Properties

Label 1792.1.bt.a.1749.1
Level $1792$
Weight $1$
Character 1792.1749
Analytic conductor $0.894$
Analytic rank $0$
Dimension $32$
Projective image $D_{64}$
CM discriminant -7
Inner twists $4$

Related objects

Downloads

Learn more

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 1749.1
Root \(0.773010 + 0.634393i\) of defining polynomial
Character \(\chi\) \(=\) 1792.1749
Dual form 1792.1.bt.a.125.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.471397 + 0.881921i) q^{2} +(-0.555570 - 0.831470i) q^{4} +(-0.0980171 + 0.995185i) q^{7} +(0.995185 - 0.0980171i) q^{8} +(-0.634393 + 0.773010i) q^{9} +O(q^{10})\) \(q+(-0.471397 + 0.881921i) q^{2} +(-0.555570 - 0.831470i) q^{4} +(-0.0980171 + 0.995185i) q^{7} +(0.995185 - 0.0980171i) q^{8} +(-0.634393 + 0.773010i) q^{9} +(-1.93773 - 0.0951944i) q^{11} +(-0.831470 - 0.555570i) q^{14} +(-0.382683 + 0.923880i) q^{16} +(-0.382683 - 0.923880i) q^{18} +(0.997391 - 1.66405i) q^{22} +(-0.728789 - 1.36347i) q^{23} +(0.956940 - 0.290285i) q^{25} +(0.881921 - 0.471397i) q^{28} +(-0.217440 - 0.197076i) q^{29} +(-0.634393 - 0.773010i) q^{32} +(0.995185 + 0.0980171i) q^{36} +(-1.71339 + 1.02697i) q^{37} +(-1.21416 - 0.574257i) q^{43} +(0.997391 + 1.66405i) q^{44} +1.54602 q^{46} +(-0.980785 - 0.195090i) q^{49} +(-0.195090 + 0.980785i) q^{50} +(-0.499238 + 0.452483i) q^{53} +1.00000i q^{56} +(0.276306 - 0.0988640i) q^{58} +(-0.707107 - 0.707107i) q^{63} +(0.980785 - 0.195090i) q^{64} +(-0.609090 + 1.70229i) q^{67} +(-0.301614 + 0.247528i) q^{71} +(-0.555570 + 0.831470i) q^{72} +(-0.0980171 - 1.99518i) q^{74} +(0.284666 - 1.91906i) q^{77} +(-0.113263 + 0.569414i) q^{79} +(-0.195090 - 0.980785i) q^{81} +(1.07880 - 0.800094i) q^{86} +(-1.93773 + 0.0951944i) q^{88} +(-0.728789 + 1.36347i) q^{92} +(0.634393 - 0.773010i) q^{98} +(1.30287 - 1.43749i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + O(q^{10}) \) \( 32q + O(q^{100}) \)

Character values

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

\(n\) \(1023\) \(1025\) \(1541\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{61}{64}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.471397 + 0.881921i −0.471397 + 0.881921i
\(3\) 0 0 −0.427555 0.903989i \(-0.640625\pi\)
0.427555 + 0.903989i \(0.359375\pi\)
\(4\) −0.555570 0.831470i −0.555570 0.831470i
\(5\) 0 0 0.989177 0.146730i \(-0.0468750\pi\)
−0.989177 + 0.146730i \(0.953125\pi\)
\(6\) 0 0
\(7\) −0.0980171 + 0.995185i −0.0980171 + 0.995185i
\(8\) 0.995185 0.0980171i 0.995185 0.0980171i
\(9\) −0.634393 + 0.773010i −0.634393 + 0.773010i
\(10\) 0 0
\(11\) −1.93773 0.0951944i −1.93773 0.0951944i −0.956940 0.290285i \(-0.906250\pi\)
−0.980785 + 0.195090i \(0.937500\pi\)
\(12\) 0 0
\(13\) 0 0 0.803208 0.595699i \(-0.203125\pi\)
−0.803208 + 0.595699i \(0.796875\pi\)
\(14\) −0.831470 0.555570i −0.831470 0.555570i
\(15\) 0 0
\(16\) −0.382683 + 0.923880i −0.382683 + 0.923880i
\(17\) 0 0 0.555570 0.831470i \(-0.312500\pi\)
−0.555570 + 0.831470i \(0.687500\pi\)
\(18\) −0.382683 0.923880i −0.382683 0.923880i
\(19\) 0 0 0.970031 0.242980i \(-0.0781250\pi\)
−0.970031 + 0.242980i \(0.921875\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0.997391 1.66405i 0.997391 1.66405i
\(23\) −0.728789 1.36347i −0.728789 1.36347i −0.923880 0.382683i \(-0.875000\pi\)
0.195090 0.980785i \(-0.437500\pi\)
\(24\) 0 0
\(25\) 0.956940 0.290285i 0.956940 0.290285i
\(26\) 0 0
\(27\) 0 0
\(28\) 0.881921 0.471397i 0.881921 0.471397i
\(29\) −0.217440 0.197076i −0.217440 0.197076i 0.555570 0.831470i \(-0.312500\pi\)
−0.773010 + 0.634393i \(0.781250\pi\)
\(30\) 0 0
\(31\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(32\) −0.634393 0.773010i −0.634393 0.773010i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0.995185 + 0.0980171i 0.995185 + 0.0980171i
