Properties

Label 384.3.e.d.257.6
Level $384$
Weight $3$
Character 384.257
Analytic conductor $10.463$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 384.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.4632421514\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
Defining polynomial: \(x^{8} + 18 x^{6} + 99 x^{4} + 170 x^{2} + 81\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{10}\cdot 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 257.6
Root \(2.55118i\) of defining polynomial
Character \(\chi\) \(=\) 384.257
Dual form 384.3.e.d.257.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1.57844 + 2.55118i) q^{3} +1.31534i q^{5} -10.2329 q^{7} +(-4.01705 + 8.05378i) q^{9} +O(q^{10})\) \(q+(1.57844 + 2.55118i) q^{3} +1.31534i q^{5} -10.2329 q^{7} +(-4.01705 + 8.05378i) q^{9} -16.6620i q^{11} -18.7454 q^{13} +(-3.35566 + 2.07618i) q^{15} +4.38114i q^{17} -11.5544 q^{19} +(-16.1520 - 26.1059i) q^{21} -16.7490i q^{23} +23.2699 q^{25} +(-26.8873 + 2.46419i) q^{27} +12.5498i q^{29} -20.3167 q^{31} +(42.5079 - 26.3001i) q^{33} -13.4597i q^{35} +18.5778 q^{37} +(-29.5885 - 47.8230i) q^{39} +78.6737i q^{41} -36.4860 q^{43} +(-10.5934 - 5.28377i) q^{45} +19.9175i q^{47} +55.7118 q^{49} +(-11.1771 + 6.91537i) q^{51} -81.3064i q^{53} +21.9162 q^{55} +(-18.2380 - 29.4775i) q^{57} -29.9477i q^{59} -72.0687 q^{61} +(41.1060 - 82.4133i) q^{63} -24.6565i q^{65} -56.3520 q^{67} +(42.7298 - 26.4374i) q^{69} +136.465i q^{71} -80.8141 q^{73} +(36.7301 + 59.3657i) q^{75} +170.501i q^{77} -86.0317 q^{79} +(-48.7266 - 64.7048i) q^{81} -80.4263i q^{83} -5.76268 q^{85} +(-32.0168 + 19.8091i) q^{87} +131.830i q^{89} +191.820 q^{91} +(-32.0687 - 51.8315i) q^{93} -15.1980i q^{95} -20.4375 q^{97} +(134.192 + 66.9323i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{3} + 8q^{7} + O(q^{10}) \) \( 8q + 4q^{3} + 8q^{7} + 16q^{15} - 24q^{19} + 16q^{21} - 40q^{25} - 44q^{27} - 56q^{31} + 8q^{33} + 32q^{37} - 104q^{39} + 136q^{43} - 80q^{45} + 72q^{49} + 176q^{51} + 192q^{55} - 40q^{57} - 160q^{61} + 264q^{63} - 280q^{67} + 80q^{69} - 80q^{73} - 348q^{75} - 408q^{79} + 72q^{81} + 192q^{85} - 368q^{87} + 336q^{91} + 160q^{93} + 96q^{97} + 432q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(133\) \(257\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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
\(3\) 1.57844 + 2.55118i 0.526147 + 0.850394i
\(4\) 0 0
\(5\) 1.31534i 0.263067i 0.991312 + 0.131534i \(0.0419902\pi\)
−0.991312 + 0.131534i \(0.958010\pi\)
\(6\) 0 0
\(7\) −10.2329 −1.46184 −0.730920 0.682463i \(-0.760909\pi\)
−0.730920 + 0.682463i \(0.760909\pi\)
\(8\) 0 0
\(9\) −4.01705 + 8.05378i −0.446339 + 0.894864i
\(10\) 0 0
\(11\) 16.6620i 1.51473i −0.652991 0.757366i \(-0.726486\pi\)
0.652991 0.757366i \(-0.273514\pi\)
\(12\) 0 0
\(13\) −18.7454 −1.44196 −0.720978 0.692958i \(-0.756307\pi\)
−0.720978 + 0.692958i \(0.756307\pi\)
\(14\) 0 0
\(15\) −3.35566 + 2.07618i −0.223711 + 0.138412i
\(16\) 0 0
\(17\) 4.38114i 0.257714i 0.991663 + 0.128857i \(0.0411308\pi\)
−0.991663 + 0.128857i \(0.958869\pi\)
\(18\) 0 0
\(19\) −11.5544 −0.608129 −0.304064 0.952652i \(-0.598344\pi\)
−0.304064 + 0.952652i \(0.598344\pi\)
\(20\) 0 0
\(21\) −16.1520 26.1059i −0.769143 1.24314i
\(22\) 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
\(27\) −26.8873 + 2.46419i −0.995827 + 0.0912663i
\(28\) 0 0
