Properties

Label 1008.2.s.r.289.1
Level $1008$
Weight $2$
Character 1008.289
Analytic conductor $8.049$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.s (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.04892052375\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-19})\)
Defining polynomial: \( x^{4} - x^{3} - 4x^{2} - 5x + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 168)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 289.1
Root \(-1.63746 + 1.52274i\) of defining polynomial
Character \(\chi\) \(=\) 1008.289
Dual form 1008.2.s.r.865.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.13746 + 3.70219i) q^{5} +(1.50000 + 2.17945i) q^{7} +O(q^{10})\) \(q+(-2.13746 + 3.70219i) q^{5} +(1.50000 + 2.17945i) q^{7} +(2.13746 + 3.70219i) q^{11} -1.27492 q^{13} +(-2.00000 - 3.46410i) q^{17} +(0.637459 - 1.10411i) q^{19} +(-2.00000 + 3.46410i) q^{23} +(-6.63746 - 11.4964i) q^{25} +2.27492 q^{29} +(-0.500000 - 0.866025i) q^{31} +(-11.2749 + 0.894797i) q^{35} +(-2.63746 + 4.56821i) q^{37} -10.5498 q^{41} +7.27492 q^{43} +(3.00000 - 5.19615i) q^{47} +(-2.50000 + 6.53835i) q^{49} +(0.862541 + 1.49397i) q^{53} -18.2749 q^{55} +(-3.13746 - 5.43424i) q^{59} +(-5.00000 + 8.66025i) q^{61} +(2.72508 - 4.71998i) q^{65} +(3.63746 + 6.30026i) q^{67} +2.00000 q^{71} +(-1.63746 - 2.83616i) q^{73} +(-4.86254 + 10.2118i) q^{77} +(-1.77492 + 3.07425i) q^{79} -0.274917 q^{83} +17.0997 q^{85} +(2.27492 - 3.94027i) q^{89} +(-1.91238 - 2.77862i) q^{91} +(2.72508 + 4.71998i) q^{95} +16.2749 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - q^{5} + 6 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - q^{5} + 6 q^{7} + q^{11} + 10 q^{13} - 8 q^{17} - 5 q^{19} - 8 q^{23} - 19 q^{25} - 6 q^{29} - 2 q^{31} - 30 q^{35} - 3 q^{37} - 12 q^{41} + 14 q^{43} + 12 q^{47} - 10 q^{49} + 11 q^{53} - 58 q^{55} - 5 q^{59} - 20 q^{61} + 26 q^{65} + 7 q^{67} + 8 q^{71} + q^{73} - 27 q^{77} + 8 q^{79} + 14 q^{83} + 8 q^{85} - 6 q^{89} + 15 q^{91} + 26 q^{95} + 50 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −2.13746 + 3.70219i −0.955901 + 1.65567i −0.223607 + 0.974679i \(0.571783\pi\)
−0.732294 + 0.680989i \(0.761550\pi\)
\(6\) 0 0
\(7\) 1.50000 + 2.17945i 0.566947 + 0.823754i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 2.13746 + 3.70219i 0.644468 + 1.11625i 0.984424 + 0.175810i \(0.0562545\pi\)
−0.339956 + 0.940441i \(0.610412\pi\)
\(12\) 0 0
\(13\) −1.27492 −0.353598 −0.176799 0.984247i \(-0.556574\pi\)
−0.176799 + 0.984247i \(0.556574\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −2.00000 3.46410i −0.485071 0.840168i 0.514782 0.857321i \(-0.327873\pi\)
−0.999853 + 0.0171533i \(0.994540\pi\)
\(18\) 0 0
\(19\) 0.637459 1.10411i 0.146243 0.253300i −0.783593 0.621275i \(-0.786615\pi\)
0.929836 + 0.367974i \(0.119949\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.00000 + 3.46410i −0.417029 + 0.722315i −0.995639 0.0932891i \(-0.970262\pi\)
0.578610 + 0.815604i \(0.303595\pi\)
\(24\) 0 0
\(25\) −6.63746 11.4964i −1.32749 2.29928i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 2.27492 0.422442 0.211221 0.977438i \(-0.432256\pi\)
0.211221 + 0.977438i \(0.432256\pi\)
\(30\) 0 0
\(31\) −0.500000 0.866025i −0.0898027 0.155543i 0.817625 0.575751i \(-0.195290\pi\)
−0.907428 + 0.420208i \(0.861957\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −11.2749 + 0.894797i −1.90581 + 0.151248i
\(36\) 0 0
\(37\) −2.63746 + 4.56821i −0.433596 + 0.751009i −0.997180 0.0750491i \(-0.976089\pi\)
0.563584 + 0.826059i \(0.309422\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −10.5498 −1.64761 −0.823804 0.566875i \(-0.808152\pi\)
−0.823804 + 0.566875i \(0.808152\pi\)
\(42\) 0 0
\(43\) 7.27492 1.10941 0.554707 0.832046i \(-0.312830\pi\)