\(37\) −1.71339 + 1.02697i −1.71339 + 1.02697i −0.831470 + 0.555570i \(0.812500\pi\)
−0.881921 + 0.471397i \(0.843750\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 −0.956940 0.290285i \(-0.906250\pi\)
0.956940 + 0.290285i \(0.0937500\pi\)
\(42\) 0 0
\(43\) −1.21416 0.574257i −1.21416 0.574257i −0.290285 0.956940i \(-0.593750\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(44\) 0.997391 + 1.66405i 0.997391 + 1.66405i
\(45\) 0 0
\(46\) 1.54602 1.54602
\(47\) 0 0 0.980785 0.195090i \(-0.0625000\pi\)
−0.980785 + 0.195090i \(0.937500\pi\)
\(48\) 0 0
\(49\) −0.980785 0.195090i −0.980785 0.195090i
\(50\) −0.195090 + 0.980785i −0.195090 + 0.980785i
\(51\) 0 0
\(52\) 0 0
\(53\) −0.499238 + 0.452483i −0.499238 + 0.452483i −0.881921 0.471397i \(-0.843750\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 1.00000i 1.00000i
\(57\) 0 0
\(58\) 0.276306 0.0988640i 0.276306 0.0988640i
\(59\) 0 0 −0.803208 0.595699i \(-0.796875\pi\)
0.803208 + 0.595699i \(0.203125\pi\)
\(60\) 0 0
\(61\) 0 0 −0.941544 0.336890i \(-0.890625\pi\)
0.941544 + 0.336890i \(0.109375\pi\)
\(62\) 0 0
\(63\) −0.707107 0.707107i −0.707107 0.707107i
\(64\) 0.980785 0.195090i 0.980785 0.195090i
\(65\) 0 0
\(66\) 0 0
\(67\) −0.609090 + 1.70229i −0.609090 + 1.70229i 0.0980171 + 0.995185i \(0.468750\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −0.301614 + 0.247528i −0.301614 + 0.247528i −0.773010 0.634393i \(-0.781250\pi\)
0.471397 + 0.881921i \(0.343750\pi\)
\(72\) −0.555570 + 0.831470i −0.555570 + 0.831470i
\(73\) 0 0 −0.0980171 0.995185i \(-0.531250\pi\)
0.0980171 + 0.995185i \(0.468750\pi\)
\(74\) −0.0980171 1.99518i −0.0980171 1.99518i
\(75\) 0 0
\(76\) 0 0
\(77\) 0.284666 1.91906i 0.284666 1.91906i
\(78\) 0 0
\(79\) −0.113263 + 0.569414i −0.113263 + 0.569414i 0.881921 + 0.471397i \(0.156250\pi\)
−0.995185 + 0.0980171i \(0.968750\pi\)
\(80\) 0 0
\(81\) −0.195090 0.980785i −0.195090 0.980785i
\(82\) 0 0
\(83\) 0 0 −0.857729 0.514103i \(-0.828125\pi\)
0.857729 + 0.514103i \(0.171875\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 1.07880 0.800094i 1.07880 0.800094i
\(87\) 0 0
\(88\) −1.93773 + 0.0951944i −1.93773 + 0.0951944i
\(89\) 0 0 0.471397 0.881921i \(-0.343750\pi\)
−0.471397 + 0.881921i \(0.656250\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −0.728789 + 1.36347i −0.728789 + 1.36347i
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(98\) 0.634393 0.773010i 0.634393 0.773010i
\(99\) 1.30287 1.43749i 1.30287 1.43749i
\(100\) −0.773010 0.634393i −0.773010 0.634393i
\(101\) 0 0 0.242980 0.970031i \(-0.421875\pi\)
−0.242980 + 0.970031i \(0.578125\pi\)
\(102\) 0 0
\(103\) 0 0 −0.290285 0.956940i \(-0.593750\pi\)
0.290285 + 0.956940i \(0.406250\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −0.163715 0.653587i −0.163715 0.653587i
\(107\) −0.634393 1.77301i −0.634393 1.77301i −0.634393 0.773010i \(-0.718750\pi\)
1.00000i \(-0.5\pi\)
\(108\) 0 0
\(109\) 0.416822 + 1.66405i 0.416822 + 1.66405i 0.707107 + 0.707107i \(0.250000\pi\)
−0.290285 + 0.956940i \(0.593750\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −0.881921 0.471397i −0.881921 0.471397i
\(113\) 0.162997 0.108911i 0.162997 0.108911i −0.471397 0.881921i \(-0.656250\pi\)
0.634393 + 0.773010i \(0.281250\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −0.0430597 + 0.290285i −0.0430597 + 0.290285i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 2.75053 + 0.270904i 2.75053 + 0.270904i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0.956940 0.290285i 0.956940 0.290285i
\(127\) 1.66294i 1.66294i 0.555570 + 0.831470i \(0.312500\pi\)
−0.555570 + 0.831470i \(0.687500\pi\)
\(128\) −0.290285 + 0.956940i −0.290285 + 0.956940i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 0.903989 0.427555i \(-0.140625\pi\)
