 1.05496i 0.704900 1.05496i −0.290285 0.956940i \(-0.593750\pi\)
0.995185 0.0980171i \(-0.0312500\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −1.47140 + 0.881921i −1.47140 + 0.881921i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −0.706439 0.579760i −0.706439 0.579760i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) −0.471397 0.881921i −0.471397 0.881921i
\(127\) 1.11114i 1.11114i 0.831470 + 0.555570i \(0.187500\pi\)
−0.831470 + 0.555570i \(0.812500\pi\)
\(128\) 0.881921 + 0.471397i 0.881921 + 0.471397i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 −0.998795 0.0490677i \(-0.984375\pi\)
0.998795 + 0.0490677i \(0.0156250\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 1.80580 0.854080i 1.80580 0.854080i
\(135\) 0 0
\(136\) 0 0
\(137\) −0.0924099 + 0.938254i −0.0924099 + 0.938254i 0.831470 + 0.555570i \(0.187500\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(138\) 0 0
\(139\) 0 0 0.336890 0.941544i \(-0.390625\pi\)
−0.336890 + 0.941544i \(0.609375\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −1.92388 0.382683i −1.92388 0.382683i
\(143\) 0 0
\(144\) −0.290285 0.956940i −0.290285 0.956940i
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) −1.88082 + 0.0923988i −1.88082 + 0.0923988i
\(149\) −0.0659037 + 0.0727135i −0.0659037 + 0.0727135i −0.773010 0.634393i \(-0.781250\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(150\) 0 0
\(151\) 0.555570 0.168530i 0.555570 0.168530i 1.00000i \(-0.5\pi\)
0.555570 + 0.831470i \(0.312500\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0.0713052 + 0.284666i 0.0713052 + 0.284666i
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 −0.903989 0.427555i \(-0.859375\pi\)
0.903989 + 0.427555i \(0.140625\pi\)
\(158\) 0.172887 1.75535i 0.172887 1.75535i
\(159\) 0 0
\(160\) 0 0
\(161\) −0.181112 0.0750191i −0.181112 0.0750191i
\(162\) −0.471397 + 0.881921i −0.471397 + 0.881921i
\(163\) −0.457553 + 0.163715i −0.457553 + 0.163715i −0.555570 0.831470i \(-0.687500\pi\)
0.0980171 + 0.995185i \(0.468750\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 0.290285 0.956940i \(-0.406250\pi\)
−0.290285 + 0.956940i \(0.593750\pi\)
\(168\) 0 0
\(169\) −0.881921 0.471397i −0.881921 0.471397i
\(170\) 0 0
\(171\) 0 0
\(172\) −1.55075 0.929487i −1.55075 0.929487i
\(173\) 0 0 −0.803208 0.595699i \(-0.796875\pi\)
0.803208 + 0.595699i \(0.203125\pi\)
\(174\) 0 0
\(175\) −0.980785 0.195090i −0.980785 0.195090i
\(176\) 0.0143994 + 0.293107i 0.0143994 + 0.293107i
\(177\) 0 0
\(178\) 0 0
\(179\) −0.577920 + 0.346392i −0.577920 + 0.346392i −0.773010 0.634393i \(-0.781250\pi\)
0.195090 + 0.980785i \(0.437500\pi\)
\(180\) 0 0
\(181\) 0 0 0.903989 0.427555i \(-0.140625\pi\)
−0.903989 + 0.427555i \(0.859375\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −0.162997 0.108911i −0.162997 0.108911i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 1.35332 + 1.35332i 1.35332 + 1.35332i 0.881921 + 0.471397i \(0.156250\pi\)
0.471397 + 0.881921i \(0.343750\pi\)
\(192\) 0 0
\(193\) −1.40740 + 1.40740i −1.40740 + 1.40740i −0.634393 + 0.773010i \(0.718750\pi\)
−0.773010 + 0.634393i \(0.781250\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −0.382683 + 0.923880i −0.382683 + 0.923880i
\(197\) −0.207775 0.829484i −0.207775 0.829484i −0.980785 0.195090i \(-0.937500\pi\)
0.773010 0.634393i \(-0.218750\pi\)