0.554707 + 0.832046i \(0.312830\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 3.00000 5.19615i 0.437595 0.757937i −0.559908 0.828554i \(-0.689164\pi\)
0.997503 + 0.0706177i \(0.0224970\pi\)
\(48\) 0 0
\(49\) −2.50000 + 6.53835i −0.357143 + 0.934050i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0.862541 + 1.49397i 0.118479 + 0.205212i 0.919165 0.393872i \(-0.128865\pi\)
−0.800686 + 0.599084i \(0.795531\pi\)
\(54\) 0 0
\(55\) −18.2749 −2.46419
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −3.13746 5.43424i −0.408462 0.707477i 0.586255 0.810126i \(-0.300602\pi\)
−0.994718 + 0.102649i \(0.967268\pi\)
\(60\) 0 0
\(61\) −5.00000 + 8.66025i −0.640184 + 1.10883i 0.345207 + 0.938527i \(0.387809\pi\)
−0.985391 + 0.170305i \(0.945525\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 2.72508 4.71998i 0.338005 0.585442i
\(66\) 0 0
\(67\) 3.63746 + 6.30026i 0.444386 + 0.769700i 0.998009 0.0630678i \(-0.0200884\pi\)
−0.553623 + 0.832767i \(0.686755\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 2.00000 0.237356 0.118678 0.992933i \(-0.462134\pi\)
0.118678 + 0.992933i \(0.462134\pi\)
\(72\) 0 0
\(73\) −1.63746 2.83616i −0.191650 0.331948i 0.754147 0.656705i \(-0.228051\pi\)
−0.945797 + 0.324758i \(0.894717\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −4.86254 + 10.2118i −0.554138 + 1.16374i
\(78\) 0 0
\(79\) −1.77492 + 3.07425i −0.199694 + 0.345880i −0.948429 0.316989i \(-0.897328\pi\)
0.748735 + 0.662869i \(0.230661\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −0.274917 −0.0301761 −0.0150880 0.999886i \(-0.504803\pi\)
−0.0150880 + 0.999886i \(0.504803\pi\)
\(84\) 0 0
\(85\) 17.0997 1.85472
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 2.27492 3.94027i 0.241141 0.417668i −0.719899 0.694079i \(-0.755812\pi\)
0.961040 + 0.276411i \(0.0891451\pi\)
\(90\) 0 0
\(91\) −1.91238 2.77862i −0.200471 0.291278i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 2.72508 + 4.71998i 0.279588 + 0.484260i
\(96\) 0 0
\(97\) 16.2749 1.65247 0.826234 0.563327i \(-0.190479\pi\)
0.826234 + 0.563327i \(0.190479\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −3.00000 5.19615i −0.298511 0.517036i 0.677284 0.735721i \(-0.263157\pi\)
−0.975796 + 0.218685i \(0.929823\pi\)
\(102\) 0 0
\(103\) −5.91238 + 10.2405i −0.582564 + 1.00903i 0.412611 + 0.910907i \(0.364617\pi\)
−0.995174 + 0.0981224i \(0.968716\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −3.41238 + 5.91041i −0.329887 + 0.571381i −0.982489 0.186320i \(-0.940344\pi\)
0.652602 + 0.757701i \(0.273677\pi\)
\(108\) 0 0
\(109\) 2.91238 + 5.04438i 0.278955 + 0.483164i 0.971125 0.238570i \(-0.0766786\pi\)
−0.692170 + 0.721734i \(0.743345\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −10.5498 −0.992445 −0.496222 0.868195i \(-0.665280\pi\)
−0.496222 + 0.868195i \(0.665280\pi\)
\(114\) 0 0
\(115\) −8.54983 14.8087i −0.797276 1.38092i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 4.54983 9.55505i 0.417083 0.875910i
\(120\) 0 0
\(121\) −3.63746 + 6.30026i −0.330678 + 0.572751i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 35.3746 3.16400
\(126\) 0 0
\(127\) 21.5498 1.91224 0.956119 0.292978i \(-0.0946462\pi\)
0.956119 + 0.292978i \(0.0946462\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0.137459 0.238085i 0.0120098 0.0208016i −0.859958 0.510365i \(-0.829510\pi\)
0.871968 + 0.489563i \(0.162844\pi\)
\(132\) 0 0
\(133\) 3.36254 0.266857i 0.291569 0.0231395i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 8.27492 + 14.3326i 0.706974 + 1.22451i 0.965974 + 0.258638i \(0.0832735\pi\)
−0.259001 + 0.965877i \(0.583393\pi\)
\(138\) 0 0
\(139\) −0.725083 −0.0615007 −0.0307504 0.999527i \(-0.509790\pi\)
−0.0307504 + 0.999527i \(0.509790\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −2.72508 4.71998i −0.227883 0.394705i
\(144\) 0 0