−0.903989 + 0.427555i \(0.859375\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −1.21416 1.33962i −1.21416 1.33962i
\(135\) 0 0
\(136\) 0 0
\(137\) 1.47945 + 1.21415i 1.47945 + 1.21415i 0.923880 + 0.382683i \(0.125000\pi\)
0.555570 + 0.831470i \(0.312500\pi\)
\(138\) 0 0
\(139\) 0 0 0.0490677 0.998795i \(-0.484375\pi\)
−0.0490677 + 0.998795i \(0.515625\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −0.0761205 0.382683i −0.0761205 0.382683i
\(143\) 0 0
\(144\) −0.471397 0.881921i −0.471397 0.881921i
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 1.80580 + 0.854080i 1.80580 + 0.854080i
\(149\) −0.288078 0.805124i −0.288078 0.805124i −0.995185 0.0980171i \(-0.968750\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(150\) 0 0
\(151\) −0.831470 + 0.444430i −0.831470 + 0.444430i −0.831470 0.555570i \(-0.812500\pi\)
1.00000i \(0.5\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 1.55827 + 1.15569i 1.55827 + 1.15569i
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.671559 0.740951i \(-0.265625\pi\)
−0.671559 + 0.740951i \(0.734375\pi\)
\(158\) −0.448786 0.368309i −0.448786 0.368309i
\(159\) 0 0
\(160\) 0 0
\(161\) 1.42834 0.591637i 1.42834 0.591637i
\(162\) 0.956940 + 0.290285i 0.956940 + 0.290285i
\(163\) 1.60448 0.0788231i 1.60448 0.0788231i 0.773010 0.634393i \(-0.218750\pi\)
0.831470 + 0.555570i \(0.187500\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 0.471397 0.881921i \(-0.343750\pi\)
−0.471397 + 0.881921i \(0.656250\pi\)
\(168\) 0 0
\(169\) 0.290285 0.956940i 0.290285 0.956940i
\(170\) 0 0
\(171\) 0 0
\(172\) 0.197076 + 1.32858i 0.197076 + 1.32858i
\(173\) 0 0 −0.857729 0.514103i \(-0.828125\pi\)
0.857729 + 0.514103i \(0.171875\pi\)
\(174\) 0 0
\(175\) 0.195090 + 0.980785i 0.195090 + 0.980785i
\(176\) 0.829484 1.75380i 0.829484 1.75380i
\(177\) 0 0
\(178\) 0 0
\(179\) −0.0143994 + 0.0970732i −0.0143994 + 0.0970732i −0.995185 0.0980171i \(-0.968750\pi\)
0.980785 + 0.195090i \(0.0625000\pi\)
\(180\) 0 0
\(181\) 0 0 −0.671559 0.740951i \(-0.734375\pi\)
0.671559 + 0.740951i \(0.265625\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −0.858923 1.28547i −0.858923 1.28547i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1.24723 + 1.24723i −1.24723 + 1.24723i −0.290285 + 0.956940i \(0.593750\pi\)
−0.956940 + 0.290285i \(0.906250\pi\)
\(192\) 0 0
\(193\) −0.897168 0.897168i −0.897168 0.897168i 0.0980171 0.995185i \(-0.468750\pi\)
−0.995185 + 0.0980171i \(0.968750\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0.382683 + 0.923880i 0.382683 + 0.923880i
\(197\) 1.19028 + 0.882768i 1.19028 + 0.882768i 0.995185 0.0980171i \(-0.0312500\pi\)
0.195090 + 0.980785i \(0.437500\pi\)
\(198\) 0.653587 + 1.82665i 0.653587 + 1.82665i
\(199\) 0 0 −0.634393 0.773010i \(-0.718750\pi\)
0.634393 + 0.773010i \(0.281250\pi\)
\(200\) 0.923880 0.382683i 0.923880 0.382683i
\(201\) 0 0
\(202\) 0 0
\(203\) 0.217440 0.197076i 0.217440 0.197076i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 1.51631 + 0.301614i 1.51631 + 0.301614i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 1.01708 1.69689i 1.01708 1.69689i 0.382683 0.923880i \(-0.375000\pi\)
0.634393 0.773010i \(-0.281250\pi\)
\(212\) 0.653587 + 0.163715i 0.653587 + 0.163715i
\(213\) 0 0
\(214\) 1.86271 + 0.276306i 1.86271 + 0.276306i
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) −1.66405 0.416822i −1.66405 0.416822i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(224\) 0.831470 0.555570i 0.831470 0.555570i
\(225\) −0.382683 + 0.923880i −0.382683 + 0.923880i
\(226\) 0.0192147 + 0.195090i 0.0192147 + 0.195090i
\(227\) 0 0 −0.740951 0.671559i \(-0.765625\pi\)
0.740951 + 0.671559i \(0.234375\pi\)
\(228\) 0 0
\(229\) 0 0 −0.970031 0.242980i \(-0.921875\pi\)