\(29\) 12.5498i 0.432752i 0.976310 + 0.216376i \(0.0694237\pi\)
−0.976310 + 0.216376i \(0.930576\pi\)
\(30\) 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
\(35\) 13.4597i 0.384562i
\(36\) 0 0
\(37\) 18.5778 0.502103 0.251052 0.967974i \(-0.419224\pi\)
0.251052 + 0.967974i \(0.419224\pi\)
\(38\) 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
\(43\) −36.4860 −0.848511 −0.424255 0.905543i \(-0.639464\pi\)
−0.424255 + 0.905543i \(0.639464\pi\)
\(44\) 0 0
\(45\) −10.5934 5.28377i −0.235410 0.117417i
\(46\) 0 0
\(47\) 19.9175i 0.423777i 0.977294 + 0.211888i \(0.0679613\pi\)
−0.977294 + 0.211888i \(0.932039\pi\)
\(48\) 0 0
\(49\) 55.7118 1.13698
\(50\) 0 0
\(51\) −11.1771 + 6.91537i −0.219158 + 0.135596i
\(52\) 0 0
\(53\) 81.3064i 1.53408i −0.641598 0.767041i \(-0.721728\pi\)
0.641598 0.767041i \(-0.278272\pi\)
\(54\) 0 0
\(55\) 21.9162 0.398476
\(56\) 0 0
\(57\) −18.2380 29.4775i −0.319965 0.517149i
\(58\) 0 0
\(59\) 29.9477i 0.507589i −0.967258 0.253794i \(-0.918321\pi\)
0.967258 0.253794i \(-0.0816787\pi\)
\(60\) 0 0
\(61\) −72.0687 −1.18145 −0.590727 0.806872i \(-0.701159\pi\)
−0.590727 + 0.806872i \(0.701159\pi\)
\(62\) 0 0
\(63\) 41.1060 82.4133i 0.652476 1.30815i
\(64\) 0 0
\(65\) 24.6565i 0.379331i
\(66\) 0 0
\(67\) −56.3520 −0.841074 −0.420537 0.907275i \(-0.638158\pi\)
−0.420537 + 0.907275i \(0.638158\pi\)
\(68\) 0 0
\(69\) 42.7298 26.4374i 0.619273 0.383150i
\(70\) 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 \(-0.686716\pi\)
−0.553521 + 0.832835i \(0.686716\pi\)
\(74\) 0 0
\(75\) 36.7301 + 59.3657i 0.489735 + 0.791543i
\(76\) 0 0
\(77\) 170.501i 2.21429i
\(78\) 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
\(83\) 80.4263i 0.968992i −0.874793 0.484496i \(-0.839003\pi\)
0.874793 0.484496i \(-0.160997\pi\)
\(84\) 0 0
\(85\) −5.76268 −0.0677962
\(86\) 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
\(91\) 191.820 2.10791
\(92\) 0 0
\(93\) −32.0687 51.8315i −0.344824 0.557328i
\(94\) 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
\(99\) 134.192 + 66.9323i 1.35548 + 0.676083i
\(100\) 0 0
\(101\) 143.374i 1.41954i 0.704431 + 0.709772i \(0.251202\pi\)
−0.704431 + 0.709772i \(0.748798\pi\)
\(102\) 0 0
\(103\) 113.748 1.10435 0.552173 0.833730i \(-0.313799\pi\)
0.552173 + 0.833730i \(0.313799\pi\)
\(104\) 0 0
\(105\) 34.3381 21.2453i 0.327029 0.202336i
\(106\) 0 0
\(107\) 6.26024i 0.0585069i 0.999572 + 0.0292535i \(0.00931300\pi\)
−0.999572 + 0.0292535i \(0.990687\pi\)
\(108\) 0 0
\(109\) 147.657 1.35465 0.677327 0.735682i \(-0.263138\pi\)
0.677327 + 0.735682i \(0.263138\pi\)
\(110\) 0 0
\(111\) 29.3240 + 47.3954i 0.264180 + 0.426986i
\(112\) 0 0
\(113\) 51.3905i 0.454783i −0.973803 0.227392i \(-0.926980\pi\)
0.973803 0.227392i \(-0.0730197\pi\)
\(114\) 0 0
\(115\) 22.0306 0.191571
\(116\) 0 0
\(117\) 75.3013 150.971i 0.643601 1.29035i
\(118\) 0 0
\(119\) 44.8317i 0.376737i
\(120\) 0 0
\(121\) −156.624 −1.29441
\(122\) 0 0
\(123\) −200.711 + 124.182i −1.63179 + 1.00961i
\(124\) 0 0
\(125\) 63.4912i 0.507929i
\(126\) 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
\(131\) 45.3993i 0.346560i −0.984873 0.173280i \(-0.944563\pi\)
0.984873 0.173280i \(-0.0554365\pi\)
\(132\) 0 0
\(133\) 118.235 0.888987
\(134\) 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
\(139\) 50.8841 0.366073 0.183036 0.983106i \(-0.441407\pi\)
0.183036 + 0.983106i \(0.441407\pi\)