\(145\) −4.86254 + 8.42217i −0.403812 + 0.699423i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 0.274917 0.476171i 0.0225221 0.0390094i −0.854545 0.519378i \(-0.826164\pi\)
0.877067 + 0.480368i \(0.159497\pi\)
\(150\) 0 0
\(151\) −7.68729 13.3148i −0.625583 1.08354i −0.988428 0.151692i \(-0.951528\pi\)
0.362845 0.931850i \(-0.381806\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 4.27492 0.343370
\(156\) 0 0
\(157\) −7.27492 12.6005i −0.580602 1.00563i −0.995408 0.0957218i \(-0.969484\pi\)
0.414807 0.909910i \(-0.363849\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −10.5498 + 0.837253i −0.831443 + 0.0659848i
\(162\) 0 0
\(163\) −6.00000 + 10.3923i −0.469956 + 0.813988i −0.999410 0.0343508i \(-0.989064\pi\)
0.529454 + 0.848339i \(0.322397\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −6.00000 −0.464294 −0.232147 0.972681i \(-0.574575\pi\)
−0.232147 + 0.972681i \(0.574575\pi\)
\(168\) 0 0
\(169\) −11.3746 −0.874968
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −3.72508 + 6.45203i −0.283213 + 0.490539i −0.972174 0.234259i \(-0.924734\pi\)
0.688961 + 0.724798i \(0.258067\pi\)
\(174\) 0 0
\(175\) 15.0997 31.7106i 1.14143 2.39710i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0.725083 + 1.25588i 0.0541952 + 0.0938689i 0.891850 0.452331i \(-0.149407\pi\)
−0.837655 + 0.546200i \(0.816074\pi\)
\(180\) 0 0
\(181\) 3.82475 0.284292 0.142146 0.989846i \(-0.454600\pi\)
0.142146 + 0.989846i \(0.454600\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −11.2749 19.5287i −0.828948 1.43578i
\(186\) 0 0
\(187\) 8.54983 14.8087i 0.625226 1.08292i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 5.27492 9.13642i 0.381680 0.661088i −0.609623 0.792692i \(-0.708679\pi\)
0.991302 + 0.131603i \(0.0420124\pi\)
\(192\) 0 0
\(193\) −7.77492 13.4666i −0.559651 0.969344i −0.997525 0.0703075i \(-0.977602\pi\)
0.437875 0.899036i \(-0.355731\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 16.5498 1.17913 0.589563 0.807722i \(-0.299300\pi\)
0.589563 + 0.807722i \(0.299300\pi\)
\(198\) 0 0
\(199\) 12.5498 + 21.7370i 0.889634 + 1.54089i 0.840308 + 0.542109i \(0.182374\pi\)
0.0493259 + 0.998783i \(0.484293\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 3.41238 + 4.95807i 0.239502 + 0.347988i
\(204\) 0 0
\(205\) 22.5498 39.0575i 1.57495 2.72789i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 5.45017 0.376996
\(210\) 0 0
\(211\) −17.6495 −1.21504 −0.607521 0.794304i \(-0.707836\pi\)
−0.607521 + 0.794304i \(0.707836\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −15.5498 + 26.9331i −1.06049 + 1.83682i
\(216\) 0 0
\(217\) 1.13746 2.38876i 0.0772157 0.162160i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 2.54983 + 4.41644i 0.171520 + 0.297082i
\(222\) 0 0
\(223\) −6.27492 −0.420200 −0.210100 0.977680i \(-0.567379\pi\)
−0.210100 + 0.977680i \(0.567379\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1.86254 + 3.22602i 0.123621 + 0.214118i 0.921193 0.389106i \(-0.127216\pi\)
−0.797572 + 0.603224i \(0.793883\pi\)
\(228\) 0 0
\(229\) −5.36254 + 9.28819i −0.354367 + 0.613781i −0.987009 0.160663i \(-0.948637\pi\)
0.632643 + 0.774444i \(0.281970\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 7.27492 12.6005i 0.476596 0.825488i −0.523045 0.852305i \(-0.675204\pi\)
0.999640 + 0.0268173i \(0.00853725\pi\)
\(234\) 0 0
\(235\) 12.8248 + 22.2131i 0.836595 + 1.44902i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 30.5498 1.97610 0.988052 0.154119i \(-0.0492540\pi\)
0.988052 + 0.154119i \(0.0492540\pi\)
\(240\) 0 0
\(241\) 6.41238 + 11.1066i 0.413057 + 0.715436i 0.995222 0.0976343i \(-0.0311275\pi\)
−0.582165 + 0.813071i \(0.697794\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −18.8625 23.2309i −1.20508 1.48417i
\(246\) 0 0
\(247\) −0.812707 + 1.40765i −0.0517113 + 0.0895666i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 19.3746 1.22291 0.611457 0.791278i \(-0.290584\pi\)