\(198\) 0.197076 0.217440i 0.197076 0.217440i
\(199\) 0 0 0.995185 0.0980171i \(-0.0312500\pi\)
−0.995185 + 0.0980171i \(0.968750\pi\)
\(200\) −0.923880 0.382683i −0.923880 0.382683i
\(201\) 0 0
\(202\) 0 0
\(203\) −0.733452 1.55075i −0.733452 1.55075i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0.0382444 + 0.192268i 0.0382444 + 0.192268i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0.612501 0.825862i 0.612501 0.825862i −0.382683 0.923880i \(-0.625000\pi\)
0.995185 + 0.0980171i \(0.0312500\pi\)
\(212\) 0.197076 1.32858i 0.197076 1.32858i
\(213\) 0 0
\(214\) −0.761850 1.27107i −0.761850 1.27107i
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) −0.235710 + 1.58903i −0.235710 + 1.58903i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(224\) −0.555570 + 0.831470i −0.555570 + 0.831470i
\(225\) 0.382683 + 0.923880i 0.382683 + 0.923880i
\(226\) 0.804910 + 0.980785i 0.804910 + 0.980785i
\(227\) 0 0 0.427555 0.903989i \(-0.359375\pi\)
−0.427555 + 0.903989i \(0.640625\pi\)
\(228\) 0 0
\(229\) 0 0 0.146730 0.989177i \(-0.453125\pi\)
−0.146730 + 0.989177i \(0.546875\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −0.416822 1.66405i −0.416822 1.66405i
\(233\) −0.512016 1.68789i −0.512016 1.68789i −0.707107 0.707107i \(-0.750000\pi\)
0.195090 0.980785i \(-0.437500\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −1.38268 + 0.923880i −1.38268 + 0.923880i −0.382683 + 0.923880i \(0.625000\pi\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) 0 0 −0.831470 0.555570i \(-0.812500\pi\)
0.831470 + 0.555570i \(0.187500\pi\)
\(242\) 0.759864 0.507725i 0.759864 0.507725i
\(243\) 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 0.514103 0.857729i \(-0.328125\pi\)
−0.514103 + 0.857729i \(0.671875\pi\)
\(252\) 0.980785 0.195090i 0.980785 0.195090i
\(253\) 0.00282279 0.0574591i 0.00282279 0.0574591i
\(254\) −1.06330 0.322547i −1.06330 0.322547i
\(255\) 0 0
\(256\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) 0.0923988 1.88082i 0.0923988 1.88082i
\(260\) 0 0
\(261\) −0.881921 + 1.47140i −0.881921 + 1.47140i
\(262\) 0 0
\(263\) −1.17221 + 1.42834i −1.17221 + 1.42834i −0.290285 + 0.956940i \(0.593750\pi\)
−0.881921 + 0.471397i \(0.843750\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0.293107 + 1.97597i 0.293107 + 1.97597i
\(269\) 0 0 0.242980 0.970031i \(-0.421875\pi\)
−0.242980 + 0.970031i \(0.578125\pi\)
\(270\) 0 0
\(271\) 0 0 −0.831470 0.555570i \(-0.812500\pi\)
0.831470 + 0.555570i \(0.187500\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) −0.871028 0.360791i −0.871028 0.360791i
\(275\) −0.0430597 0.290285i −0.0430597 0.290285i
\(276\) 0 0
\(277\) 0.882768 + 0.800094i 0.882768 + 0.800094i 0.980785 0.195090i \(-0.0625000\pi\)
−0.0980171 + 0.995185i \(0.531250\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0.273678 + 0.512016i 0.273678 + 0.512016i 0.980785 0.195090i \(-0.0625000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(282\) 0 0
\(283\) 0 0 0.146730 0.989177i \(-0.453125\pi\)
−0.146730 + 0.989177i \(0.546875\pi\)
\(284\) 0.924678 1.72995i 0.924678 1.72995i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 1.00000 1.00000
\(289\) 0.382683 0.923880i 0.382683 0.923880i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 0.803208 0.595699i \(-0.203125\pi\)
−0.803208 + 0.595699i \(0.796875\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0.457553 1.82665i 0.457553 1.82665i