\(140\) 0 0
\(141\) −50.8131 + 31.4386i −0.360377 + 0.222969i
\(142\) 0 0
\(143\) 312.337i 2.18418i
\(144\) 0 0
\(145\) −16.5072 −0.113843
\(146\) 0 0
\(147\) 87.9378 + 142.131i 0.598216 + 0.966877i
\(148\) 0 0
\(149\) 76.0410i 0.510342i 0.966896 + 0.255171i \(0.0821318\pi\)
−0.966896 + 0.255171i \(0.917868\pi\)
\(150\) 0 0
\(151\) 179.918 1.19151 0.595754 0.803167i \(-0.296853\pi\)
0.595754 + 0.803167i \(0.296853\pi\)
\(152\) 0 0
\(153\) −35.2847 17.5993i −0.230619 0.115028i
\(154\) 0 0
\(155\) 26.7233i 0.172408i
\(156\) 0 0
\(157\) 67.2180 0.428140 0.214070 0.976818i \(-0.431328\pi\)
0.214070 + 0.976818i \(0.431328\pi\)
\(158\) 0 0
\(159\) 207.427 128.337i 1.30457 0.807153i
\(160\) 0 0
\(161\) 171.391i 1.06454i
\(162\) 0 0
\(163\) −102.723 −0.630204 −0.315102 0.949058i \(-0.602039\pi\)
−0.315102 + 0.949058i \(0.602039\pi\)
\(164\) 0 0
\(165\) 34.5934 + 55.9122i 0.209657 + 0.338862i
\(166\) 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
\(171\) 46.4148 93.0569i 0.271431 0.544192i
\(172\) 0 0
\(173\) 169.185i 0.977950i −0.872298 0.488975i \(-0.837371\pi\)
0.872298 0.488975i \(-0.162629\pi\)
\(174\) 0 0
\(175\) −238.118 −1.36067
\(176\) 0 0
\(177\) 76.4021 47.2707i 0.431650 0.267066i
\(178\) 0 0
\(179\) 170.982i 0.955205i 0.878576 + 0.477602i \(0.158494\pi\)
−0.878576 + 0.477602i \(0.841506\pi\)
\(180\) 0 0
\(181\) −39.6292 −0.218946 −0.109473 0.993990i \(-0.534916\pi\)
−0.109473 + 0.993990i \(0.534916\pi\)
\(182\) 0 0
\(183\) −113.756 183.860i −0.621618 1.00470i
\(184\) 0 0
\(185\) 24.4361i 0.132087i
\(186\) 0 0
\(187\) 72.9988 0.390368
\(188\) 0 0
\(189\) 275.135 25.2158i 1.45574 0.133417i
\(190\) 0 0
\(191\) 239.917i 1.25611i −0.778170 0.628054i \(-0.783852\pi\)
0.778170 0.628054i \(-0.216148\pi\)
\(192\) 0 0
\(193\) −13.4972 −0.0699337 −0.0349669 0.999388i \(-0.511133\pi\)
−0.0349669 + 0.999388i \(0.511133\pi\)
\(194\) 0 0
\(195\) 62.9033 38.9189i 0.322581 0.199584i
\(196\) 0 0
\(197\) 16.6040i 0.0842843i 0.999112 + 0.0421422i \(0.0134182\pi\)
−0.999112 + 0.0421422i \(0.986582\pi\)
\(198\) 0 0
\(199\) −143.674 −0.721979 −0.360990 0.932570i \(-0.617561\pi\)
−0.360990 + 0.932570i \(0.617561\pi\)
\(200\) 0 0
\(201\) −88.9483 143.764i −0.442529 0.715244i
\(202\) 0 0
\(203\) 128.421i 0.632614i
\(204\) 0 0
\(205\) −103.482 −0.504792
\(206\) 0 0
\(207\) 134.893 + 67.2817i 0.651657 + 0.325032i
\(208\) 0 0
\(209\) 192.521i 0.921151i
\(210\) 0 0
\(211\) −83.6553 −0.396471 −0.198235 0.980154i \(-0.563521\pi\)
−0.198235 + 0.980154i \(0.563521\pi\)
\(212\) 0 0
\(213\) −348.146 + 215.402i −1.63449 + 1.01128i
\(214\) 0 0
\(215\) 47.9913i 0.223215i
\(216\) 0 0
\(217\) 207.898 0.958056
\(218\) 0 0
\(219\) −127.560 206.171i −0.582467 0.941422i
\(220\) 0 0
\(221\) 82.1263i 0.371612i
\(222\) 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
\(227\) 28.5250i 0.125661i 0.998024 + 0.0628304i \(0.0200127\pi\)
−0.998024 + 0.0628304i \(0.979987\pi\)
\(228\) 0 0
\(229\) −345.118 −1.50707 −0.753533 0.657410i \(-0.771652\pi\)
−0.753533 + 0.657410i \(0.771652\pi\)
\(230\) 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
\(235\) −26.1982 −0.111482
\(236\) 0 0
\(237\) −135.796 219.482i −0.572978 0.926086i
\(238\) 0 0
\(239\) 280.456i 1.17346i 0.809783 + 0.586729i \(0.199585\pi\)
−0.809783 + 0.586729i \(0.800415\pi\)
\(240\) 0 0
\(241\) −369.833 −1.53458 −0.767289 0.641302i \(-0.778395\pi\)