0.970031 + 0.242980i \(0.0781250\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −0.235710 0.174814i −0.235710 0.174814i
\(233\) 0.273678 + 0.512016i 0.273678 + 0.512016i 0.980785 0.195090i \(-0.0625000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −0.617317 + 0.923880i −0.617317 + 0.923880i 0.382683 + 0.923880i \(0.375000\pi\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) 0 0 −0.555570 0.831470i \(-0.687500\pi\)
0.555570 + 0.831470i \(0.312500\pi\)
\(242\) −1.53551 + 2.29805i −1.53551 + 2.29805i
\(243\) 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 0.989177 0.146730i \(-0.0468750\pi\)
−0.989177 + 0.146730i \(0.953125\pi\)
\(252\) −0.195090 + 0.980785i −0.195090 + 0.980785i
\(253\) 1.28240 + 2.71140i 1.28240 + 2.71140i
\(254\) −1.46658 0.783904i −1.46658 0.783904i
\(255\) 0 0
\(256\) −0.707107 0.707107i −0.707107 0.707107i
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) −0.854080 1.80580i −0.854080 1.80580i
\(260\) 0 0
\(261\) 0.290285 0.0430597i 0.290285 0.0430597i
\(262\) 0 0
\(263\) −0.181112 + 1.83886i −0.181112 + 1.83886i 0.290285 + 0.956940i \(0.406250\pi\)
−0.471397 + 0.881921i \(0.656250\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 1.75380 0.439303i 1.75380 0.439303i
\(269\) 0 0 0.803208 0.595699i \(-0.203125\pi\)
−0.803208 + 0.595699i \(0.796875\pi\)
\(270\) 0 0
\(271\) 0 0 −0.555570 0.831470i \(-0.687500\pi\)
0.555570 + 0.831470i \(0.312500\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) −1.76820 + 0.732410i −1.76820 + 0.732410i
\(275\) −1.88192 + 0.471397i −1.88192 + 0.471397i
\(276\) 0 0
\(277\) −0.968101 + 0.346392i −0.968101 + 0.346392i −0.773010 0.634393i \(-0.781250\pi\)
−0.195090 + 0.980785i \(0.562500\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −0.902197 + 0.273678i −0.902197 + 0.273678i −0.707107 0.707107i \(-0.750000\pi\)
−0.195090 + 0.980785i \(0.562500\pi\)
\(282\) 0 0
\(283\) 0 0 −0.970031 0.242980i \(-0.921875\pi\)
0.970031 + 0.242980i \(0.0781250\pi\)
\(284\) 0.373380 + 0.113263i 0.373380 + 0.113263i
\(285\) 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 0.857729 0.514103i \(-0.171875\pi\)
−0.857729 + 0.514103i \(0.828125\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −1.60448 + 1.18996i −1.60448 + 1.18996i
\(297\) 0 0
\(298\) 0.845855 + 0.125471i 0.845855 + 0.125471i
\(299\) 0 0
\(300\) 0 0
\(301\) 0.690501 1.15203i 0.690501 1.15203i
\(302\) 0.942793i 0.942793i
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 −0.989177 0.146730i \(-0.953125\pi\)
0.989177 + 0.146730i \(0.0468750\pi\)
\(308\) −1.75380 + 0.829484i −1.75380 + 0.829484i
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.995185 0.0980171i \(-0.0312500\pi\)
−0.995185 + 0.0980171i \(0.968750\pi\)
\(312\) 0 0
\(313\) 0 0 −0.634393 0.773010i \(-0.718750\pi\)
0.634393 + 0.773010i \(0.281250\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0.536376 0.222174i 0.536376 0.222174i
\(317\) −1.51251 0.541185i −1.51251 0.541185i −0.555570 0.831470i \(-0.687500\pi\)
−0.956940 + 0.290285i \(0.906250\pi\)
\(318\) 0 0
\(319\) 0.402579 + 0.402579i 0.402579 + 0.402579i
\(320\) 0 0
\(321\) 0 0
\(322\) −0.151537 + 1.53858i −0.151537 + 1.53858i
\(323\) 0 0
\(324\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(325\) 0 0
\(326\) −0.686831 + 1.45218i −0.686831 + 1.45218i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0.800094 + 0.882768i 0.800094 + 0.882768i 0.995185 0.0980171i \(-0.0312500\pi\)
−0.195090 + 0.980785i \(0.562500\pi\)
\(332\) 0 0
\(333\) 0.293107 1.97597i 0.293107 1.97597i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0.388302 + 1.95213i 0.388302 + 1.95213i 0.290285 + 0.956940i \(0.406250\pi\)
0.0980171 + 0.995185i \(0.468750\pi\)
\(338\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0.290285 0.956940i 0.290285 0.956940i