\(297\) 0 0
\(298\) −0.0504517 0.0841735i −0.0504517 0.0841735i
\(299\) 0 0
\(300\) 0 0
\(301\) 1.07701 1.45218i 1.07701 1.45218i
\(302\) 0.580569i 0.580569i
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 −0.514103 0.857729i \(-0.671875\pi\)
0.514103 + 0.857729i \(0.328125\pi\)
\(308\) −0.293107 0.0143994i −0.293107 0.0143994i
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.773010 0.634393i \(-0.218750\pi\)
−0.773010 + 0.634393i \(0.781250\pi\)
\(312\) 0 0
\(313\) 0 0 0.995185 0.0980171i \(-0.0312500\pi\)
−0.995185 + 0.0980171i \(0.968750\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 1.62958 + 0.674993i 1.62958 + 0.674993i
\(317\) −0.360073 + 0.326351i −0.360073 + 0.326351i −0.831470 0.555570i \(-0.812500\pi\)
0.471397 + 0.881921i \(0.343750\pi\)
\(318\) 0 0
\(319\) 0.355971 0.355971i 0.355971 0.355971i
\(320\) 0 0
\(321\) 0 0
\(322\) 0.124363 0.151537i 0.124363 0.151537i
\(323\) 0 0
\(324\) −0.707107 0.707107i −0.707107 0.707107i
\(325\) 0 0
\(326\) −0.0238449 0.485375i −0.0238449 0.485375i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 1.75380 0.829484i 1.75380 0.829484i 0.773010 0.634393i \(-0.218750\pi\)
0.980785 0.195090i \(-0.0625000\pi\)
\(332\) 0 0
\(333\) −1.61518 + 0.968101i −1.61518 + 0.968101i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −1.51631 0.301614i −1.51631 0.301614i −0.634393 0.773010i \(-0.718750\pi\)
−0.881921 + 0.471397i \(0.843750\pi\)
\(338\) 0.707107 0.707107i 0.707107 0.707107i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −0.881921 0.471397i −0.881921 0.471397i
\(344\) 1.33962 1.21416i 1.33962 1.21416i
\(345\) 0 0
\(346\) 0 0
\(347\) 1.15569 + 1.55827i 1.15569 + 1.55827i 0.773010 + 0.634393i \(0.218750\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(348\) 0 0
\(349\) 0 0 0.941544 0.336890i \(-0.109375\pi\)
−0.941544 + 0.336890i \(0.890625\pi\)
\(350\) 0.471397 0.881921i 0.471397 0.881921i
\(351\) 0 0
\(352\) −0.284666 0.0713052i −0.284666 0.0713052i
\(353\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) −0.163715 0.653587i −0.163715 0.653587i
\(359\) 1.36347 0.728789i 1.36347 0.728789i 0.382683 0.923880i \(-0.375000\pi\)
0.980785 + 0.195090i \(0.0625000\pi\)
\(360\) 0 0
\(361\) −0.956940 + 0.290285i −0.956940 + 0.290285i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 −0.555570 0.831470i \(-0.687500\pi\)
0.555570 + 0.831470i \(0.312500\pi\)
\(368\) 0.151537 0.124363i 0.151537 0.124363i
\(369\) 0 0
\(370\) 0 0
\(371\) 1.30287 + 0.326351i 1.30287 + 0.326351i
\(372\) 0 0
\(373\) −0.666487 + 1.86271i −0.666487 + 1.86271i −0.195090 + 0.980785i \(0.562500\pi\)
−0.471397 + 0.881921i \(0.656250\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −1.15203 0.690501i −1.15203 0.690501i −0.195090 0.980785i \(-0.562500\pi\)
−0.956940 + 0.290285i \(0.906250\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −1.68789 + 0.902197i −1.68789 + 0.902197i
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −0.938254 1.75535i −0.938254 1.75535i
\(387\) −1.80580 0.0887133i −1.80580 0.0887133i
\(388\) 0 0
\(389\) 1.55075 + 0.929487i 1.55075 + 0.929487i 0.995185 + 0.0980171i \(0.0312500\pi\)
0.555570 + 0.831470i \(0.312500\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.773010 0.634393i −0.773010 0.634393i
\(393\) 0 0
\(394\) 0.854080 + 0.0419583i 0.854080 + 0.0419583i
