Properties

Label 768.3.h.g.641.3
Level $768$
Weight $3$
Character 768.641
Analytic conductor $20.926$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 768 = 2^{8} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 768.h (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(20.9264843029\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 4 x^{15} + 14 x^{14} - 28 x^{13} + 50 x^{12} - 104 x^{11} - 66 x^{10} + 640 x^{9} + 555 x^{8} - 7060 x^{7} + 17714 x^{6} - 25496 x^{5} + 24840 x^{4} - 17932 x^{3} + 11724 x^{2} - 7056 x + 2401\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{34}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 384)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 641.3
Root \(0.463678 - 1.11942i\) of defining polynomial
Character \(\chi\) \(=\) 768.641
Dual form 768.3.h.g.641.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.55118 - 1.57844i) q^{3} +1.31534 q^{5} +10.2329 q^{7} +(4.01705 + 8.05378i) q^{9} +O(q^{10})\) \(q+(-2.55118 - 1.57844i) q^{3} +1.31534 q^{5} +10.2329 q^{7} +(4.01705 + 8.05378i) q^{9} -16.6620 q^{11} +18.7454i q^{13} +(-3.35566 - 2.07618i) q^{15} -4.38114i q^{17} +11.5544i q^{19} +(-26.1059 - 16.1520i) q^{21} -16.7490i q^{23} -23.2699 q^{25} +(2.46419 - 26.8873i) q^{27} -12.5498 q^{29} -20.3167 q^{31} +(42.5079 + 26.3001i) q^{33} +13.4597 q^{35} +18.5778i q^{37} +(29.5885 - 47.8230i) q^{39} +78.6737i q^{41} -36.4860i q^{43} +(5.28377 + 10.5934i) q^{45} -19.9175i q^{47} +55.7118 q^{49} +(-6.91537 + 11.1771i) q^{51} -81.3064 q^{53} -21.9162 q^{55} +(18.2380 - 29.4775i) q^{57} -29.9477 q^{59} +72.0687i q^{61} +(41.1060 + 82.4133i) q^{63} +24.6565i q^{65} +56.3520i q^{67} +(-26.4374 + 42.7298i) q^{69} +136.465i q^{71} +80.8141 q^{73} +(59.3657 + 36.7301i) q^{75} -170.501 q^{77} -86.0317 q^{79} +(-48.7266 + 64.7048i) q^{81} +80.4263 q^{83} -5.76268i q^{85} +(32.0168 + 19.8091i) q^{87} +131.830i q^{89} +191.820i q^{91} +(51.8315 + 32.0687i) q^{93} +15.1980i q^{95} -20.4375 q^{97} +(-66.9323 - 134.192i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 16q^{7} + O(q^{10}) \) \( 16q - 16q^{7} + 32q^{15} + 80q^{25} - 112q^{31} + 16q^{33} + 208q^{39} + 144q^{49} - 384q^{55} + 80q^{57} + 528q^{63} + 160q^{73} - 816q^{79} + 144q^{81} + 736q^{87} + 192q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).

\(n\) \(257\) \(511\) \(517\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

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
\(3\) −2.55118 1.57844i −0.850394 0.526147i
\(4\) 0 0
\(5\) 1.31534 0.263067 0.131534 0.991312i \(-0.458010\pi\)
0.131534 + 0.991312i \(0.458010\pi\)
\(6\) 0 0
\(7\) 10.2329 1.46184 0.730920 0.682463i \(-0.239091\pi\)
0.730920 + 0.682463i \(0.239091\pi\)
\(8\) 0 0
\(9\) 4.01705 + 8.05378i 0.446339 + 0.894864i
\(10\) 0 0
\(11\) −16.6620 −1.51473 −0.757366 0.652991i \(-0.773514\pi\)
−0.757366 + 0.652991i \(0.773514\pi\)
\(12\) 0 0
\(13\) 18.7454i 1.44196i 0.692958 + 0.720978i \(0.256307\pi\)
−0.692958 + 0.720978i \(0.743693\pi\)
\(14\) 0 0
\(15\) −3.35566 2.07618i −0.223711 0.138412i
\(16\) 0 0
\(17\) 4.38114i 0.257714i −0.991663 0.128857i \(-0.958869\pi\)
0.991663 0.128857i \(-0.0411308\pi\)
\(18\) 0 0
\(19\) 11.5544i 0.608129i 0.952652 + 0.304064i \(0.0983438\pi\)
−0.952652 + 0.304064i \(0.901656\pi\)
\(20\) 0 0
\(21\) −26.1059 16.1520i −1.24314 0.769143i
\(22\) 0 0
\(23\) 16.7490i 0.728219i −0.931356 0.364109i \(-0.881373\pi\)
0.931356 0.364109i \(-0.118627\pi\)
\(24\) 0 0
\(25\) −23.2699 −0.930796
\(26\) 0 0
\(27\) 2.46419 26.8873i 0.0912663 0.995827i
\(28\) 0 0
\(29\) −12.5498 −0.432752 −0.216376 0.976310i \(-0.569424\pi\)
−0.216376 + 0.976310i \(0.569424\pi\)
\(30\) 0 0
\(31\) −20.3167 −0.655377 −0.327688 0.944786i \(-0.606270\pi\)
−0.327688 + 0.944786i \(0.606270\pi\)
\(32\) 0 0
\(33\) 42.5079 + 26.3001i 1.28812 + 0.796971i
\(34\) 0 0
\(35\) 13.4597 0.384562