\(344\) −1.26460 0.452483i −1.26460 0.452483i
\(345\) 0 0
\(346\) 0 0
\(347\) 0.612501 + 1.02190i 0.612501 + 1.02190i 0.995185 + 0.0980171i \(0.0312500\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(348\) 0 0
\(349\) 0 0 0.998795 0.0490677i \(-0.0156250\pi\)
−0.998795 + 0.0490677i \(0.984375\pi\)
\(350\) −0.956940 0.290285i −0.956940 0.290285i
\(351\) 0 0
\(352\) 1.15569 + 1.55827i 1.15569 + 1.55827i
\(353\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) −0.0788231 0.0584592i −0.0788231 0.0584592i
\(359\) −0.577774 1.90466i −0.577774 1.90466i −0.382683 0.923880i \(-0.625000\pi\)
−0.195090 0.980785i \(-0.562500\pi\)
\(360\) 0 0
\(361\) 0.881921 0.471397i 0.881921 0.471397i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 −0.831470 0.555570i \(-0.812500\pi\)
0.831470 + 0.555570i \(0.187500\pi\)
\(368\) 1.53858 0.151537i 1.53858 0.151537i
\(369\) 0 0
\(370\) 0 0
\(371\) −0.401370 0.541185i −0.401370 0.541185i
\(372\) 0 0
\(373\) −0.0238449 + 0.485375i −0.0238449 + 0.485375i 0.956940 + 0.290285i \(0.0937500\pi\)
−0.980785 + 0.195090i \(0.937500\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −0.0988640 0.666487i −0.0988640 0.666487i −0.980785 0.195090i \(-0.937500\pi\)
0.881921 0.471397i \(-0.156250\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −0.512016 1.68789i −0.512016 1.68789i
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 1.21415 0.368309i 1.21415 0.368309i
\(387\) 1.21416 0.574257i 1.21416 0.574257i
\(388\) 0 0
\(389\) −0.197076 1.32858i −0.197076 1.32858i −0.831470 0.555570i \(-0.812500\pi\)
0.634393 0.773010i \(-0.281250\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.995185 0.0980171i −0.995185 0.0980171i
\(393\) 0 0
\(394\) −1.33962 + 0.633595i −1.33962 + 0.633595i
\(395\) 0 0
\(396\) −1.91906 0.284666i −1.91906 0.284666i
\(397\) 0 0 −0.595699 0.803208i \(-0.703125\pi\)
0.595699 + 0.803208i \(0.296875\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.0980171 + 0.995185i −0.0980171 + 0.995185i
\(401\) 1.65493 + 1.10579i 1.65493 + 1.10579i 0.881921 + 0.471397i \(0.156250\pi\)
0.773010 + 0.634393i \(0.218750\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0.0713052 + 0.284666i 0.0713052 + 0.284666i
\(407\) 3.41784 1.82688i 3.41784 1.82688i
\(408\) 0 0
\(409\) 0 0 −0.290285 0.956940i \(-0.593750\pi\)
0.290285 + 0.956940i \(0.406250\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) −0.980785 + 1.19509i −0.980785 + 1.19509i
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 0.998795 0.0490677i \(-0.0156250\pi\)
−0.998795 + 0.0490677i \(0.984375\pi\)
\(420\) 0 0
\(421\) 0.825862 + 1.37787i 0.825862 + 1.37787i 0.923880 + 0.382683i \(0.125000\pi\)
−0.0980171 + 0.995185i \(0.531250\pi\)
\(422\) 1.01708 + 1.69689i 1.01708 + 1.69689i
\(423\) 0 0
\(424\) −0.452483 + 0.499238i −0.452483 + 0.499238i
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) −1.12175 + 1.51251i −1.12175 + 1.51251i
\(429\) 0 0
\(430\) 0 0
\(431\) 0.149316 + 0.750661i 0.149316 + 0.750661i 0.980785 + 0.195090i \(0.0625000\pi\)
−0.831470 + 0.555570i \(0.812500\pi\)
\(432\) 0 0
\(433\) 0 0 0.195090 0.980785i \(-0.437500\pi\)
−0.195090 + 0.980785i \(0.562500\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 1.15203 1.27107i 1.15203 1.27107i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 −0.0980171 0.995185i \(-0.531250\pi\)
0.0980171 + 0.995185i \(0.468750\pi\)
\(440\) 0 0
\(441\) 0.773010 0.634393i 0.773010 0.634393i
\(442\) 0 0
\(443\) −1.18996 + 1.60448i −1.18996 + 1.60448i −0.555570 + 0.831470i \(0.687500\pi\)
−0.634393 + 0.773010i \(0.718750\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0.0980171 + 0.995185i 0.0980171 + 0.995185i
\(449\) −1.38704 1.38704i −1.38704 1.38704i −0.831470 0.555570i \(-0.812500\pi\)