\(395\) 0 0
\(396\) 0.150869 + 0.251710i 0.150869 + 0.251710i
\(397\) 0 0 −0.970031 0.242980i \(-0.921875\pi\)
0.970031 + 0.242980i \(0.0781250\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.634393 0.773010i 0.634393 0.773010i
\(401\) −0.858923 1.28547i −0.858923 1.28547i −0.956940 0.290285i \(-0.906250\pi\)
0.0980171 0.995185i \(-0.468750\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 1.69689 0.251710i 1.69689 0.251710i
\(407\) 0.528818 0.160415i 0.528818 0.160415i
\(408\) 0 0
\(409\) 0 0 0.881921 0.471397i \(-0.156250\pi\)
−0.881921 + 0.471397i \(0.843750\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) −0.195090 0.0192147i −0.195090 0.0192147i
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 0.941544 0.336890i \(-0.109375\pi\)
−0.941544 + 0.336890i \(0.890625\pi\)
\(420\) 0 0
\(421\) −0.289486 0.390327i −0.289486 0.390327i 0.634393 0.773010i \(-0.281250\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(422\) 0.612501 + 0.825862i 0.612501 + 0.825862i
\(423\) 0 0
\(424\) 1.21416 + 0.574257i 1.21416 + 0.574257i
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 1.43749 0.360073i 1.43749 0.360073i
\(429\) 0 0
\(430\) 0 0
\(431\) 0.750661 + 0.149316i 0.750661 + 0.149316i 0.555570 0.831470i \(-0.312500\pi\)
0.195090 + 0.980785i \(0.437500\pi\)
\(432\) 0 0
\(433\) 0 0 0.980785 0.195090i \(-0.0625000\pi\)
−0.980785 + 0.195090i \(0.937500\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −1.45218 0.686831i −1.45218 0.686831i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 −0.634393 0.773010i \(-0.718750\pi\)
0.634393 + 0.773010i \(0.281250\pi\)
\(440\) 0 0
\(441\) 0.0980171 + 0.995185i 0.0980171 + 0.995185i
\(442\) 0 0
\(443\) −1.82665 + 0.457553i −1.82665 + 0.457553i −0.995185 0.0980171i \(-0.968750\pi\)
−0.831470 + 0.555570i \(0.812500\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) −0.634393 0.773010i −0.634393 0.773010i
\(449\) −0.275899 + 0.275899i −0.275899 + 0.275899i −0.831470 0.555570i \(-0.812500\pi\)
0.555570 + 0.831470i \(0.312500\pi\)
\(450\) −0.995185 + 0.0980171i −0.995185 + 0.0980171i
\(451\) 0 0
\(452\) −1.17221 + 0.485544i −1.17221 + 0.485544i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −1.28547 + 1.05496i −1.28547 + 1.05496i −0.290285 + 0.956940i \(0.593750\pi\)
−0.995185 + 0.0980171i \(0.968750\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 −0.514103 0.857729i \(-0.671875\pi\)
0.514103 + 0.857729i \(0.328125\pi\)
\(462\) 0 0
\(463\) 0.301614 + 1.51631i 0.301614 + 1.51631i 0.773010 + 0.634393i \(0.218750\pi\)
−0.471397 + 0.881921i \(0.656250\pi\)
\(464\) 1.71339 + 0.0841735i 1.71339 + 0.0841735i
\(465\) 0 0
\(466\) 1.76384 1.76384
\(467\) 0 0 0.595699 0.803208i \(-0.296875\pi\)
−0.595699 + 0.803208i \(0.703125\pi\)
\(468\) 0 0
\(469\) −1.99518 + 0.0980171i −1.99518 + 0.0980171i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0.507725 + 0.154017i 0.507725 + 0.154017i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −0.452483 1.26460i −0.452483 1.26460i
\(478\) −0.482726 1.59133i −0.482726 1.59133i
\(479\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0.265286 + 0.874529i 0.265286 + 0.874529i
\(485\) 0 0
\(486\) 0 0
\(487\) 0.444430 + 0.831470i 0.444430 + 0.831470i 1.00000 \(0\)
−0.555570 + 0.831470i \(0.687500\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 0.0727135 + 0.0659037i 0.0727135 + 0.0659037i 0.707107 0.707107i \(-0.250000\pi\)