\(36\) 0 0
\(37\) 18.5778i 0.502103i 0.967974 + 0.251052i \(0.0807764\pi\)
−0.967974 + 0.251052i \(0.919224\pi\)
\(38\) 0 0
\(39\) 29.5885 47.8230i 0.758681 1.22623i
\(40\) 0 0
\(41\) 78.6737i 1.91887i 0.281930 + 0.959435i \(0.409025\pi\)
−0.281930 + 0.959435i \(0.590975\pi\)
\(42\) 0 0
\(43\) 36.4860i 0.848511i −0.905543 0.424255i \(-0.860536\pi\)
0.905543 0.424255i \(-0.139464\pi\)
\(44\) 0 0
\(45\) 5.28377 + 10.5934i 0.117417 + 0.235410i
\(46\) 0 0
\(47\) 19.9175i 0.423777i −0.977294 0.211888i \(-0.932039\pi\)
0.977294 0.211888i \(-0.0679613\pi\)
\(48\) 0 0
\(49\) 55.7118 1.13698
\(50\) 0 0
\(51\) −6.91537 + 11.1771i −0.135596 + 0.219158i
\(52\) 0 0
\(53\) −81.3064 −1.53408 −0.767041 0.641598i \(-0.778272\pi\)
−0.767041 + 0.641598i \(0.778272\pi\)
\(54\) 0 0
\(55\) −21.9162 −0.398476
\(56\) 0 0
\(57\) 18.2380 29.4775i 0.319965 0.517149i
\(58\) 0 0
\(59\) −29.9477 −0.507589 −0.253794 0.967258i \(-0.581679\pi\)
−0.253794 + 0.967258i \(0.581679\pi\)
\(60\) 0 0
\(61\) 72.0687i 1.18145i 0.806872 + 0.590727i \(0.201159\pi\)
−0.806872 + 0.590727i \(0.798841\pi\)
\(62\) 0 0
\(63\) 41.1060 + 82.4133i 0.652476 + 1.30815i
\(64\) 0 0
\(65\) 24.6565i 0.379331i
\(66\) 0 0
\(67\) 56.3520i 0.841074i 0.907275 + 0.420537i \(0.138158\pi\)
−0.907275 + 0.420537i \(0.861842\pi\)
\(68\) 0 0
\(69\) −26.4374 + 42.7298i −0.383150 + 0.619273i
\(70\) 0 0
\(71\) 136.465i 1.92204i 0.276479 + 0.961020i \(0.410832\pi\)
−0.276479 + 0.961020i \(0.589168\pi\)
\(72\) 0 0
\(73\) 80.8141 1.10704 0.553521 0.832835i \(-0.313284\pi\)
0.553521 + 0.832835i \(0.313284\pi\)
\(74\) 0 0
\(75\) 59.3657 + 36.7301i 0.791543 + 0.489735i
\(76\) 0 0
\(77\) −170.501 −2.21429
\(78\) 0 0
\(79\) −86.0317 −1.08901 −0.544504 0.838758i \(-0.683282\pi\)
−0.544504 + 0.838758i \(0.683282\pi\)
\(80\) 0 0
\(81\) −48.7266 + 64.7048i −0.601563 + 0.798825i
\(82\) 0 0
\(83\) 80.4263 0.968992 0.484496 0.874793i \(-0.339003\pi\)
0.484496 + 0.874793i \(0.339003\pi\)
\(84\) 0 0
\(85\) 5.76268i 0.0677962i
\(86\) 0 0
\(87\) 32.0168 + 19.8091i 0.368009 + 0.227691i
\(88\) 0 0
\(89\) 131.830i 1.48124i 0.671923 + 0.740621i \(0.265468\pi\)
−0.671923 + 0.740621i \(0.734532\pi\)
\(90\) 0 0
\(91\) 191.820i 2.10791i
\(92\) 0 0
\(93\) 51.8315 + 32.0687i 0.557328 + 0.344824i
\(94\) 0 0
\(95\) 15.1980i 0.159979i
\(96\) 0 0
\(97\) −20.4375 −0.210696 −0.105348 0.994435i \(-0.533596\pi\)
−0.105348 + 0.994435i \(0.533596\pi\)
\(98\) 0 0
\(99\) −66.9323 134.192i −0.676083 1.35548i
\(100\) 0 0
\(101\) 143.374 1.41954 0.709772 0.704431i \(-0.248798\pi\)
0.709772 + 0.704431i \(0.248798\pi\)
\(102\) 0 0
\(103\) −113.748 −1.10435 −0.552173 0.833730i \(-0.686201\pi\)
−0.552173 + 0.833730i \(0.686201\pi\)
\(104\) 0 0
\(105\) −34.3381 21.2453i −0.327029 0.202336i
\(106\) 0 0
\(107\) 6.26024 0.0585069 0.0292535 0.999572i \(-0.490687\pi\)
0.0292535 + 0.999572i \(0.490687\pi\)
\(108\) 0 0
\(109\) 147.657i 1.35465i −0.735682 0.677327i \(-0.763138\pi\)
0.735682 0.677327i \(-0.236862\pi\)
\(110\) 0 0
\(111\) 29.3240 47.3954i 0.264180 0.426986i
\(112\) 0 0
\(113\) 51.3905i 0.454783i 0.973803 + 0.227392i \(0.0730197\pi\)
−0.973803 + 0.227392i \(0.926980\pi\)
\(114\) 0 0
\(115\) 22.0306i 0.191571i
\(116\) 0 0
\(117\) −150.971 + 75.3013i −1.29035 + 0.643601i
\(118\) 0 0
\(119\) 44.8317i 0.376737i
\(120\) 0 0
\(121\) 156.624 1.29441
\(122\) 0 0
\(123\) 124.182 200.711i 1.00961 1.63179i
\(124\) 0 0
\(125\) −63.4912 −0.507929
\(126\) 0 0
\(127\) 145.579 1.14629 0.573147 0.819452i \(-0.305722\pi\)
0.573147 + 0.819452i \(0.305722\pi\)
\(128\) 0 0
\(129\) −57.5909 + 93.0823i −0.446441 + 0.721568i
\(130\) 0 0
\(131\) 45.3993 0.346560 0.173280 0.984873i \(-0.444563\pi\)
0.173280 + 0.984873i \(0.444563\pi\)
\(132\) 0 0
\(133\) 118.235i 0.888987i
\(134\) 0 0
\(135\) 3.24124 35.3659i 0.0240092 0.261969i
\(136\) 0 0
\(137\) 179.157i 1.30771i −0.756618 0.653857i \(-0.773150\pi\)