−0.767289 + 0.641302i \(0.778395\pi\)
\(242\) 0 0
\(243\) 88.1616 226.443i 0.362805 0.931865i
\(244\) 0 0
\(245\) 73.2798i 0.299101i
\(246\) 0 0
\(247\) 216.593 0.876894
\(248\) 0 0
\(249\) 205.182 126.948i 0.824025 0.509832i
\(250\) 0 0
\(251\) 27.4959i 0.109545i 0.998499 + 0.0547727i \(0.0174434\pi\)
−0.998499 + 0.0547727i \(0.982557\pi\)
\(252\) 0 0
\(253\) −279.073 −1.10306
\(254\) 0 0
\(255\) −9.09604 14.7016i −0.0356708 0.0576534i
\(256\) 0 0
\(257\) 4.92447i 0.0191614i 0.999954 + 0.00958068i \(0.00304967\pi\)
−0.999954 + 0.00958068i \(0.996950\pi\)
\(258\) 0 0
\(259\) −190.105 −0.733995
\(260\) 0 0
\(261\) −101.073 50.4132i −0.387254 0.193154i
\(262\) 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
\(267\) −336.323 + 208.087i −1.25964 + 0.779351i
\(268\) 0 0
\(269\) 236.023i 0.877409i −0.898631 0.438704i \(-0.855438\pi\)
0.898631 0.438704i \(-0.144562\pi\)
\(270\) 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
\(275\) 387.724i 1.40991i
\(276\) 0 0
\(277\) 244.067 0.881107 0.440553 0.897726i \(-0.354782\pi\)
0.440553 + 0.897726i \(0.354782\pi\)
\(278\) 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
\(283\) 35.1843 0.124326 0.0621631 0.998066i \(-0.480200\pi\)
0.0621631 + 0.998066i \(0.480200\pi\)
\(284\) 0 0
\(285\) 38.7728 23.9891i 0.136045 0.0841723i
\(286\) 0 0
\(287\) 805.058i 2.80508i
\(288\) 0 0
\(289\) 269.806 0.933583
\(290\) 0 0
\(291\) −32.2594 52.1397i −0.110857 0.179174i
\(292\) 0 0
\(293\) 214.900i 0.733446i −0.930330 0.366723i \(-0.880480\pi\)
0.930330 0.366723i \(-0.119520\pi\)
\(294\) 0 0
\(295\) 39.3914 0.133530
\(296\) 0 0
\(297\) 41.0585 + 447.998i 0.138244 + 1.50841i
\(298\) 0 0
\(299\) 313.968i 1.05006i
\(300\) 0 0
\(301\) 373.356 1.24039
\(302\) 0 0
\(303\) −365.773 + 226.307i −1.20717 + 0.746889i
\(304\) 0 0
\(305\) 94.7946i 0.310802i
\(306\) 0 0
\(307\) −425.639 −1.38645 −0.693223 0.720723i \(-0.743810\pi\)
−0.693223 + 0.720723i \(0.743810\pi\)
\(308\) 0 0
\(309\) 179.544 + 290.191i 0.581048 + 0.939128i
\(310\) 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 \(-0.332770\pi\)
0.501532 + 0.865139i \(0.332770\pi\)
\(314\) 0 0
\(315\) 108.401 + 54.0682i 0.344131 + 0.171645i
\(316\) 0 0
\(317\) 361.930i 1.14174i −0.821042 0.570868i \(-0.806607\pi\)
0.821042 0.570868i \(-0.193393\pi\)
\(318\) 0 0
\(319\) 209.105 0.655503
\(320\) 0 0
\(321\) −15.9710 + 9.88142i −0.0497539 + 0.0307832i
\(322\) 0 0
\(323\) 50.6216i 0.156723i
\(324\) 0 0
\(325\) −436.204 −1.34217
\(326\) 0 0
\(327\) 233.068 + 376.701i 0.712748 + 1.15199i
\(328\) 0 0
\(329\) 203.813i 0.619493i
\(330\) 0 0
\(331\) 283.000 0.854984 0.427492 0.904019i \(-0.359397\pi\)
0.427492 + 0.904019i \(0.359397\pi\)
\(332\) 0 0
\(333\) −74.6280 + 149.622i −0.224108 + 0.449314i
\(334\) 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
\(339\) 131.106 81.1168i 0.386745 0.239283i
\(340\) 0 0
\(341\) 338.517i 0.992720i
\(342\) 0 0
\(343\) −68.6810 −0.200236
\(344\) 0 0
\(345\) 34.7740 + 56.2041i 0.100794 + 0.162910i
\(346\) 0 0
\(347\) 35.8055i 0.103186i 0.998668 + 0.0515929i \(0.0164298\pi\)
−0.998668 + 0.0515929i \(0.983570\pi\)
\(348\) 0 0
\(349\) −119.019 −0.341030 −0.170515 0.985355i \(-0.554543\pi\)
−0.170515 + 0.985355i \(0.554543\pi\)
\(350\) 0 0
\(351\) 504.014 46.1923i 1.43594 0.131602i
\(352\) 0 0
\(353\) 158.225i 0.448230i −0.974563 0.224115i \(-0.928051\pi\)
0.974563 0.224115i \(-0.0719492\pi\)