−0.634393 + 0.773010i \(0.718750\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 1.63099 + 1.08979i 1.63099 + 1.08979i
\(498\) 0 0
\(499\) −0.0238449 + 0.0951944i −0.0238449 + 0.0951944i −0.980785 0.195090i \(-0.937500\pi\)
0.956940 + 0.290285i \(0.0937500\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 −0.995185 0.0980171i \(-0.968750\pi\)
0.995185 + 0.0980171i \(0.0312500\pi\)
\(504\) −0.0980171 + 0.995185i −0.0980171 + 0.995185i
\(505\) 0 0
\(506\) 0.0541655 + 0.0193807i 0.0541655 + 0.0193807i
\(507\) 0 0
\(508\) 0.617317 0.923880i 0.617317 0.923880i
\(509\) 0 0 0.0490677 0.998795i \(-0.484375\pi\)
−0.0490677 + 0.998795i \(0.515625\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.471397 0.881921i −0.471397 0.881921i
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 1.77301 + 0.634393i 1.77301 + 0.634393i
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 −0.995185 0.0980171i \(-0.968750\pi\)
0.995185 + 0.0980171i \(0.0312500\pi\)
\(522\) −1.15203 1.27107i −1.15203 1.27107i
\(523\) 0 0 −0.941544 0.336890i \(-0.890625\pi\)
0.941544 + 0.336890i \(0.109375\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) −1.02656 1.53636i −1.02656 1.53636i
\(527\) 0 0
\(528\) 0 0
\(529\) 0.799517 0.534220i 0.799517 0.534220i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) −1.97597 0.293107i −1.97597 0.293107i
\(537\) 0 0
\(538\) 0 0
\(539\) 0.0430597 0.290285i 0.0430597 0.290285i
\(540\) 0 0
\(541\) 0.633595 1.33962i 0.633595 1.33962i −0.290285 0.956940i \(-0.593750\pi\)
0.923880 0.382683i \(-0.125000\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0.346392 + 0.968101i 0.346392 + 0.968101i 0.980785 + 0.195090i \(0.0625000\pi\)
−0.634393 + 0.773010i \(0.718750\pi\)
\(548\) 0.598102 0.728789i 0.598102 0.728789i
\(549\) 0 0
\(550\) 0.290285 + 0.0430597i 0.290285 + 0.0430597i
\(551\) 0 0
\(552\) 0 0
\(553\) −0.831470 + 1.55557i −0.831470 + 1.55557i
\(554\) −1.02190 + 0.612501i −1.02190 + 0.612501i
\(555\) 0 0
\(556\) 0 0
\(557\) −0.709715 + 0.956940i −0.709715 + 0.956940i 0.290285 + 0.956940i \(0.406250\pi\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −0.569414 + 0.113263i −0.569414 + 0.113263i
\(563\) 0 0 −0.514103 0.857729i \(-0.671875\pi\)
0.514103 + 0.857729i \(0.328125\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0.773010 0.634393i 0.773010 0.634393i
\(568\) 1.38704 + 1.38704i 1.38704 + 1.38704i
\(569\) 1.10579 0.108911i 1.10579 0.108911i 0.471397 0.881921i \(-0.343750\pi\)
0.634393 + 0.773010i \(0.281250\pi\)
\(570\) 0 0
\(571\) 0.416822 + 1.66405i 0.416822 + 1.66405i 0.707107 + 0.707107i \(0.250000\pi\)
−0.290285 + 0.956940i \(0.593750\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −0.138617 + 0.138617i −0.138617 + 0.138617i
\(576\) −0.290285 + 0.956940i −0.290285 + 0.956940i
\(577\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(578\) 0.773010 + 0.634393i 0.773010 + 0.634393i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0.0386337 + 0.392255i 0.0386337 + 0.392255i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 0.903989 0.427555i \(-0.140625\pi\)
−0.903989 + 0.427555i \(0.859375\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 1.61518 + 0.968101i 1.61518 + 0.968101i
\(593\) 0 0 −0.980785 0.195090i \(-0.937500\pi\)