0.756618 0.653857i \(-0.226850\pi\)
\(138\) 0 0
\(139\) 50.8841i 0.366073i 0.983106 + 0.183036i \(0.0585926\pi\)
−0.983106 + 0.183036i \(0.941407\pi\)
\(140\) 0 0
\(141\) −31.4386 + 50.8131i −0.222969 + 0.360377i
\(142\) 0 0
\(143\) 312.337i 2.18418i
\(144\) 0 0
\(145\) −16.5072 −0.113843
\(146\) 0 0
\(147\) −142.131 87.9378i −0.966877 0.598216i
\(148\) 0 0
\(149\) 76.0410 0.510342 0.255171 0.966896i \(-0.417868\pi\)
0.255171 + 0.966896i \(0.417868\pi\)
\(150\) 0 0
\(151\) −179.918 −1.19151 −0.595754 0.803167i \(-0.703147\pi\)
−0.595754 + 0.803167i \(0.703147\pi\)
\(152\) 0 0
\(153\) 35.2847 17.5993i 0.230619 0.115028i
\(154\) 0 0
\(155\) −26.7233 −0.172408
\(156\) 0 0
\(157\) 67.2180i 0.428140i −0.976818 0.214070i \(-0.931328\pi\)
0.976818 0.214070i \(-0.0686720\pi\)
\(158\) 0 0
\(159\) 207.427 + 128.337i 1.30457 + 0.807153i
\(160\) 0 0
\(161\) 171.391i 1.06454i
\(162\) 0 0
\(163\) 102.723i 0.630204i 0.949058 + 0.315102i \(0.102039\pi\)
−0.949058 + 0.315102i \(0.897961\pi\)
\(164\) 0 0
\(165\) 55.9122 + 34.5934i 0.338862 + 0.209657i
\(166\) 0 0
\(167\) 80.7935i 0.483793i 0.970302 + 0.241897i \(0.0777695\pi\)
−0.970302 + 0.241897i \(0.922231\pi\)
\(168\) 0 0
\(169\) −182.391 −1.07924
\(170\) 0 0
\(171\) −93.0569 + 46.4148i −0.544192 + 0.271431i
\(172\) 0 0
\(173\) 169.185 0.977950 0.488975 0.872298i \(-0.337371\pi\)
0.488975 + 0.872298i \(0.337371\pi\)
\(174\) 0 0
\(175\) −238.118 −1.36067
\(176\) 0 0
\(177\) 76.4021 + 47.2707i 0.431650 + 0.267066i
\(178\) 0 0
\(179\) −170.982 −0.955205 −0.477602 0.878576i \(-0.658494\pi\)
−0.477602 + 0.878576i \(0.658494\pi\)
\(180\) 0 0
\(181\) 39.6292i 0.218946i −0.993990 0.109473i \(-0.965084\pi\)
0.993990 0.109473i \(-0.0349163\pi\)
\(182\) 0 0
\(183\) 113.756 183.860i 0.621618 1.00470i
\(184\) 0 0
\(185\) 24.4361i 0.132087i
\(186\) 0 0
\(187\) 72.9988i 0.390368i
\(188\) 0 0
\(189\) 25.2158 275.135i 0.133417 1.45574i
\(190\) 0 0
\(191\) 239.917i 1.25611i 0.778170 + 0.628054i \(0.216148\pi\)
−0.778170 + 0.628054i \(0.783852\pi\)
\(192\) 0 0
\(193\) −13.4972 −0.0699337 −0.0349669 0.999388i \(-0.511133\pi\)
−0.0349669 + 0.999388i \(0.511133\pi\)
\(194\) 0 0
\(195\) 38.9189 62.9033i 0.199584 0.322581i
\(196\) 0 0
\(197\) 16.6040 0.0842843 0.0421422 0.999112i \(-0.486582\pi\)
0.0421422 + 0.999112i \(0.486582\pi\)
\(198\) 0 0
\(199\) 143.674 0.721979 0.360990 0.932570i \(-0.382439\pi\)
0.360990 + 0.932570i \(0.382439\pi\)
\(200\) 0 0
\(201\) 88.9483 143.764i 0.442529 0.715244i
\(202\) 0 0
\(203\) −128.421 −0.632614
\(204\) 0 0
\(205\) 103.482i 0.504792i
\(206\) 0 0
\(207\) 134.893 67.2817i 0.651657 0.325032i
\(208\) 0 0
\(209\) 192.521i 0.921151i
\(210\) 0 0
\(211\) 83.6553i 0.396471i 0.980154 + 0.198235i \(0.0635210\pi\)
−0.980154 + 0.198235i \(0.936479\pi\)
\(212\) 0 0
\(213\) 215.402 348.146i 1.01128 1.63449i
\(214\) 0 0
\(215\) 47.9913i 0.223215i
\(216\) 0 0
\(217\) −207.898 −0.958056
\(218\) 0 0
\(219\) −206.171 127.560i −0.941422 0.582467i
\(220\) 0 0
\(221\) 82.1263 0.371612
\(222\) 0 0
\(223\) −146.898 −0.658734 −0.329367 0.944202i \(-0.606835\pi\)
−0.329367 + 0.944202i \(0.606835\pi\)
\(224\) 0 0
\(225\) −93.4763 187.410i −0.415450 0.832936i
\(226\) 0 0
\(227\) −28.5250 −0.125661 −0.0628304 0.998024i \(-0.520013\pi\)
−0.0628304 + 0.998024i \(0.520013\pi\)
\(228\) 0 0
\(229\) 345.118i 1.50707i −0.657410 0.753533i \(-0.728348\pi\)
0.657410 0.753533i \(-0.271652\pi\)
\(230\) 0 0
\(231\) 434.978 + 269.125i 1.88302 + 1.16504i
\(232\) 0 0
\(233\) 105.272i 0.451809i 0.974149 + 0.225905i \(0.0725338\pi\)
−0.974149 + 0.225905i \(0.927466\pi\)
\(234\) 0 0
\(235\) 26.1982i 0.111482i
\(236\) 0 0
\(237\) 219.482 + 135.796i 0.926086 + 0.572978i
\(238\) 0 0
\(239\) 280.456i 1.17346i −0.809783 0.586729i \(-0.800415\pi\)
0.809783 0.586729i \(-0.199585\pi\)
\(240\) 0 0
\(241\) −369.833 −1.53458 −0.767289 0.641302i \(-0.778395\pi\)