\(354\) 0 0
\(355\) −179.497 −0.505626
\(356\) 0 0
\(357\) 114.374 70.7641i 0.320375 0.198219i
\(358\) 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
\(363\) −247.221 399.576i −0.681051 1.10076i
\(364\) 0 0
\(365\) 106.298i 0.291227i
\(366\) 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
\(371\) 831.998i 2.24258i
\(372\) 0 0
\(373\) −9.37918 −0.0251453 −0.0125726 0.999921i \(-0.504002\pi\)
−0.0125726 + 0.999921i \(0.504002\pi\)
\(374\) 0 0
\(375\) −161.977 + 100.217i −0.431940 + 0.267245i
\(376\) 0 0
\(377\) 235.251i 0.624009i
\(378\) 0 0
\(379\) −353.377 −0.932392 −0.466196 0.884681i \(-0.654376\pi\)
−0.466196 + 0.884681i \(0.654376\pi\)
\(380\) 0 0
\(381\) 229.789 + 371.400i 0.603120 + 0.974802i
\(382\) 0 0
\(383\) 106.620i 0.278382i −0.990266 0.139191i \(-0.955550\pi\)
0.990266 0.139191i \(-0.0444502\pi\)
\(384\) 0 0
\(385\) −224.266 −0.582509
\(386\) 0 0
\(387\) 146.566 293.850i 0.378723 0.759302i
\(388\) 0 0
\(389\) 659.144i 1.69446i −0.531227 0.847229i \(-0.678269\pi\)
0.531227 0.847229i \(-0.321731\pi\)
\(390\) 0 0
\(391\) 73.3799 0.187672
\(392\) 0 0
\(393\) 115.822 71.6601i 0.294712 0.182341i
\(394\) 0 0
\(395\) 113.161i 0.286483i
\(396\) 0 0
\(397\) 523.170 1.31781 0.658904 0.752227i \(-0.271020\pi\)
0.658904 + 0.752227i \(0.271020\pi\)
\(398\) 0 0
\(399\) 186.627 + 301.639i 0.467738 + 0.755989i
\(400\) 0 0
\(401\) 255.566i 0.637323i 0.947869 + 0.318661i \(0.103233\pi\)
−0.947869 + 0.318661i \(0.896767\pi\)
\(402\) 0 0
\(403\) 380.845 0.945024
\(404\) 0 0
\(405\) 85.1086 64.0919i 0.210145 0.158252i
\(406\) 0 0
\(407\) 309.545i 0.760552i
\(408\) 0 0
\(409\) −630.598 −1.54180 −0.770902 0.636954i \(-0.780194\pi\)
−0.770902 + 0.636954i \(0.780194\pi\)
\(410\) 0 0
\(411\) 457.061 282.788i 1.11207 0.688050i
\(412\) 0 0
\(413\) 306.452i 0.742014i
\(414\) 0 0
\(415\) 105.788 0.254910
\(416\) 0 0
\(417\) 80.3175 + 129.815i 0.192608 + 0.311306i
\(418\) 0 0
\(419\) 475.721i 1.13537i 0.823245 + 0.567686i \(0.192161\pi\)
−0.823245 + 0.567686i \(0.807839\pi\)
\(420\) 0 0
\(421\) 239.614 0.569155 0.284578 0.958653i \(-0.408147\pi\)
0.284578 + 0.958653i \(0.408147\pi\)
\(422\) 0 0
\(423\) −160.411 80.0096i −0.379222 0.189148i
\(424\) 0 0
\(425\) 101.949i 0.239879i
\(426\) 0 0
\(427\) 737.470 1.72710
\(428\) 0 0
\(429\) −796.828 + 493.006i −1.85741 + 1.14920i
\(430\) 0 0
\(431\) 618.539i 1.43513i 0.696494 + 0.717563i \(0.254742\pi\)
−0.696494 + 0.717563i \(0.745258\pi\)
\(432\) 0 0
\(433\) 211.763 0.489061 0.244530 0.969642i \(-0.421366\pi\)
0.244530 + 0.969642i \(0.421366\pi\)
\(434\) 0 0
\(435\) −26.0557 42.1129i −0.0598981 0.0968112i
\(436\) 0 0
\(437\) 193.526i 0.442851i
\(438\) 0 0
\(439\) 56.6884 0.129131 0.0645654 0.997913i \(-0.479434\pi\)
0.0645654 + 0.997913i \(0.479434\pi\)
\(440\) 0 0
\(441\) −223.797 + 448.690i −0.507476 + 1.01744i
\(442\) 0 0
\(443\) 687.493i 1.55190i 0.630792 + 0.775952i \(0.282730\pi\)
−0.630792 + 0.775952i \(0.717270\pi\)
\(444\) 0 0
\(445\) −173.401 −0.389666
\(446\) 0 0
\(447\) −193.994 + 120.026i −0.433992 + 0.268515i
\(448\) 0 0
\(449\) 490.455i 1.09233i −0.837679 0.546163i \(-0.816088\pi\)
0.837679 0.546163i \(-0.183912\pi\)
\(450\) 0 0
\(451\) 1310.86 2.90657
\(452\) 0 0
\(453\) 283.989 + 459.002i 0.626908 + 1.01325i
\(454\) 0 0
\(455\) 252.307i 0.554522i
\(456\) 0 0
\(457\) −537.122 −1.17532 −0.587661 0.809107i \(-0.699951\pi\)