0.611457 + 0.791278i \(0.290584\pi\)
\(252\) 0 0
\(253\) −17.0997 −1.07505
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −9.54983 + 16.5408i −0.595702 + 1.03179i 0.397745 + 0.917496i \(0.369793\pi\)
−0.993447 + 0.114291i \(0.963540\pi\)
\(258\) 0 0
\(259\) −13.9124 + 1.10411i −0.864473 + 0.0686061i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 12.2749 + 21.2608i 0.756904 + 1.31100i 0.944422 + 0.328735i \(0.106622\pi\)
−0.187518 + 0.982261i \(0.560044\pi\)
\(264\) 0 0
\(265\) −7.37459 −0.453017
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 14.1375 + 24.4868i 0.861976 + 1.49299i 0.870019 + 0.493019i \(0.164107\pi\)
−0.00804266 + 0.999968i \(0.502560\pi\)
\(270\) 0 0
\(271\) −3.13746 + 5.43424i −0.190587 + 0.330106i −0.945445 0.325782i \(-0.894372\pi\)
0.754858 + 0.655888i \(0.227706\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 28.3746 49.1462i 1.71105 2.96363i
\(276\) 0 0
\(277\) 2.08762 + 3.61587i 0.125433 + 0.217257i 0.921902 0.387423i \(-0.126635\pi\)
−0.796469 + 0.604679i \(0.793301\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 11.4502 0.683060 0.341530 0.939871i \(-0.389055\pi\)
0.341530 + 0.939871i \(0.389055\pi\)
\(282\) 0 0
\(283\) 13.4622 + 23.3172i 0.800245 + 1.38607i 0.919454 + 0.393196i \(0.128631\pi\)
−0.119209 + 0.992869i \(0.538036\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −15.8248 22.9928i −0.934106 1.35722i
\(288\) 0 0
\(289\) 0.500000 0.866025i 0.0294118 0.0509427i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 5.17525 0.302341 0.151171 0.988508i \(-0.451696\pi\)
0.151171 + 0.988508i \(0.451696\pi\)
\(294\) 0 0
\(295\) 26.8248 1.56180
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 2.54983 4.41644i 0.147461 0.255409i
\(300\) 0 0
\(301\) 10.9124 + 15.8553i 0.628979 + 0.913885i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −21.3746 37.0219i −1.22391 2.11987i
\(306\) 0 0
\(307\) 26.3746 1.50528 0.752639 0.658434i \(-0.228781\pi\)
0.752639 + 0.658434i \(0.228781\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −5.27492 9.13642i −0.299113 0.518079i 0.676820 0.736148i \(-0.263357\pi\)
−0.975933 + 0.218069i \(0.930024\pi\)
\(312\) 0 0
\(313\) 2.22508 3.85396i 0.125769 0.217838i −0.796264 0.604949i \(-0.793193\pi\)
0.922033 + 0.387111i \(0.126527\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2.58762 + 4.48190i −0.145335 + 0.251728i −0.929498 0.368827i \(-0.879759\pi\)
0.784163 + 0.620555i \(0.213093\pi\)
\(318\) 0 0
\(319\) 4.86254 + 8.42217i 0.272250 + 0.471551i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −5.09967 −0.283753
\(324\) 0 0
\(325\) 8.46221 + 14.6570i 0.469399 + 0.813023i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 15.8248 1.25588i 0.872447 0.0692389i
\(330\) 0 0
\(331\) 11.9124 20.6328i 0.654763 1.13408i −0.327190 0.944959i \(-0.606102\pi\)
0.981953 0.189125i \(-0.0605651\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −31.0997 −1.69916
\(336\) 0 0
\(337\) 6.09967 0.332270 0.166135 0.986103i \(-0.446871\pi\)
0.166135 + 0.986103i \(0.446871\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 2.13746 3.70219i 0.115750 0.200485i
\(342\) 0 0
\(343\) −18.0000 + 4.35890i −0.971909 + 0.235358i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 15.0997 + 26.1534i 0.810593 + 1.40399i 0.912450 + 0.409189i \(0.134188\pi\)
−0.101857 + 0.994799i \(0.532478\pi\)
\(348\) 0 0
\(349\) −6.00000 −0.321173 −0.160586 0.987022i \(-0.551338\pi\)
−0.160586 + 0.987022i \(0.551338\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −2.72508 4.71998i −0.145042 0.251219i 0.784347 0.620322i \(-0.212998\pi\)
−0.929388 + 0.369103i \(0.879665\pi\)
\(354\) 0 0
\(355\) −4.27492 + 7.40437i −0.226889 + 0.392983i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −12.8248 + 22.2131i −0.676865 + 1.17236i 0.299056 + 0.954236i \(0.403328\pi\)