−0.767289 + 0.641302i \(0.778395\pi\)
\(242\) 0 0
\(243\) 226.443 88.1616i 0.931865 0.362805i
\(244\) 0 0
\(245\) 73.2798 0.299101
\(246\) 0 0
\(247\) −216.593 −0.876894
\(248\) 0 0
\(249\) −205.182 126.948i −0.824025 0.509832i
\(250\) 0 0
\(251\) 27.4959 0.109545 0.0547727 0.998499i \(-0.482557\pi\)
0.0547727 + 0.998499i \(0.482557\pi\)
\(252\) 0 0
\(253\) 279.073i 1.10306i
\(254\) 0 0
\(255\) −9.09604 + 14.7016i −0.0356708 + 0.0576534i
\(256\) 0 0
\(257\) 4.92447i 0.0191614i −0.999954 0.00958068i \(-0.996950\pi\)
0.999954 0.00958068i \(-0.00304967\pi\)
\(258\) 0 0
\(259\) 190.105i 0.733995i
\(260\) 0 0
\(261\) −50.4132 101.073i −0.193154 0.387254i
\(262\) 0 0
\(263\) 263.575i 1.00219i −0.865394 0.501093i \(-0.832932\pi\)
0.865394 0.501093i \(-0.167068\pi\)
\(264\) 0 0
\(265\) −106.945 −0.403567
\(266\) 0 0
\(267\) 208.087 336.323i 0.779351 1.25964i
\(268\) 0 0
\(269\) 236.023 0.877409 0.438704 0.898631i \(-0.355438\pi\)
0.438704 + 0.898631i \(0.355438\pi\)
\(270\) 0 0
\(271\) −433.288 −1.59885 −0.799424 0.600767i \(-0.794862\pi\)
−0.799424 + 0.600767i \(0.794862\pi\)
\(272\) 0 0
\(273\) 302.776 489.367i 1.10907 1.79255i
\(274\) 0 0
\(275\) 387.724 1.40991
\(276\) 0 0
\(277\) 244.067i 0.881107i 0.897726 + 0.440553i \(0.145218\pi\)
−0.897726 + 0.440553i \(0.854782\pi\)
\(278\) 0 0
\(279\) −81.6131 163.626i −0.292520 0.586473i
\(280\) 0 0
\(281\) 431.627i 1.53604i −0.640426 0.768020i \(-0.721242\pi\)
0.640426 0.768020i \(-0.278758\pi\)
\(282\) 0 0
\(283\) 35.1843i 0.124326i 0.998066 + 0.0621631i \(0.0197999\pi\)
−0.998066 + 0.0621631i \(0.980200\pi\)
\(284\) 0 0
\(285\) 23.9891 38.7728i 0.0841723 0.136045i
\(286\) 0 0
\(287\) 805.058i 2.80508i
\(288\) 0 0
\(289\) 269.806 0.933583
\(290\) 0 0
\(291\) 52.1397 + 32.2594i 0.179174 + 0.110857i
\(292\) 0 0
\(293\) −214.900 −0.733446 −0.366723 0.930330i \(-0.619520\pi\)
−0.366723 + 0.930330i \(0.619520\pi\)
\(294\) 0 0
\(295\) −39.3914 −0.133530
\(296\) 0 0
\(297\) −41.0585 + 447.998i −0.138244 + 1.50841i
\(298\) 0 0
\(299\) 313.968 1.05006
\(300\) 0 0
\(301\) 373.356i 1.24039i
\(302\) 0 0
\(303\) −365.773 226.307i −1.20717 0.746889i
\(304\) 0 0
\(305\) 94.7946i 0.310802i
\(306\) 0 0
\(307\) 425.639i 1.38645i 0.720723 + 0.693223i \(0.243810\pi\)
−0.720723 + 0.693223i \(0.756190\pi\)
\(308\) 0 0
\(309\) 290.191 + 179.544i 0.939128 + 0.581048i
\(310\) 0 0
\(311\) 7.67121i 0.0246663i 0.999924 + 0.0123331i \(0.00392586\pi\)
−0.999924 + 0.0123331i \(0.996074\pi\)
\(312\) 0 0
\(313\) −313.959 −1.00306 −0.501532 0.865139i \(-0.667230\pi\)
−0.501532 + 0.865139i \(0.667230\pi\)
\(314\) 0 0
\(315\) 54.0682 + 108.401i 0.171645 + 0.344131i
\(316\) 0 0
\(317\) 361.930 1.14174 0.570868 0.821042i \(-0.306607\pi\)
0.570868 + 0.821042i \(0.306607\pi\)
\(318\) 0 0
\(319\) 209.105 0.655503
\(320\) 0 0
\(321\) −15.9710 9.88142i −0.0497539 0.0307832i
\(322\) 0 0
\(323\) 50.6216 0.156723
\(324\) 0 0
\(325\) 436.204i 1.34217i
\(326\) 0 0
\(327\) −233.068 + 376.701i −0.712748 + 1.15199i
\(328\) 0 0
\(329\) 203.813i 0.619493i
\(330\) 0 0
\(331\) 283.000i 0.854984i 0.904019 + 0.427492i \(0.140603\pi\)
−0.904019 + 0.427492i \(0.859397\pi\)
\(332\) 0 0
\(333\) −149.622 + 74.6280i −0.449314 + 0.224108i
\(334\) 0 0
\(335\) 74.1218i 0.221259i
\(336\) 0 0
\(337\) 242.847 0.720614 0.360307 0.932834i \(-0.382672\pi\)
0.360307 + 0.932834i \(0.382672\pi\)
\(338\) 0 0
\(339\) 81.1168 131.106i 0.239283 0.386745i
\(340\) 0 0
\(341\) 338.517 0.992720
\(342\) 0 0
\(343\) 68.6810 0.200236
\(344\) 0 0
\(345\) −34.7740 + 56.2041i −0.100794 + 0.162910i
\(346\) 0 0
\(347\) 35.8055 0.103186 0.0515929 0.998668i \(-0.483570\pi\)
0.0515929 + 0.998668i \(0.483570\pi\)
\(348\) 0 0
\(349\) 119.019i 0.341030i 0.985355 + 0.170515i \(0.0545431\pi\)
−0.985355 + 0.170515i \(0.945457\pi\)
\(350\) 0 0
\(351\) 504.014 + 46.1923i 1.43594 + 0.131602i
\(352\) 0 0