−0.587661 + 0.809107i \(0.699951\pi\)
\(458\) 0 0
\(459\) −10.7960 117.797i −0.0235206 0.256639i
\(460\) 0 0
\(461\) 129.931i 0.281847i −0.990021 0.140923i \(-0.954993\pi\)
0.990021 0.140923i \(-0.0450071\pi\)
\(462\) 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
\(467\) 418.978i 0.897169i −0.893740 0.448585i \(-0.851928\pi\)
0.893740 0.448585i \(-0.148072\pi\)
\(468\) 0 0
\(469\) 576.643 1.22952
\(470\) 0 0
\(471\) 106.100 + 171.485i 0.225264 + 0.364087i
\(472\) 0 0
\(473\) 607.931i 1.28527i
\(474\) 0 0
\(475\) −268.871 −0.566043
\(476\) 0 0
\(477\) 654.823 + 326.612i 1.37280 + 0.684720i
\(478\) 0 0
\(479\) 306.699i 0.640290i 0.947369 + 0.320145i \(0.103732\pi\)
−0.947369 + 0.320145i \(0.896268\pi\)
\(480\) 0 0
\(481\) −348.249 −0.724011
\(482\) 0 0
\(483\) −437.249 + 270.530i −0.905278 + 0.560104i
\(484\) 0 0
\(485\) 26.8822i 0.0554272i
\(486\) 0 0
\(487\) 387.411 0.795506 0.397753 0.917493i \(-0.369790\pi\)
0.397753 + 0.917493i \(0.369790\pi\)
\(488\) 0 0
\(489\) −162.143 262.066i −0.331580 0.535922i
\(490\) 0 0
\(491\) 13.1250i 0.0267311i 0.999911 + 0.0133655i \(0.00425451\pi\)
−0.999911 + 0.0133655i \(0.995745\pi\)
\(492\) 0 0
\(493\) −54.9824 −0.111526
\(494\) 0 0
\(495\) −88.0385 + 176.508i −0.177855 + 0.356582i
\(496\) 0 0
\(497\) 1396.43i 2.80971i
\(498\) 0 0
\(499\) −239.526 −0.480012 −0.240006 0.970771i \(-0.577149\pi\)
−0.240006 + 0.970771i \(0.577149\pi\)
\(500\) 0 0
\(501\) −206.119 + 127.528i −0.411415 + 0.254546i
\(502\) 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
\(507\) 287.893 + 465.312i 0.567837 + 0.917775i
\(508\) 0 0
\(509\) 600.556i 1.17987i 0.807449 + 0.589937i \(0.200847\pi\)
−0.807449 + 0.589937i \(0.799153\pi\)
\(510\) 0 0
\(511\) 826.961 1.61832
\(512\) 0 0
\(513\) 310.668 28.4724i 0.605591 0.0555017i
\(514\) 0 0
\(515\) 149.616i 0.290517i
\(516\) 0 0
\(517\) 331.866 0.641908
\(518\) 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
\(523\) −639.213 −1.22221 −0.611103 0.791551i \(-0.709274\pi\)
−0.611103 + 0.791551i \(0.709274\pi\)
\(524\) 0 0
\(525\) −375.855 607.482i −0.715914 1.15711i
\(526\) 0 0
\(527\) 89.0102i 0.168900i
\(528\) 0 0
\(529\) 248.470 0.469697
\(530\) 0 0
\(531\) 241.192 + 120.302i 0.454223 + 0.226557i
\(532\) 0 0
\(533\) 1474.77i 2.76692i
\(534\) 0 0
\(535\) −8.23433 −0.0153913
\(536\) 0 0
\(537\) −436.205 + 269.884i −0.812300 + 0.502578i
\(538\) 0 0
\(539\) 928.273i 1.72221i
\(540\) 0 0
\(541\) −606.241 −1.12059 −0.560296 0.828292i \(-0.689313\pi\)
−0.560296 + 0.828292i \(0.689313\pi\)
\(542\) 0 0
\(543\) −62.5524 101.101i −0.115198 0.186190i
\(544\) 0 0
\(545\) 194.219i 0.356365i
\(546\) 0 0
\(547\) −409.425 −0.748492 −0.374246 0.927330i \(-0.622098\pi\)
−0.374246 + 0.927330i \(0.622098\pi\)
\(548\) 0 0
\(549\) 289.503 580.425i 0.527329 1.05724i
\(550\) 0 0
\(551\) 145.006i 0.263169i
\(552\) 0 0
\(553\) 880.352 1.59196
\(554\) 0 0
\(555\) −62.3409 + 38.5709i −0.112326 + 0.0694972i
\(556\) 0 0
\(557\) 994.040i 1.78463i 0.451411 + 0.892316i \(0.350921\pi\)
−0.451411 + 0.892316i \(0.649079\pi\)
\(558\) 0 0
\(559\) 683.945 1.22351
\(560\) 0 0
\(561\) 115.224 + 186.233i 0.205391 + 0.331966i
\(562\) 0 0
\(563\) 29.5954i 0.0525673i 0.999655 + 0.0262837i \(0.00836731\pi\)
−0.999655 + 0.0262837i \(0.991633\pi\)
\(564\) 0 0
\(565\) 67.5958 0.119639
\(566\) 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