−0.975920 + 0.218128i \(0.930005\pi\)
\(360\) 0 0
\(361\) 8.68729 + 15.0468i 0.457226 + 0.791939i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 14.0000 0.732793
\(366\) 0 0
\(367\) −4.04983 7.01452i −0.211400 0.366155i 0.740753 0.671777i \(-0.234469\pi\)
−0.952153 + 0.305622i \(0.901135\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −1.96221 + 4.12081i −0.101873 + 0.213942i
\(372\) 0 0
\(373\) −0.637459 + 1.10411i −0.0330064 + 0.0571687i −0.882057 0.471143i \(-0.843841\pi\)
0.849050 + 0.528312i \(0.177175\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −2.90033 −0.149375
\(378\) 0 0
\(379\) −35.8248 −1.84019 −0.920097 0.391691i \(-0.871890\pi\)
−0.920097 + 0.391691i \(0.871890\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 2.27492 3.94027i 0.116243 0.201339i −0.802033 0.597280i \(-0.796248\pi\)
0.918276 + 0.395941i \(0.129582\pi\)
\(384\) 0 0
\(385\) −27.4124 39.8293i −1.39706 2.02989i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −1.00000 1.73205i −0.0507020 0.0878185i 0.839561 0.543266i \(-0.182813\pi\)
−0.890263 + 0.455448i \(0.849479\pi\)
\(390\) 0 0
\(391\) 16.0000 0.809155
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −7.58762 13.1422i −0.381775 0.661253i
\(396\) 0 0
\(397\) −17.1873 + 29.7693i −0.862606 + 1.49408i 0.00679974 + 0.999977i \(0.497836\pi\)
−0.869405 + 0.494100i \(0.835498\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 12.0000 20.7846i 0.599251 1.03793i −0.393680 0.919247i \(-0.628798\pi\)
0.992932 0.118686i \(-0.0378683\pi\)
\(402\) 0 0
\(403\) 0.637459 + 1.10411i 0.0317541 + 0.0549997i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −22.5498 −1.11775
\(408\) 0 0
\(409\) −12.7749 22.1268i −0.631679 1.09410i −0.987208 0.159435i \(-0.949033\pi\)
0.355529 0.934665i \(-0.384301\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 7.13746 14.9893i 0.351211 0.737575i
\(414\) 0 0
\(415\) 0.587624 1.01779i 0.0288453 0.0499616i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 13.4502 0.657084 0.328542 0.944489i \(-0.393443\pi\)
0.328542 + 0.944489i \(0.393443\pi\)
\(420\) 0 0
\(421\) −13.8248 −0.673777 −0.336889 0.941545i \(-0.609375\pi\)
−0.336889 + 0.941545i \(0.609375\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −26.5498 + 45.9857i −1.28786 + 2.23063i
\(426\) 0 0
\(427\) −26.3746 + 2.09313i −1.27636 + 0.101294i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −13.8248 23.9452i −0.665915 1.15340i −0.979036 0.203685i \(-0.934708\pi\)
0.313122 0.949713i \(-0.398625\pi\)
\(432\) 0 0
\(433\) 25.8248 1.24106 0.620529 0.784183i \(-0.286918\pi\)
0.620529 + 0.784183i \(0.286918\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2.54983 + 4.41644i 0.121975 + 0.211267i
\(438\) 0 0
\(439\) 4.86254 8.42217i 0.232076 0.401968i −0.726343 0.687333i \(-0.758781\pi\)
0.958419 + 0.285365i \(0.0921147\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −15.6873 + 27.1712i −0.745326 + 1.29094i 0.204717 + 0.978821i \(0.434373\pi\)
−0.950042 + 0.312121i \(0.898961\pi\)
\(444\) 0 0
\(445\) 9.72508 + 16.8443i 0.461013 + 0.798498i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −5.45017 −0.257209 −0.128605 0.991696i \(-0.541050\pi\)
−0.128605 + 0.991696i \(0.541050\pi\)
\(450\) 0 0
\(451\) −22.5498 39.0575i −1.06183 1.83914i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 14.3746 1.14079i 0.673891 0.0534812i
\(456\) 0 0
\(457\) 4.32475 7.49069i 0.202303 0.350400i −0.746967 0.664861i \(-0.768491\pi\)
0.949270 + 0.314462i \(0.101824\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −41.6495 −1.93981 −0.969905 0.243482i \(-0.921710\pi\)
−0.969905 + 0.243482i \(0.921710\pi\)
\(462\) 0 0
\(463\) −35.8248 −1.66492 −0.832459 0.554087i \(-0.813067\pi\)