−0.555570 0.831470i \(-0.687500\pi\)
\(450\) −0.634393 0.773010i −0.634393 0.773010i
\(451\) 0 0
\(452\) −0.181112 0.0750191i −0.181112 0.0750191i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −1.10579 + 0.108911i −1.10579 + 0.108911i −0.634393 0.773010i \(-0.718750\pi\)
−0.471397 + 0.881921i \(0.656250\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 −0.989177 0.146730i \(-0.953125\pi\)
0.989177 + 0.146730i \(0.0468750\pi\)
\(462\) 0 0
\(463\) 1.95213 + 0.388302i 1.95213 + 0.388302i 0.995185 + 0.0980171i \(0.0312500\pi\)
0.956940 + 0.290285i \(0.0937500\pi\)
\(464\) 0.265286 0.125471i 0.265286 0.125471i
\(465\) 0 0
\(466\) −0.580569 −0.580569
\(467\) 0 0 0.514103 0.857729i \(-0.328125\pi\)
−0.514103 + 0.857729i \(0.671875\pi\)
\(468\) 0 0
\(469\) −1.63439 0.773010i −1.63439 0.773010i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 2.29805 + 1.22833i 2.29805 + 1.22833i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −0.0330608 0.672968i −0.0330608 0.672968i
\(478\) −0.523788 0.979938i −0.523788 0.979938i
\(479\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −1.30287 2.43749i −1.30287 2.43749i
\(485\) 0 0
\(486\) 0 0
\(487\) 1.83147 0.555570i 1.83147 0.555570i 0.831470 0.555570i \(-0.187500\pi\)
1.00000 \(0\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 0.805124 0.288078i 0.805124 0.288078i 0.0980171 0.995185i \(-0.468750\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −0.216773 0.324423i −0.216773 0.324423i
\(498\) 0 0
\(499\) −0.686831 + 0.509389i −0.686831 + 0.509389i −0.881921 0.471397i \(-0.843750\pi\)
0.195090 + 0.980785i \(0.437500\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 0.634393 0.773010i \(-0.281250\pi\)
−0.634393 + 0.773010i \(0.718750\pi\)
\(504\) −0.773010 0.634393i −0.773010 0.634393i
\(505\) 0 0
\(506\) −2.99576 0.147172i −2.99576 0.147172i
\(507\) 0 0
\(508\) 1.38268 0.923880i 1.38268 0.923880i
\(509\) 0 0 −0.427555 0.903989i \(-0.640625\pi\)
0.427555 + 0.903989i \(0.359375\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.956940 0.290285i 0.956940 0.290285i
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 1.99518 + 0.0980171i 1.99518 + 0.0980171i
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 0.634393 0.773010i \(-0.281250\pi\)
−0.634393 + 0.773010i \(0.718750\pi\)
\(522\) −0.0988640 + 0.276306i −0.0988640 + 0.276306i
\(523\) 0 0 −0.998795 0.0490677i \(-0.984375\pi\)
0.998795 + 0.0490677i \(0.0156250\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) −1.53636 1.02656i −1.53636 1.02656i
\(527\) 0 0
\(528\) 0 0
\(529\) −0.772343 + 1.15589i −0.772343 + 1.15589i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) −0.439303 + 1.75380i −0.439303 + 1.75380i
\(537\) 0 0
\(538\) 0 0
\(539\) 1.88192 + 0.471397i 1.88192 + 0.471397i
\(540\) 0 0
\(541\) −1.39528 1.26460i −1.39528 1.26460i −0.923880 0.382683i \(-0.875000\pi\)
−0.471397 0.881921i \(-0.656250\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −0.0970732 1.97597i −0.0970732 1.97597i −0.195090 0.980785i \(-0.562500\pi\)
0.0980171 0.995185i \(-0.468750\pi\)
\(548\) 0.187593 1.90466i 0.187593 1.90466i
\(549\) 0 0
\(550\) 0.471397 1.88192i 0.471397 1.88192i
\(551\) 0 0
\(552\) 0 0
\(553\) −0.555570 0.168530i −0.555570 0.168530i
\(554\) 0.150869 1.01708i 0.150869 1.01708i
\(555\) 0 0
\(556\) 0 0
\(557\) −0.528603 + 0.881921i −0.528603 + 0.881921i 0.471397 + 0.881921i \(0.343750\pi\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0.183930 0.924678i 0.183930 0.924678i
\(563\) 0 0 −0.989177 0.146730i \(-0.953125\pi\)
0.989177 + 0.146730i \(0.0468750\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0.995185 0.0980171i 0.995185 0.0980171i
\(568\) −0.275899 + 0.275899i −0.275899 + 0.275899i
\(569\) −1.05496 1.28547i −1.05496 1.28547i −0.956940 0.290285i \(-0.906250\pi\)