\(571\) −133.482 −0.233769 −0.116885 0.993145i \(-0.537291\pi\)
−0.116885 + 0.993145i \(0.537291\pi\)
\(572\) 0 0
\(573\) 612.071 378.694i 1.06819 0.660898i
\(574\) 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
\(579\) −21.3046 34.4338i −0.0367954 0.0594712i
\(580\) 0 0
\(581\) 822.993i 1.41651i
\(582\) 0 0
\(583\) −1354.73 −2.32372
\(584\) 0 0
\(585\) 198.578 + 99.0465i 0.339450 + 0.169310i
\(586\) 0 0
\(587\) 633.349i 1.07896i 0.841998 + 0.539480i \(0.181379\pi\)
−0.841998 + 0.539480i \(0.818621\pi\)
\(588\) 0 0
\(589\) 234.748 0.398553
\(590\) 0 0
\(591\) −42.3598 + 26.2084i −0.0716748 + 0.0443459i
\(592\) 0 0
\(593\) 189.510i 0.319578i 0.987151 + 0.159789i \(0.0510813\pi\)
−0.987151 + 0.159789i \(0.948919\pi\)
\(594\) 0 0
\(595\) 58.9688 0.0991071
\(596\) 0 0
\(597\) −226.781 366.538i −0.379867 0.613967i
\(598\) 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 \(-0.355118\pi\)
0.439605 + 0.898191i \(0.355118\pi\)
\(602\) 0 0
\(603\) 226.369 453.846i 0.375404 0.752647i
\(604\) 0 0
\(605\) 206.013i 0.340517i
\(606\) 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
\(611\) 373.362i 0.611067i
\(612\) 0 0
\(613\) −67.7073 −0.110452 −0.0552262 0.998474i \(-0.517588\pi\)
−0.0552262 + 0.998474i \(0.517588\pi\)
\(614\) 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
\(619\) −122.858 −0.198479 −0.0992393 0.995064i \(-0.531641\pi\)
−0.0992393 + 0.995064i \(0.531641\pi\)
\(620\) 0 0
\(621\) 41.2728 + 450.337i 0.0664619 + 0.725180i
\(622\) 0 0
\(623\) 1349.01i 2.16534i
\(624\) 0 0
\(625\) 498.235 0.797176
\(626\) 0 0
\(627\) −491.155 + 303.882i −0.783341 + 0.484661i
\(628\) 0 0
\(629\) 81.3921i 0.129399i
\(630\) 0 0
\(631\) −141.286 −0.223908 −0.111954 0.993713i \(-0.535711\pi\)
−0.111954 + 0.993713i \(0.535711\pi\)
\(632\) 0 0
\(633\) −132.045 213.420i −0.208602 0.337156i
\(634\) 0 0
\(635\) 191.486i 0.301553i
\(636\) 0 0
\(637\) −1044.34 −1.63947
\(638\) 0 0
\(639\) −1099.06 548.186i −1.71996 0.857881i
\(640\) 0 0
\(641\) 240.601i 0.375352i −0.982231 0.187676i \(-0.939904\pi\)
0.982231 0.187676i \(-0.0600955\pi\)
\(642\) 0 0
\(643\) −774.975 −1.20525 −0.602624 0.798025i \(-0.705878\pi\)
−0.602624 + 0.798025i \(0.705878\pi\)
\(644\) 0 0
\(645\) 122.435 75.7515i 0.189821 0.117444i
\(646\) 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
\(651\) 328.155 + 530.386i 0.504078 + 0.814724i
\(652\) 0 0
\(653\) 142.733i 0.218581i −0.994010 0.109290i \(-0.965142\pi\)
0.994010 0.109290i \(-0.0348579\pi\)
\(654\) 0 0
\(655\) 59.7154 0.0911685
\(656\) 0 0
\(657\) 324.634 650.859i 0.494116 0.990652i
\(658\) 0 0
\(659\) 485.418i 0.736598i −0.929707 0.368299i \(-0.879940\pi\)
0.929707 0.368299i \(-0.120060\pi\)
\(660\) 0 0
\(661\) 89.9502 0.136082 0.0680410 0.997683i \(-0.478325\pi\)
0.0680410 + 0.997683i \(0.478325\pi\)
\(662\) 0 0
\(663\) 209.519 129.632i 0.316017 0.195523i
\(664\) 0 0
\(665\) 155.519i 0.233863i
\(666\) 0 0
\(667\) 210.197 0.315138
\(668\) 0 0
\(669\) −231.869 374.763i −0.346591 0.560184i
\(670\) 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
\(675\) −625.665 + 57.3415i −0.926911 + 0.0849503i
\(676\) 0 0
\(677\) 207.151i 0.305984i −0.988227 0.152992i \(-0.951109\pi\)
0.988227 0.152992i \(-0.0488909\pi\)
\(678\) 0 0
\(679\) 209.134 0.308003
\(680\) 0 0
\(681\) −72.7724 + 45.0250i −0.106861 + 0.0661160i
\(682\) 0 0
\(683\) 680.228i 0.995941i −0.867194 0.497970i \(-0.834079\pi\)