0.980785 + 0.195090i \(0.0625000\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0.0951944 0.0238449i 0.0951944 0.0238449i
\(597\) 0 0
\(598\) 0 0
\(599\) −1.62958 0.871028i −1.62958 0.871028i −0.995185 0.0980171i \(-0.968750\pi\)
−0.634393 0.773010i \(-0.718750\pi\)
\(600\) 0 0
\(601\) 0 0 0.290285 0.956940i \(-0.406250\pi\)
−0.290285 + 0.956940i \(0.593750\pi\)
\(602\) 1.07701 + 1.45218i 1.07701 + 1.45218i
\(603\) 1.18996 + 1.60448i 1.18996 + 1.60448i
\(604\) −0.555570 0.168530i −0.555570 0.168530i
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 1.91906 + 0.284666i 1.91906 + 0.284666i 0.995185 0.0980171i \(-0.0312500\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0.0988640 0.276306i 0.0988640 0.276306i
\(617\) 1.59133 0.482726i 1.59133 0.482726i 0.634393 0.773010i \(-0.281250\pi\)
0.956940 + 0.290285i \(0.0937500\pi\)
\(618\) 0 0
\(619\) 0 0 0.671559 0.740951i \(-0.265625\pi\)
−0.671559 + 0.740951i \(0.734375\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.555570 + 0.831470i −0.555570 + 0.831470i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) −0.0382444 + 0.388302i −0.0382444 + 0.388302i 0.956940 + 0.290285i \(0.0937500\pi\)
−0.995185 + 0.0980171i \(0.968750\pi\)
\(632\) −1.11897 + 1.36347i −1.11897 + 1.36347i
\(633\) 0 0
\(634\) −0.207775 0.439303i −0.207775 0.439303i
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0.237310 + 0.443977i 0.237310 + 0.443977i
\(639\) 1.96157i 1.96157i
\(640\) 0 0
\(641\) 1.99037i 1.99037i 0.0980171 + 0.995185i \(0.468750\pi\)
−0.0980171 + 0.995185i \(0.531250\pi\)
\(642\) 0 0
\(643\) 0 0 −0.998795 0.0490677i \(-0.984375\pi\)
0.998795 + 0.0490677i \(0.0156250\pi\)
\(644\) 0.108911 + 0.162997i 0.108911 + 0.162997i
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 −0.773010 0.634393i \(-0.781250\pi\)
0.773010 + 0.634393i \(0.218750\pi\)
\(648\) 0.881921 0.471397i 0.881921 0.471397i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0.471397 + 0.118079i 0.471397 + 0.118079i
\(653\) 1.91906 + 0.480701i 1.91906 + 0.480701i 0.995185 + 0.0980171i \(0.0312500\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 1.58903 0.235710i 1.58903 0.235710i 0.707107 0.707107i \(-0.250000\pi\)
0.881921 + 0.471397i \(0.156250\pi\)
\(660\) 0 0
\(661\) 0 0 0.671559 0.740951i \(-0.265625\pi\)
−0.671559 + 0.740951i \(0.734375\pi\)
\(662\) 0.284666 + 1.91906i 0.284666 + 1.91906i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) −0.457553 1.82665i −0.457553 1.82665i
\(667\) −0.332649 0.0493438i −0.332649 0.0493438i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0.360480 + 0.149316i 0.360480 + 0.149316i 0.555570 0.831470i \(-0.312500\pi\)
−0.195090 + 0.980785i \(0.562500\pi\)
\(674\) 0.728789 1.36347i 0.728789 1.36347i
\(675\) 0 0
\(676\) 0.471397 + 0.881921i 0.471397 + 0.881921i
\(677\) 0 0 −0.595699 0.803208i \(-0.703125\pi\)
0.595699 + 0.803208i \(0.296875\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0.0330608 + 0.672968i 0.0330608 + 0.672968i 0.956940 + 0.290285i \(0.0937500\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0.707107 0.707107i 0.707107 0.707107i
\(687\) 0 0
\(688\) 0.773010 + 1.63439i 0.773010 + 1.63439i
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 0.857729 0.514103i \(-0.171875\pi\)
−0.857729 + 0.514103i \(0.828125\pi\)
\(692\) 0 0
\(693\) −0.265286 + 0.125471i −0.265286 + 0.125471i