\(353\) 158.225i 0.448230i 0.974563 + 0.224115i \(0.0719492\pi\)
−0.974563 + 0.224115i \(0.928051\pi\)
\(354\) 0 0
\(355\) 179.497i 0.505626i
\(356\) 0 0
\(357\) −70.7641 + 114.374i −0.198219 + 0.320375i
\(358\) 0 0
\(359\) 127.881i 0.356214i 0.984011 + 0.178107i \(0.0569974\pi\)
−0.984011 + 0.178107i \(0.943003\pi\)
\(360\) 0 0
\(361\) 227.495 0.630180
\(362\) 0 0
\(363\) −399.576 247.221i −1.10076 0.681051i
\(364\) 0 0
\(365\) 106.298 0.291227
\(366\) 0 0
\(367\) 92.6498 0.252452 0.126226 0.992002i \(-0.459714\pi\)
0.126226 + 0.992002i \(0.459714\pi\)
\(368\) 0 0
\(369\) −633.620 + 316.036i −1.71713 + 0.856466i
\(370\) 0 0
\(371\) −831.998 −2.24258
\(372\) 0 0
\(373\) 9.37918i 0.0251453i −0.999921 0.0125726i \(-0.995998\pi\)
0.999921 0.0125726i \(-0.00400210\pi\)
\(374\) 0 0
\(375\) 161.977 + 100.217i 0.431940 + 0.267245i
\(376\) 0 0
\(377\) 235.251i 0.624009i
\(378\) 0 0
\(379\) 353.377i 0.932392i −0.884681 0.466196i \(-0.845624\pi\)
0.884681 0.466196i \(-0.154376\pi\)
\(380\) 0 0
\(381\) −371.400 229.789i −0.974802 0.603120i
\(382\) 0 0
\(383\) 106.620i 0.278382i 0.990266 + 0.139191i \(0.0444502\pi\)
−0.990266 + 0.139191i \(0.955550\pi\)
\(384\) 0 0
\(385\) −224.266 −0.582509
\(386\) 0 0
\(387\) 293.850 146.566i 0.759302 0.378723i
\(388\) 0 0
\(389\) −659.144 −1.69446 −0.847229 0.531227i \(-0.821731\pi\)
−0.847229 + 0.531227i \(0.821731\pi\)
\(390\) 0 0
\(391\) −73.3799 −0.187672
\(392\) 0 0
\(393\) −115.822 71.6601i −0.294712 0.182341i
\(394\) 0 0
\(395\) −113.161 −0.286483
\(396\) 0 0
\(397\) 523.170i 1.31781i −0.752227 0.658904i \(-0.771020\pi\)
0.752227 0.658904i \(-0.228980\pi\)
\(398\) 0 0
\(399\) 186.627 301.639i 0.467738 0.755989i
\(400\) 0 0
\(401\) 255.566i 0.637323i −0.947869 0.318661i \(-0.896767\pi\)
0.947869 0.318661i \(-0.103233\pi\)
\(402\) 0 0
\(403\) 380.845i 0.945024i
\(404\) 0 0
\(405\) −64.0919 + 85.1086i −0.158252 + 0.210145i
\(406\) 0 0
\(407\) 309.545i 0.760552i
\(408\) 0 0
\(409\) 630.598 1.54180 0.770902 0.636954i \(-0.219806\pi\)
0.770902 + 0.636954i \(0.219806\pi\)
\(410\) 0 0
\(411\) −282.788 + 457.061i −0.688050 + 1.11207i
\(412\) 0 0
\(413\) −306.452 −0.742014
\(414\) 0 0
\(415\) 105.788 0.254910
\(416\) 0 0
\(417\) 80.3175 129.815i 0.192608 0.311306i
\(418\) 0 0
\(419\) −475.721 −1.13537 −0.567686 0.823245i \(-0.692161\pi\)
−0.567686 + 0.823245i \(0.692161\pi\)
\(420\) 0 0
\(421\) 239.614i 0.569155i 0.958653 + 0.284578i \(0.0918534\pi\)
−0.958653 + 0.284578i \(0.908147\pi\)
\(422\) 0 0
\(423\) 160.411 80.0096i 0.379222 0.189148i
\(424\) 0 0
\(425\) 101.949i 0.239879i
\(426\) 0 0
\(427\) 737.470i 1.72710i
\(428\) 0 0
\(429\) −493.006 + 796.828i −1.14920 + 1.85741i
\(430\) 0 0
\(431\) 618.539i 1.43513i −0.696494 0.717563i \(-0.745258\pi\)
0.696494 0.717563i \(-0.254742\pi\)
\(432\) 0 0
\(433\) 211.763 0.489061 0.244530 0.969642i \(-0.421366\pi\)
0.244530 + 0.969642i \(0.421366\pi\)
\(434\) 0 0
\(435\) 42.1129 + 26.0557i 0.0968112 + 0.0598981i
\(436\) 0 0
\(437\) 193.526 0.442851
\(438\) 0 0
\(439\) −56.6884 −0.129131 −0.0645654 0.997913i \(-0.520566\pi\)
−0.0645654 + 0.997913i \(0.520566\pi\)
\(440\) 0 0
\(441\) 223.797 + 448.690i 0.507476 + 1.01744i
\(442\) 0 0
\(443\) 687.493 1.55190 0.775952 0.630792i \(-0.217270\pi\)
0.775952 + 0.630792i \(0.217270\pi\)
\(444\) 0 0
\(445\) 173.401i 0.389666i
\(446\) 0 0
\(447\) −193.994 120.026i −0.433992 0.268515i
\(448\) 0 0
\(449\) 490.455i 1.09233i 0.837679 + 0.546163i \(0.183912\pi\)
−0.837679 + 0.546163i \(0.816088\pi\)
\(450\) 0 0
\(451\) 1310.86i 2.90657i
\(452\) 0 0
\(453\) 459.002 + 283.989i 1.01325 + 0.626908i
\(454\) 0 0
\(455\) 252.307i 0.554522i
\(456\) 0 0
\(457\) 537.122 1.17532 0.587661 0.809107i \(-0.300049\pi\)
0.587661 + 0.809107i \(0.300049\pi\)
\(458\) 0 0
\(459\) −117.797 10.7960i −0.256639 0.0235206i
\(460\) 0 0
\(461\) 129.931 0.281847 0.140923 0.990021i \(-0.454993\pi\)