−0.0980171 0.995185i \(-0.531250\pi\)
\(570\) 0 0
\(571\) 0.235710 + 0.174814i 0.235710 + 0.174814i 0.707107 0.707107i \(-0.250000\pi\)
−0.471397 + 0.881921i \(0.656250\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1.09320 1.09320i −1.09320 1.09320i
\(576\) −0.471397 + 0.881921i −0.471397 + 0.881921i
\(577\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(578\) 0.995185 + 0.0980171i 0.995185 + 0.0980171i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 1.01046 0.829263i 1.01046 0.829263i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 −0.671559 0.740951i \(-0.734375\pi\)
0.671559 + 0.740951i \(0.265625\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −0.293107 1.97597i −0.293107 1.97597i
\(593\) 0 0 −0.195090 0.980785i \(-0.562500\pi\)
0.195090 + 0.980785i \(0.437500\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −0.509389 + 0.686831i −0.509389 + 0.686831i
\(597\) 0 0
\(598\) 0 0
\(599\) −0.536376 + 1.76820i −0.536376 + 1.76820i 0.0980171 + 0.995185i \(0.468750\pi\)
−0.634393 + 0.773010i \(0.718750\pi\)
\(600\) 0 0
\(601\) 0 0 0.471397 0.881921i \(-0.343750\pi\)
−0.471397 + 0.881921i \(0.656250\pi\)
\(602\) 0.690501 + 1.15203i 0.690501 + 1.15203i
\(603\) −0.929487 1.55075i −0.929487 1.55075i
\(604\) 0.831470 + 0.444430i 0.831470 + 0.444430i
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −0.289486 + 1.15569i −0.289486 + 1.15569i 0.634393 + 0.773010i \(0.281250\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0.0951944 1.93773i 0.0951944 1.93773i
\(617\) −0.979938 + 0.523788i −0.979938 + 0.523788i −0.881921 0.471397i \(-0.843750\pi\)
−0.0980171 + 0.995185i \(0.531250\pi\)
\(618\) 0 0
\(619\) 0 0 −0.336890 0.941544i \(-0.609375\pi\)
0.336890 + 0.941544i \(0.390625\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0.831470 0.555570i 0.831470 0.555570i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) −1.51631 1.24441i −1.51631 1.24441i −0.881921 0.471397i \(-0.843750\pi\)
−0.634393 0.773010i \(-0.718750\pi\)
\(632\) −0.0569057 + 0.577774i −0.0569057 + 0.577774i
\(633\) 0 0
\(634\) 1.19028 1.07880i 1.19028 1.07880i
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) −0.544817 + 0.165269i −0.544817 + 0.165269i
\(639\) 0.390181i 0.390181i
\(640\) 0 0
\(641\) 1.26879i 1.26879i −0.773010 0.634393i \(-0.781250\pi\)
0.773010 0.634393i \(-0.218750\pi\)
\(642\) 0 0
\(643\) 0 0 0.903989 0.427555i \(-0.140625\pi\)
−0.903989 + 0.427555i \(0.859375\pi\)
\(644\) −1.28547 0.858923i −1.28547 0.858923i
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 −0.995185 0.0980171i \(-0.968750\pi\)
0.995185 + 0.0980171i \(0.0312500\pi\)
\(648\) −0.290285 0.956940i −0.290285 0.956940i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −0.956940 1.29028i −0.956940 1.29028i
\(653\) −0.289486 0.390327i −0.289486 0.390327i 0.634393 0.773010i \(-0.281250\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0.416822 + 1.66405i 0.416822 + 1.66405i 0.707107 + 0.707107i \(0.250000\pi\)
−0.290285 + 0.956940i \(0.593750\pi\)
\(660\) 0 0
\(661\) 0 0 −0.336890 0.941544i \(-0.609375\pi\)
0.336890 + 0.941544i \(0.390625\pi\)
\(662\) −1.15569 + 0.289486i −1.15569 + 0.289486i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 1.60448 + 1.18996i 1.60448 + 1.18996i
\(667\) −0.110239 + 0.440100i −0.110239 + 0.440100i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −1.81225 + 0.750661i −1.81225 + 0.750661i −0.831470 + 0.555570i \(0.812500\pi\)
−0.980785 + 0.195090i \(0.937500\pi\)
\(674\) −1.90466 0.577774i −1.90466 0.577774i
\(675\) 0 0
\(676\) −0.956940 + 0.290285i −0.956940 + 0.290285i
\(677\) 0 0 −0.514103 0.857729i \(-0.671875\pi\)