−0.832459 + 0.554087i \(0.813067\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −12.7251 + 22.0405i −0.588847 + 1.01991i 0.405537 + 0.914079i \(0.367084\pi\)
−0.994384 + 0.105834i \(0.966249\pi\)
\(468\) 0 0
\(469\) −8.27492 + 17.3781i −0.382100 + 0.802444i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 15.5498 + 26.9331i 0.714982 + 1.23839i
\(474\) 0 0
\(475\) −16.9244 −0.776546
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 10.2749 + 17.7967i 0.469473 + 0.813151i 0.999391 0.0348979i \(-0.0111106\pi\)
−0.529918 + 0.848049i \(0.677777\pi\)
\(480\) 0 0
\(481\) 3.36254 5.82409i 0.153319 0.265556i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −34.7870 + 60.2528i −1.57959 + 2.73594i
\(486\) 0 0
\(487\) 0.500000 + 0.866025i 0.0226572 + 0.0392434i 0.877132 0.480250i \(-0.159454\pi\)
−0.854475 + 0.519493i \(0.826121\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −15.9244 −0.718659 −0.359330 0.933211i \(-0.616995\pi\)
−0.359330 + 0.933211i \(0.616995\pi\)
\(492\) 0 0
\(493\) −4.54983 7.88054i −0.204914 0.354922i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 3.00000 + 4.35890i 0.134568 + 0.195523i
\(498\) 0 0
\(499\) 12.3625 21.4125i 0.553423 0.958557i −0.444601 0.895729i \(-0.646655\pi\)
0.998024 0.0628286i \(-0.0200122\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 7.64950 0.341074 0.170537 0.985351i \(-0.445450\pi\)
0.170537 + 0.985351i \(0.445450\pi\)
\(504\) 0 0
\(505\) 25.6495 1.14139
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −1.86254 + 3.22602i −0.0825557 + 0.142991i −0.904347 0.426798i \(-0.859642\pi\)
0.821791 + 0.569789i \(0.192975\pi\)
\(510\) 0 0
\(511\) 3.72508 7.82300i 0.164788 0.346069i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −25.2749 43.7774i −1.11375 1.92906i
\(516\) 0 0
\(517\) 25.6495 1.12806
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0.274917 + 0.476171i 0.0120443 + 0.0208614i 0.871985 0.489533i \(-0.162833\pi\)
−0.859940 + 0.510394i \(0.829499\pi\)
\(522\) 0 0
\(523\) −12.6375 + 21.8887i −0.552597 + 0.957127i 0.445489 + 0.895288i \(0.353030\pi\)
−0.998086 + 0.0618393i \(0.980303\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −2.00000 + 3.46410i −0.0871214 + 0.150899i
\(528\) 0 0
\(529\) 3.50000 + 6.06218i 0.152174 + 0.263573i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 13.4502 0.582591
\(534\) 0 0
\(535\) −14.5876 25.2665i −0.630678 1.09237i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −29.5498 + 4.71998i −1.27280 + 0.203304i
\(540\) 0 0
\(541\) 0.362541 0.627940i 0.0155869 0.0269973i −0.858127 0.513438i \(-0.828372\pi\)
0.873714 + 0.486441i \(0.161705\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −24.9003 −1.06661
\(546\) 0 0
\(547\) 28.0000 1.19719 0.598597 0.801050i \(-0.295725\pi\)
0.598597 + 0.801050i \(0.295725\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 1.45017 2.51176i 0.0617791 0.107005i
\(552\) 0 0
\(553\) −9.36254 + 0.743028i −0.398136 + 0.0315968i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −3.58762 6.21395i −0.152013 0.263293i 0.779955 0.625836i \(-0.215242\pi\)
−0.931967 + 0.362543i \(0.881909\pi\)
\(558\) 0 0
\(559\) −9.27492 −0.392287
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −3.86254 6.69012i −0.162787 0.281955i 0.773080 0.634308i \(-0.218715\pi\)
−0.935867 + 0.352353i \(0.885382\pi\)
\(564\) 0 0
\(565\) 22.5498 39.0575i 0.948679 1.64316i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 13.2749 22.9928i 0.556513 0.963910i −0.441271 0.897374i \(-0.645472\pi\)
0.997784 0.0665355i \(-0.0211946\pi\)
\(570\) 0 0
\(571\) 0.362541 + 0.627940i 0.0151719 + 0.0262785i 0.873512 0.486803i \(-0.161837\pi\)
−0.858340 + 0.513082i \(0.828504\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 53.0997 2.21441
\(576\) 0 0
\(577\) 12.5000 + 21.6506i 0.520382 + 0.901328i 0.999719 + 0.0236970i \(0.00754370\pi\)