0.140923 + 0.990021i \(0.454993\pi\)
\(462\) 0 0
\(463\) −262.112 −0.566118 −0.283059 0.959103i \(-0.591349\pi\)
−0.283059 + 0.959103i \(0.591349\pi\)
\(464\) 0 0
\(465\) 68.1759 + 42.1811i 0.146615 + 0.0907121i
\(466\) 0 0
\(467\) 418.978 0.897169 0.448585 0.893740i \(-0.351928\pi\)
0.448585 + 0.893740i \(0.351928\pi\)
\(468\) 0 0
\(469\) 576.643i 1.22952i
\(470\) 0 0
\(471\) −106.100 + 171.485i −0.225264 + 0.364087i
\(472\) 0 0
\(473\) 607.931i 1.28527i
\(474\) 0 0
\(475\) 268.871i 0.566043i
\(476\) 0 0
\(477\) −326.612 654.823i −0.684720 1.37280i
\(478\) 0 0
\(479\) 306.699i 0.640290i −0.947369 0.320145i \(-0.896268\pi\)
0.947369 0.320145i \(-0.103732\pi\)
\(480\) 0 0
\(481\) −348.249 −0.724011
\(482\) 0 0
\(483\) −270.530 + 437.249i −0.560104 + 0.905278i
\(484\) 0 0
\(485\) −26.8822 −0.0554272
\(486\) 0 0
\(487\) −387.411 −0.795506 −0.397753 0.917493i \(-0.630210\pi\)
−0.397753 + 0.917493i \(0.630210\pi\)
\(488\) 0 0
\(489\) 162.143 262.066i 0.331580 0.535922i
\(490\) 0 0
\(491\) 13.1250 0.0267311 0.0133655 0.999911i \(-0.495745\pi\)
0.0133655 + 0.999911i \(0.495745\pi\)
\(492\) 0 0
\(493\) 54.9824i 0.111526i
\(494\) 0 0
\(495\) −88.0385 176.508i −0.177855 0.356582i
\(496\) 0 0
\(497\) 1396.43i 2.80971i
\(498\) 0 0
\(499\) 239.526i 0.480012i 0.970771 + 0.240006i \(0.0771494\pi\)
−0.970771 + 0.240006i \(0.922851\pi\)
\(500\) 0 0
\(501\) 127.528 206.119i 0.254546 0.411415i
\(502\) 0 0
\(503\) 595.462i 1.18382i −0.806004 0.591911i \(-0.798374\pi\)
0.806004 0.591911i \(-0.201626\pi\)
\(504\) 0 0
\(505\) 188.585 0.373436
\(506\) 0 0
\(507\) 465.312 + 287.893i 0.917775 + 0.567837i
\(508\) 0 0
\(509\) −600.556 −1.17987 −0.589937 0.807449i \(-0.700847\pi\)
−0.589937 + 0.807449i \(0.700847\pi\)
\(510\) 0 0
\(511\) 826.961 1.61832
\(512\) 0 0
\(513\) 310.668 + 28.4724i 0.605591 + 0.0555017i
\(514\) 0 0
\(515\) −149.616 −0.290517
\(516\) 0 0
\(517\) 331.866i 0.641908i
\(518\) 0 0
\(519\) −431.622 267.049i −0.831642 0.514545i
\(520\) 0 0
\(521\) 394.528i 0.757251i −0.925550 0.378626i \(-0.876397\pi\)
0.925550 0.378626i \(-0.123603\pi\)
\(522\) 0 0
\(523\) 639.213i 1.22221i −0.791551 0.611103i \(-0.790726\pi\)
0.791551 0.611103i \(-0.209274\pi\)
\(524\) 0 0
\(525\) 607.482 + 375.855i 1.15711 + 0.715914i
\(526\) 0 0
\(527\) 89.0102i 0.168900i
\(528\) 0 0
\(529\) 248.470 0.469697
\(530\) 0 0
\(531\) −120.302 241.192i −0.226557 0.454223i
\(532\) 0 0
\(533\) −1474.77 −2.76692
\(534\) 0 0
\(535\) 8.23433 0.0153913
\(536\) 0 0
\(537\) 436.205 + 269.884i 0.812300 + 0.502578i
\(538\) 0 0
\(539\) −928.273 −1.72221
\(540\) 0 0
\(541\) 606.241i 1.12059i 0.828292 + 0.560296i \(0.189313\pi\)
−0.828292 + 0.560296i \(0.810687\pi\)
\(542\) 0 0
\(543\) −62.5524 + 101.101i −0.115198 + 0.186190i
\(544\) 0 0
\(545\) 194.219i 0.356365i
\(546\) 0 0
\(547\) 409.425i 0.748492i 0.927330 + 0.374246i \(0.122098\pi\)
−0.927330 + 0.374246i \(0.877902\pi\)
\(548\) 0 0
\(549\) −580.425 + 289.503i −1.05724 + 0.527329i
\(550\) 0 0
\(551\) 145.006i 0.263169i
\(552\) 0 0
\(553\) −880.352 −1.59196
\(554\) 0 0
\(555\) 38.5709 62.3409i 0.0694972 0.112326i
\(556\) 0 0
\(557\) −994.040 −1.78463 −0.892316 0.451411i \(-0.850921\pi\)
−0.892316 + 0.451411i \(0.850921\pi\)
\(558\) 0 0
\(559\) 683.945 1.22351
\(560\) 0 0
\(561\) 115.224 186.233i 0.205391 0.331966i
\(562\) 0 0
\(563\) −29.5954 −0.0525673 −0.0262837 0.999655i \(-0.508367\pi\)
−0.0262837 + 0.999655i \(0.508367\pi\)
\(564\) 0 0
\(565\) 67.5958i 0.119639i
\(566\) 0 0
\(567\) −498.614 + 662.117i −0.879389 + 1.16775i
\(568\) 0 0
\(569\) 355.324i 0.624471i 0.950005 + 0.312235i \(0.101078\pi\)
−0.950005 + 0.312235i \(0.898922\pi\)
\(570\) 0 0
\(571\) 133.482i 0.233769i −0.993145 0.116885i \(-0.962709\pi\)
0.993145 0.116885i \(-0.0372908\pi\)
\(572\) 0 0
\(573\) 378.694 612.071i 0.660898 1.06819i
\(574\) 0 0
\(575\) 389.748i 0.677823i