0.514103 + 0.857729i \(0.328125\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0.0419583 0.0887133i 0.0419583 0.0887133i −0.881921 0.471397i \(-0.843750\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(687\) 0 0
\(688\) 0.995185 0.901983i 0.995185 0.901983i
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 0.146730 0.989177i \(-0.453125\pi\)
−0.146730 + 0.989177i \(0.546875\pi\)
\(692\) 0 0
\(693\) 1.30287 + 1.43749i 1.30287 + 1.43749i
\(694\) −1.18996 + 0.0584592i −1.18996 + 0.0584592i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0.707107 0.707107i 0.707107 0.707107i
\(701\) 0.499238 1.39528i 0.499238 1.39528i −0.382683 0.923880i \(-0.625000\pi\)
0.881921 0.471397i \(-0.156250\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −1.91906 + 0.284666i −1.91906 + 0.284666i
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 0.390327 + 0.289486i 0.390327 + 0.289486i 0.773010 0.634393i \(-0.218750\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(710\) 0 0
\(711\) −0.368309 0.448786i −0.368309 0.448786i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0.0887133 0.0419583i 0.0887133 0.0419583i
\(717\) 0 0
\(718\) 1.95213 + 0.388302i 1.95213 + 0.388302i
\(719\) 0 0 −0.980785 0.195090i \(-0.937500\pi\)
0.980785 + 0.195090i \(0.0625000\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 1.00000i 1.00000i
\(723\) 0 0
\(724\) 0 0
\(725\) −0.265286 0.125471i −0.265286 0.125471i
\(726\) 0 0
\(727\) 0 0 −0.956940 0.290285i \(-0.906250\pi\)
0.956940 + 0.290285i \(0.0937500\pi\)
\(728\) 0 0
\(729\) 0.881921 + 0.471397i 0.881921 + 0.471397i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 −0.0490677 0.998795i \(-0.515625\pi\)
0.0490677 + 0.998795i \(0.484375\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) −0.591637 + 1.42834i −0.591637 + 1.42834i
\(737\) 1.34230 3.24059i 1.34230 3.24059i
\(738\) 0 0
\(739\) 0.761850 + 0.690501i 0.761850 + 0.690501i 0.956940 0.290285i \(-0.0937500\pi\)
−0.195090 + 0.980785i \(0.562500\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0.666487 0.0988640i 0.666487 0.0988640i
\(743\) −1.68789 + 0.512016i −1.68789 + 0.512016i −0.980785 0.195090i \(-0.937500\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −0.416822 0.249834i −0.416822 0.249834i
\(747\) 0 0
\(748\) 0 0
\(749\) 1.82665 0.457553i 1.82665 0.457553i
\(750\) 0 0
\(751\) 1.08979 1.63099i 1.08979 1.63099i 0.382683 0.923880i \(-0.375000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −1.88082 0.0923988i −1.88082 0.0923988i −0.923880 0.382683i \(-0.875000\pi\)
−0.956940 + 0.290285i \(0.906250\pi\)
\(758\) 0.634393 + 0.226990i 0.634393 + 0.226990i
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 0.0980171 0.995185i \(-0.468750\pi\)
−0.0980171 + 0.995185i \(0.531250\pi\)
\(762\) 0 0
\(763\) −1.69689 + 0.251710i −1.69689 + 0.251710i
\(764\) 1.72995 + 0.344109i 1.72995 + 0.344109i
\(765\) 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
\(772\) −0.247528 + 1.24441i −0.247528 + 1.24441i
\(773\) 0 0 0.989177 0.146730i \(-0.0468750\pi\)
−0.989177 + 0.146730i \(0.953125\pi\)
\(774\) −0.0659037 + 1.34150i −0.0659037 + 1.34150i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 1.26460 + 0.452483i 1.26460 + 0.452483i
\(779\) 0 0
\(780\) 0 0
\(781\) 0.608008 0.450929i 0.608008 0.450929i
\(782\) 0 0
\(783\) 0 0
\(784\) 0.555570 0.831470i 0.555570 0.831470i
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 0.970031 0.242980i \(-0.0781250\pi\)
−0.970031 + 0.242980i \(0.921875\pi\)
\(788\) 0.0727135 1.48012i 0.0727135 1.48012i
\(789\) 0 0
\(790\) 0 0
\(791\) 0.0924099 + 0.172887i 0.0924099 + 0.172887i
\(792\) 1.15569 1.55827i 1.15569 1.55827i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 −0.740951 0.671559i \(-0.765625\pi\)
0.740951 + 0.671559i \(0.234375\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −0.831470 0.555570i −0.831470 0.555570i </