−0.479337 + 0.877631i \(0.659123\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −0.412376 0.599168i −0.0171082 0.0248577i
\(582\) 0 0
\(583\) −3.68729 + 6.38658i −0.152712 + 0.264505i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1.72508 0.0712018 0.0356009 0.999366i \(-0.488665\pi\)
0.0356009 + 0.999366i \(0.488665\pi\)
\(588\) 0 0
\(589\) −1.27492 −0.0525320
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 7.27492 12.6005i 0.298745 0.517442i −0.677104 0.735887i \(-0.736765\pi\)
0.975849 + 0.218446i \(0.0700986\pi\)
\(594\) 0 0
\(595\) 25.6495 + 37.2679i 1.05153 + 1.52783i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −3.72508 6.45203i −0.152203 0.263623i 0.779834 0.625986i \(-0.215303\pi\)
−0.932037 + 0.362363i \(0.881970\pi\)
\(600\) 0 0
\(601\) −26.0997 −1.06463 −0.532314 0.846547i \(-0.678677\pi\)
−0.532314 + 0.846547i \(0.678677\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −15.5498 26.9331i −0.632191 1.09499i
\(606\) 0 0
\(607\) −3.50000 + 6.06218i −0.142061 + 0.246056i −0.928272 0.371901i \(-0.878706\pi\)
0.786212 + 0.617957i \(0.212039\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −3.82475 + 6.62466i −0.154733 + 0.268005i
\(612\) 0 0
\(613\) −3.27492 5.67232i −0.132273 0.229103i 0.792280 0.610158i \(-0.208894\pi\)
−0.924552 + 0.381055i \(0.875561\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 6.00000 0.241551 0.120775 0.992680i \(-0.461462\pi\)
0.120775 + 0.992680i \(0.461462\pi\)
\(618\) 0 0
\(619\) 3.08762 + 5.34792i 0.124102 + 0.214951i 0.921382 0.388659i \(-0.127062\pi\)
−0.797280 + 0.603610i \(0.793728\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 12.0000 0.952341i 0.480770 0.0381547i
\(624\) 0 0
\(625\) −42.4244 + 73.4813i −1.69698 + 2.93925i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 21.0997 0.841299
\(630\) 0 0
\(631\) 2.82475 0.112452 0.0562258 0.998418i \(-0.482093\pi\)
0.0562258 + 0.998418i \(0.482093\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −46.0619 + 79.7815i −1.82791 + 3.16603i
\(636\) 0 0
\(637\) 3.18729 8.33585i 0.126285 0.330279i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 20.8248 + 36.0695i 0.822528 + 1.42466i 0.903794 + 0.427968i \(0.140770\pi\)
−0.0812655 + 0.996692i \(0.525896\pi\)
\(642\) 0 0
\(643\) 32.3746 1.27673 0.638365 0.769734i \(-0.279611\pi\)
0.638365 + 0.769734i \(0.279611\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 17.0000 + 29.4449i 0.668339 + 1.15760i 0.978368 + 0.206870i \(0.0663277\pi\)
−0.310029 + 0.950727i \(0.600339\pi\)
\(648\) 0 0
\(649\) 13.4124 23.2309i 0.526482 0.911893i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 22.9622 39.7717i 0.898581 1.55639i 0.0692713 0.997598i \(-0.477933\pi\)
0.829309 0.558790i \(-0.188734\pi\)
\(654\) 0 0
\(655\) 0.587624 + 1.01779i 0.0229604 + 0.0397685i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 18.1993 0.708946 0.354473 0.935066i \(-0.384660\pi\)
0.354473 + 0.935066i \(0.384660\pi\)
\(660\) 0 0
\(661\) −14.9124 25.8290i −0.580024 1.00463i −0.995476 0.0950161i \(-0.969710\pi\)
0.415452 0.909615i \(-0.363624\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −6.19934 + 13.0192i −0.240400 + 0.504861i
\(666\) 0 0
\(667\) −4.54983 + 7.88054i −0.176170 + 0.305136i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −42.7492 −1.65031
\(672\) 0 0
\(673\) 26.4502 1.01958 0.509789 0.860299i \(-0.329723\pi\)
0.509789 + 0.860299i \(0.329723\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −2.86254 + 4.95807i −0.110016 + 0.190554i −0.915777 0.401688i \(-0.868424\pi\)
0.805760 + 0.592242i \(0.201757\pi\)
\(678\) 0 0
\(679\) 24.4124 + 35.4704i 0.936861 + 1.36123i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −17.4124 30.1591i −0.666266 1.15401i −0.978940 0.204146i \(-0.934558\pi\)
0.312674 0.949860i \(-0.398775\pi\)