\(576\) 0 0
\(577\) −228.735 −0.396422 −0.198211 0.980159i \(-0.563513\pi\)
−0.198211 + 0.980159i \(0.563513\pi\)
\(578\) 0 0
\(579\) 34.4338 + 21.3046i 0.0594712 + 0.0367954i
\(580\) 0 0
\(581\) 822.993 1.41651
\(582\) 0 0
\(583\) 1354.73 2.32372
\(584\) 0 0
\(585\) −198.578 + 99.0465i −0.339450 + 0.169310i
\(586\) 0 0
\(587\) 633.349 1.07896 0.539480 0.841998i \(-0.318621\pi\)
0.539480 + 0.841998i \(0.318621\pi\)
\(588\) 0 0
\(589\) 234.748i 0.398553i
\(590\) 0 0
\(591\) −42.3598 26.2084i −0.0716748 0.0443459i
\(592\) 0 0
\(593\) 189.510i 0.319578i −0.987151 0.159789i \(-0.948919\pi\)
0.987151 0.159789i \(-0.0510813\pi\)
\(594\) 0 0
\(595\) 58.9688i 0.0991071i
\(596\) 0 0
\(597\) −366.538 226.781i −0.613967 0.379867i
\(598\) 0 0
\(599\) 340.082i 0.567750i 0.958861 + 0.283875i \(0.0916200\pi\)
−0.958861 + 0.283875i \(0.908380\pi\)
\(600\) 0 0
\(601\) −528.406 −0.879211 −0.439605 0.898191i \(-0.644882\pi\)
−0.439605 + 0.898191i \(0.644882\pi\)
\(602\) 0 0
\(603\) −453.846 + 226.369i −0.752647 + 0.375404i
\(604\) 0 0
\(605\) 206.013 0.340517
\(606\) 0 0
\(607\) −659.649 −1.08674 −0.543368 0.839495i \(-0.682851\pi\)
−0.543368 + 0.839495i \(0.682851\pi\)
\(608\) 0 0
\(609\) 327.624 + 202.704i 0.537971 + 0.332848i
\(610\) 0 0
\(611\) 373.362 0.611067
\(612\) 0 0
\(613\) 67.7073i 0.110452i −0.998474 0.0552262i \(-0.982412\pi\)
0.998474 0.0552262i \(-0.0175880\pi\)
\(614\) 0 0
\(615\) 163.341 264.002i 0.265595 0.429272i
\(616\) 0 0
\(617\) 807.698i 1.30907i 0.756031 + 0.654536i \(0.227136\pi\)
−0.756031 + 0.654536i \(0.772864\pi\)
\(618\) 0 0
\(619\) 122.858i 0.198479i −0.995064 0.0992393i \(-0.968359\pi\)
0.995064 0.0992393i \(-0.0316409\pi\)
\(620\) 0 0
\(621\) −450.337 41.2728i −0.725180 0.0664619i
\(622\) 0 0
\(623\) 1349.01i 2.16534i
\(624\) 0 0
\(625\) 498.235 0.797176
\(626\) 0 0
\(627\) −303.882 + 491.155i −0.484661 + 0.783341i
\(628\) 0 0
\(629\) 81.3921 0.129399
\(630\) 0 0
\(631\) 141.286 0.223908 0.111954 0.993713i \(-0.464289\pi\)
0.111954 + 0.993713i \(0.464289\pi\)
\(632\) 0 0
\(633\) 132.045 213.420i 0.208602 0.337156i
\(634\) 0 0
\(635\) 191.486 0.301553
\(636\) 0 0
\(637\) 1044.34i 1.63947i
\(638\) 0 0
\(639\) −1099.06 + 548.186i −1.71996 + 0.857881i
\(640\) 0 0
\(641\) 240.601i 0.375352i 0.982231 + 0.187676i \(0.0600955\pi\)
−0.982231 + 0.187676i \(0.939904\pi\)
\(642\) 0 0
\(643\) 774.975i 1.20525i 0.798025 + 0.602624i \(0.205878\pi\)
−0.798025 + 0.602624i \(0.794122\pi\)
\(644\) 0 0
\(645\) −75.7515 + 122.435i −0.117444 + 0.189821i
\(646\) 0 0
\(647\) 823.719i 1.27314i 0.771220 + 0.636568i \(0.219647\pi\)
−0.771220 + 0.636568i \(0.780353\pi\)
\(648\) 0 0
\(649\) 498.991 0.768861
\(650\) 0 0
\(651\) 530.386 + 328.155i 0.814724 + 0.504078i
\(652\) 0 0
\(653\) 142.733 0.218581 0.109290 0.994010i \(-0.465142\pi\)
0.109290 + 0.994010i \(0.465142\pi\)
\(654\) 0 0
\(655\) 59.7154 0.0911685
\(656\) 0 0
\(657\) 324.634 + 650.859i 0.494116 + 0.990652i
\(658\) 0 0
\(659\) 485.418 0.736598 0.368299 0.929707i \(-0.379940\pi\)
0.368299 + 0.929707i \(0.379940\pi\)
\(660\) 0 0
\(661\) 89.9502i 0.136082i 0.997683 + 0.0680410i \(0.0216749\pi\)
−0.997683 + 0.0680410i \(0.978325\pi\)
\(662\) 0 0
\(663\) −209.519 129.632i −0.316017 0.195523i
\(664\) 0 0
\(665\) 155.519i 0.233863i
\(666\) 0 0
\(667\) 210.197i 0.315138i
\(668\) 0 0
\(669\) 374.763 + 231.869i 0.560184 + 0.346591i
\(670\) 0 0
\(671\) 1200.81i 1.78958i
\(672\) 0 0
\(673\) 779.599 1.15839 0.579197 0.815188i \(-0.303366\pi\)
0.579197 + 0.815188i \(0.303366\pi\)
\(674\) 0 0
\(675\) −57.3415 + 625.665i −0.0849503 + 0.926911i
\(676\) 0 0
\(677\) −207.151 −0.305984 −0.152992 0.988227i \(-0.548891\pi\)
−0.152992 + 0.988227i \(0.548891\pi\)
\(678\) 0 0
\(679\) −209.134 −0.308003
\(680\) 0 0
\(681\) 72.7724 + 45.0250i 0.106861 + 0.0661160i
\(682\) 0 0
\(683\) −680.228 −0.995941 −0.497970 0.867194i \(-0.665921\pi\)