\(694\) −1.82665 + 0.653587i −1.82665 + 0.653587i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(701\) −0.574257 0.633595i −0.574257 0.633595i 0.382683 0.923880i \(-0.375000\pi\)
−0.956940 + 0.290285i \(0.906250\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0.150869 0.251710i 0.150869 0.251710i
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 0.480701 + 1.91906i 0.480701 + 1.91906i 0.382683 + 0.923880i \(0.375000\pi\)
0.0980171 + 0.995185i \(0.468750\pi\)
\(710\) 0 0
\(711\) 1.75535 0.172887i 1.75535 0.172887i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0.672968 + 0.0330608i 0.672968 + 0.0330608i
\(717\) 0 0
\(718\) 0.301614 + 1.51631i 0.301614 + 1.51631i
\(719\) 0 0 −0.195090 0.980785i \(-0.562500\pi\)
0.195090 + 0.980785i \(0.437500\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 1.00000i 1.00000i
\(723\) 0 0
\(724\) 0 0
\(725\) −1.71339 + 0.0841735i −1.71339 + 0.0841735i
\(726\) 0 0
\(727\) 0 0 0.471397 0.881921i \(-0.343750\pi\)
−0.471397 + 0.881921i \(0.656250\pi\)
\(728\) 0 0
\(729\) −0.956940 0.290285i −0.956940 0.290285i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 −0.336890 0.941544i \(-0.609375\pi\)
0.336890 + 0.941544i \(0.390625\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0.0750191 + 0.181112i 0.0750191 + 0.181112i
\(737\) −0.224335 0.541592i −0.224335 0.541592i
\(738\) 0 0
\(739\) 0.509389 1.07701i 0.509389 1.07701i −0.471397 0.881921i \(-0.656250\pi\)
0.980785 0.195090i \(-0.0625000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −0.690501 + 1.15203i −0.690501 + 1.15203i
\(743\) −0.902197 1.68789i −0.902197 1.68789i −0.707107 0.707107i \(-0.750000\pi\)
−0.195090 0.980785i \(-0.562500\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −1.58903 1.17850i −1.58903 1.17850i
\(747\) 0 0
\(748\) 0 0
\(749\) 0.217440 + 1.46586i 0.217440 + 1.46586i
\(750\) 0 0
\(751\) 0.324423 0.216773i 0.324423 0.216773i −0.382683 0.923880i \(-0.625000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 1.39528 + 0.499238i 1.39528 + 0.499238i 0.923880 0.382683i \(-0.125000\pi\)
0.471397 + 0.881921i \(0.343750\pi\)
\(758\) 0.995185 0.901983i 0.995185 0.901983i
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 0.634393 0.773010i \(-0.281250\pi\)
−0.634393 + 0.773010i \(0.718750\pi\)
\(762\) 0 0
\(763\) 0.825862 1.37787i 0.825862 1.37787i
\(764\) −0.373380 1.87711i −0.373380 1.87711i
\(765\) 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
\(772\) 1.95213 0.388302i 1.95213 0.388302i
\(773\) 0 0 0.514103 0.857729i \(-0.328125\pi\)
−0.514103 + 0.857729i \(0.671875\pi\)
\(774\) 0.609090 1.70229i 0.609090 1.70229i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) −1.33962 + 1.21416i −1.33962 + 1.21416i
\(779\) 0 0
\(780\) 0 0
\(781\) −0.139870 + 0.558393i −0.139870 + 0.558393i
\(782\) 0 0
\(783\) 0 0
\(784\) 0.831470 0.555570i 0.831470 0.555570i
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 −0.146730 0.989177i \(-0.546875\pi\)
0.146730 + 0.989177i \(0.453125\pi\)
\(788\) −0.288078 + 0.805124i −0.288078 + 0.805124i
\(789\) 0 0
\(790\) 0 0
\(791\) −0.368309 1.21415i −0.368309 1.21415i
\(792\) −0.284666 + 0.0713052i −0.284666 + 0.0713052i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 0.427555 0.903989i \(-0.359375\pi\)
−0.427555 + 0.903989i \(0.640625\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0.555570 + 0.831470i 0.555570 + 0.831470i
\(801\)