0.867194 0.497970i \(-0.165921\pi\)
\(684\) 0 0
\(685\) 235.652 0.344017
\(686\) 0 0
\(687\) −544.748 880.458i −0.792938 1.28160i
\(688\) 0 0
\(689\) 1524.12i 2.21208i
\(690\) 0 0
\(691\) 480.570 0.695470 0.347735 0.937593i \(-0.386951\pi\)
0.347735 + 0.937593i \(0.386951\pi\)
\(692\) 0 0
\(693\) −1373.17 684.910i −1.98149 0.988326i
\(694\) 0 0
\(695\) 66.9297i 0.0963018i
\(696\) 0 0
\(697\) −344.680 −0.494520
\(698\) 0 0
\(699\) −268.567 + 166.165i −0.384216 + 0.237718i
\(700\) 0 0
\(701\) 854.903i 1.21955i −0.792575 0.609774i \(-0.791260\pi\)
0.792575 0.609774i \(-0.208740\pi\)
\(702\) 0 0
\(703\) −214.656 −0.305343
\(704\) 0 0
\(705\) −41.3523 66.8364i −0.0586558 0.0948034i
\(706\) 0 0
\(707\) 1467.13i 2.07515i
\(708\) 0 0
\(709\) −990.069 −1.39643 −0.698215 0.715888i \(-0.746022\pi\)
−0.698215 + 0.715888i \(0.746022\pi\)
\(710\) 0 0
\(711\) 345.593 692.880i 0.486067 0.974514i
\(712\) 0 0
\(713\) 340.285i 0.477258i
\(714\) 0 0
\(715\) −410.828 −0.574585
\(716\) 0 0
\(717\) −715.495 + 442.684i −0.997901 + 0.617411i
\(718\) 0 0
\(719\) 502.244i 0.698531i 0.937024 + 0.349266i \(0.113569\pi\)
−0.937024 + 0.349266i \(0.886431\pi\)
\(720\) 0 0
\(721\) −1163.97 −1.61438
\(722\) 0 0
\(723\) −583.760 943.511i −0.807413 1.30499i
\(724\) 0 0
\(725\) 292.032i 0.402803i
\(726\) 0 0
\(727\) −718.280 −0.988005 −0.494002 0.869461i \(-0.664467\pi\)
−0.494002 + 0.869461i \(0.664467\pi\)
\(728\) 0 0
\(729\) 716.856 132.511i 0.983341 0.181771i
\(730\) 0 0
\(731\) 159.850i 0.218673i
\(732\) 0 0
\(733\) −1362.31 −1.85854 −0.929272 0.369397i \(-0.879564\pi\)
−0.929272 + 0.369397i \(0.879564\pi\)
\(734\) 0 0
\(735\) −186.950 + 115.668i −0.254354 + 0.157371i
\(736\) 0 0
\(737\) 938.939i 1.27400i
\(738\) 0 0
\(739\) 1057.01 1.43033 0.715164 0.698957i \(-0.246352\pi\)
0.715164 + 0.698957i \(0.246352\pi\)
\(740\) 0 0
\(741\) 341.879 + 552.568i 0.461375 + 0.745705i
\(742\) 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
\(747\) 647.736 + 323.076i 0.867116 + 0.432499i
\(748\) 0 0
\(749\) 64.0603i 0.0855278i
\(750\) 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
\(755\) 236.652i 0.313447i
\(756\) 0 0
\(757\) 38.6736 0.0510879 0.0255440 0.999674i \(-0.491868\pi\)
0.0255440 + 0.999674i \(0.491868\pi\)
\(758\) 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
\(763\) −1510.96 −1.98029
\(764\) 0 0
\(765\) 23.1489 46.4113i 0.0302601 0.0606684i
\(766\) 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
\(771\) −12.5632 + 7.77298i −0.0162947 + 0.0100817i
\(772\) 0 0
\(773\) 747.603i 0.967145i 0.875304 + 0.483572i \(0.160661\pi\)
−0.875304 + 0.483572i \(0.839339\pi\)
\(774\) 0 0
\(775\) −472.767 −0.610022
\(776\) 0 0
\(777\) −300.069 484.991i −0.386189 0.624184i
\(778\) 0 0
\(779\) 909.030i 1.16692i
\(780\) 0 0
\(781\) 2273.78 2.91137
\(782\) 0 0
\(783\) −30.9251 337.430i −0.0394957 0.430946i
\(784\) 0 0
\(785\) 88.4143i 0.112630i
\(786\) 0 0
\(787\) 975.671 1.23973 0.619867 0.784707i \(-0.287186\pi\)
0.619867 + 0.784707i \(0.287186\pi\)
\(788\) 0 0
\(789\) 672.427 416.037i 0.852252 0.527297i
\(790\) 0 0
\(791\) 525.873i 0.664820i
\(792\) 0 0
\(793\) 1350.96 1.70360
\(794\) 0 0
\(795\) 168.807 + 272.837i 0.212336 + 0.343191i
\(796\) 0 0
\(797\) 417.874i 0.524309i 0.965026 + 0.262154i \(0.0844330\pi\)
−0.965026 + 0.262154i \(0.915567\pi\)
\(798\) 0 0
\(799\) −87.2613 −0.109213
\(800\) 0 0
\(801\) −1061.73