−0.497970 + 0.867194i \(0.665921\pi\)
\(684\) 0 0
\(685\) 235.652i 0.344017i
\(686\) 0 0
\(687\) −544.748 + 880.458i −0.792938 + 1.28160i
\(688\) 0 0
\(689\) 1524.12i 2.21208i
\(690\) 0 0
\(691\) 480.570i 0.695470i −0.937593 0.347735i \(-0.886951\pi\)
0.937593 0.347735i \(-0.113049\pi\)
\(692\) 0 0
\(693\) −684.910 1373.17i −0.988326 1.98149i
\(694\) 0 0
\(695\) 66.9297i 0.0963018i
\(696\) 0 0
\(697\) 344.680 0.494520
\(698\) 0 0
\(699\) 166.165 268.567i 0.237718 0.384216i
\(700\) 0 0
\(701\) 854.903 1.21955 0.609774 0.792575i \(-0.291260\pi\)
0.609774 + 0.792575i \(0.291260\pi\)
\(702\) 0 0
\(703\) −214.656 −0.305343
\(704\) 0 0
\(705\) −41.3523 + 66.8364i −0.0586558 + 0.0948034i
\(706\) 0 0
\(707\) 1467.13 2.07515
\(708\) 0 0
\(709\) 990.069i 1.39643i −0.715888 0.698215i \(-0.753978\pi\)
0.715888 0.698215i \(-0.246022\pi\)
\(710\) 0 0
\(711\) −345.593 692.880i −0.486067 0.974514i
\(712\) 0 0
\(713\) 340.285i 0.477258i
\(714\) 0 0
\(715\) 410.828i 0.574585i
\(716\) 0 0
\(717\) −442.684 + 715.495i −0.617411 + 0.997901i
\(718\) 0 0
\(719\) 502.244i 0.698531i −0.937024 0.349266i \(-0.886431\pi\)
0.937024 0.349266i \(-0.113569\pi\)
\(720\) 0 0
\(721\) −1163.97 −1.61438
\(722\) 0 0
\(723\) 943.511 + 583.760i 1.30499 + 0.807413i
\(724\) 0 0
\(725\) 292.032 0.402803
\(726\) 0 0
\(727\) 718.280 0.988005 0.494002 0.869461i \(-0.335533\pi\)
0.494002 + 0.869461i \(0.335533\pi\)
\(728\) 0 0
\(729\) −716.856 132.511i −0.983341 0.181771i
\(730\) 0 0
\(731\) −159.850 −0.218673
\(732\) 0 0
\(733\) 1362.31i 1.85854i 0.369397 + 0.929272i \(0.379564\pi\)
−0.369397 + 0.929272i \(0.620436\pi\)
\(734\) 0 0
\(735\) −186.950 115.668i −0.254354 0.157371i
\(736\) 0 0
\(737\) 938.939i 1.27400i
\(738\) 0 0
\(739\) 1057.01i 1.43033i −0.698957 0.715164i \(-0.746352\pi\)
0.698957 0.715164i \(-0.253648\pi\)
\(740\) 0 0
\(741\) 552.568 + 341.879i 0.745705 + 0.461375i
\(742\) 0 0
\(743\) 88.0799i 0.118546i −0.998242 0.0592731i \(-0.981122\pi\)
0.998242 0.0592731i \(-0.0188783\pi\)
\(744\) 0 0
\(745\) 100.019 0.134254
\(746\) 0 0
\(747\) 323.076 + 647.736i 0.432499 + 0.867116i
\(748\) 0 0
\(749\) 64.0603 0.0855278
\(750\) 0 0
\(751\) 11.4389 0.0152315 0.00761576 0.999971i \(-0.497576\pi\)
0.00761576 + 0.999971i \(0.497576\pi\)
\(752\) 0 0
\(753\) −70.1470 43.4006i −0.0931566 0.0576369i
\(754\) 0 0
\(755\) −236.652 −0.313447
\(756\) 0 0
\(757\) 38.6736i 0.0510879i 0.999674 + 0.0255440i \(0.00813178\pi\)
−0.999674 + 0.0255440i \(0.991868\pi\)
\(758\) 0 0
\(759\) 440.501 711.966i 0.580370 0.938032i
\(760\) 0 0
\(761\) 814.341i 1.07009i −0.844822 0.535047i \(-0.820294\pi\)
0.844822 0.535047i \(-0.179706\pi\)
\(762\) 0 0
\(763\) 1510.96i 1.98029i
\(764\) 0 0
\(765\) 46.4113 23.1489i 0.0606684 0.0302601i
\(766\) 0 0
\(767\) 561.383i 0.731921i
\(768\) 0 0
\(769\) 490.085 0.637302 0.318651 0.947872i \(-0.396770\pi\)
0.318651 + 0.947872i \(0.396770\pi\)
\(770\) 0 0
\(771\) −7.77298 + 12.5632i −0.0100817 + 0.0162947i
\(772\) 0 0
\(773\) 747.603 0.967145 0.483572 0.875304i \(-0.339339\pi\)
0.483572 + 0.875304i \(0.339339\pi\)
\(774\) 0 0
\(775\) 472.767 0.610022
\(776\) 0 0
\(777\) 300.069 484.991i 0.386189 0.624184i
\(778\) 0 0
\(779\) −909.030 −1.16692
\(780\) 0 0
\(781\) 2273.78i 2.91137i
\(782\) 0 0
\(783\) −30.9251 + 337.430i −0.0394957 + 0.430946i
\(784\) 0 0
\(785\) 88.4143i 0.112630i
\(786\) 0 0
\(787\) 975.671i 1.23973i −0.784707 0.619867i \(-0.787186\pi\)
0.784707 0.619867i \(-0.212814\pi\)
\(788\) 0 0
\(789\) −416.037 + 672.427i −0.527297 + 0.852252i
\(790\) 0 0
\(791\) 525.873i 0.664820i
\(792\) 0 0
\(793\) −1350.96 −1.70360
\(794\) 0 0
\(795\) 272.837 + 168.807i 0.343191 + 0.212336i
\(796\) 0 0
\(797\) −417.874 −0.524309 −0.262154 0.965026i \(-0.584433\pi\)
−0.262154 + 0.965026i \(0.584433\pi\)
\(798\) 0 0
\(799\) −87.2613 −0.109213
\(800\) 0 0
\(801\) −1061.73 + 529.569i