\(684\) 0 0
\(685\) −70.7492 −2.70319
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −1.09967 1.90468i −0.0418940 0.0725626i
\(690\) 0 0
\(691\) 5.91238 10.2405i 0.224917 0.389568i −0.731377 0.681973i \(-0.761122\pi\)
0.956295 + 0.292405i \(0.0944554\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1.54983 2.68439i 0.0587886 0.101825i
\(696\) 0 0
\(697\) 21.0997 + 36.5457i 0.799207 + 1.38427i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −39.9244 −1.50792 −0.753962 0.656918i \(-0.771860\pi\)
−0.753962 + 0.656918i \(0.771860\pi\)
\(702\) 0 0
\(703\) 3.36254 + 5.82409i 0.126821 + 0.219660i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 6.82475 14.3326i 0.256671 0.539032i
\(708\) 0 0
\(709\) −16.0997 + 27.8854i −0.604636 + 1.04726i 0.387473 + 0.921881i \(0.373348\pi\)
−0.992109 + 0.125379i \(0.959985\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 4.00000 0.149801
\(714\) 0 0
\(715\) 23.2990 0.871333
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 16.0997 27.8854i 0.600416 1.03995i −0.392342 0.919820i \(-0.628335\pi\)
0.992758 0.120132i \(-0.0383318\pi\)
\(720\) 0 0
\(721\) −31.1873 + 2.47508i −1.16148 + 0.0921767i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −15.0997 26.1534i −0.560788 0.971313i
\(726\) 0 0
\(727\) −16.4502 −0.610103 −0.305051 0.952336i \(-0.598674\pi\)
−0.305051 + 0.952336i \(0.598674\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −14.5498 25.2011i −0.538145 0.932095i
\(732\) 0 0
\(733\) 23.4622 40.6377i 0.866597 1.50099i 0.00114334 0.999999i \(-0.499636\pi\)
0.865453 0.500990i \(-0.167031\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −15.5498 + 26.9331i −0.572786 + 0.992094i
\(738\) 0 0
\(739\) −18.1873 31.5013i −0.669030 1.15879i −0.978176 0.207780i \(-0.933376\pi\)
0.309145 0.951015i \(-0.399957\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 16.1993 0.594296 0.297148 0.954831i \(-0.403965\pi\)
0.297148 + 0.954831i \(0.403965\pi\)
\(744\) 0 0
\(745\) 1.17525 + 2.03559i 0.0430578 + 0.0745782i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −18.0000 + 1.42851i −0.657706 + 0.0521967i
\(750\) 0 0
\(751\) −12.7749 + 22.1268i −0.466163 + 0.807419i −0.999253 0.0386400i \(-0.987697\pi\)
0.533090 + 0.846059i \(0.321031\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 65.7251 2.39198
\(756\) 0 0
\(757\) −22.0000 −0.799604 −0.399802 0.916602i \(-0.630921\pi\)
−0.399802 + 0.916602i \(0.630921\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 2.54983 4.41644i 0.0924314 0.160096i −0.816102 0.577907i \(-0.803869\pi\)
0.908534 + 0.417812i \(0.137203\pi\)
\(762\) 0 0
\(763\) −6.62541 + 13.9140i −0.239856 + 0.503719i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 4.00000 + 6.92820i 0.144432 + 0.250163i
\(768\) 0 0
\(769\) 12.6495 0.456153 0.228076 0.973643i \(-0.426756\pi\)
0.228076 + 0.973643i \(0.426756\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −13.5498 23.4690i −0.487354 0.844121i 0.512541 0.858663i \(-0.328704\pi\)
−0.999894 + 0.0145417i \(0.995371\pi\)
\(774\) 0 0
\(775\) −6.63746 + 11.4964i −0.238425 + 0.412963i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −6.72508 + 11.6482i −0.240951 + 0.417340i
\(780\) 0 0
\(781\) 4.27492 + 7.40437i 0.152969 + 0.264949i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 62.1993 2.21999
\(786\) 0 0
\(787\) −6.27492 10.8685i −0.223677 0.387419i 0.732245 0.681041i \(-0.238473\pi\)
−0.955922 + 0.293622i \(0.905139\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −15.8248 22.9928i −0.562663 0.817531i
\(792\) 0 0
\(793\) 6.37459 11.0411i 0.226368 0.392081i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −36.4743 −1.29198 −0.645992 0.763344i \(-0.723556\pi\)
−0.645992 + 0.763344i \(0.723556\pi\)
\(798\) 0 0
\(799\) −24.0000 −0.849059
\(800\) 0 0
\(801\) 0 0