Properties

Label 1400.2.q.f.1201.1
Level $1400$
Weight $2$
Character 1400.1201
Analytic conductor $11.179$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1400.q (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.1790562830\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1201.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1400.1201
Dual form 1400.2.q.f.401.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 - 1.73205i) q^{3} +(-0.500000 + 2.59808i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(1.00000 - 1.73205i) q^{3} +(-0.500000 + 2.59808i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-2.00000 + 3.46410i) q^{11} +2.00000 q^{13} +(-1.50000 + 2.59808i) q^{17} +(4.00000 + 3.46410i) q^{21} +(1.50000 + 2.59808i) q^{23} +4.00000 q^{27} -6.00000 q^{29} +(-4.50000 + 7.79423i) q^{31} +(4.00000 + 6.92820i) q^{33} +(2.00000 - 3.46410i) q^{39} +5.00000 q^{41} +6.00000 q^{43} +(4.50000 + 7.79423i) q^{47} +(-6.50000 - 2.59808i) q^{49} +(3.00000 + 5.19615i) q^{51} +(-3.00000 + 5.19615i) q^{53} +(-4.00000 + 6.92820i) q^{59} +(-4.00000 - 6.92820i) q^{61} +(2.50000 - 0.866025i) q^{63} +(7.00000 - 12.1244i) q^{67} +6.00000 q^{69} +11.0000 q^{71} +(-1.00000 + 1.73205i) q^{73} +(-8.00000 - 6.92820i) q^{77} +(-4.50000 - 7.79423i) q^{79} +(5.50000 - 9.52628i) q^{81} +6.00000 q^{83} +(-6.00000 + 10.3923i) q^{87} +(-5.50000 - 9.52628i) q^{89} +(-1.00000 + 5.19615i) q^{91} +(9.00000 + 15.5885i) q^{93} +11.0000 q^{97} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{3} - q^{7} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{3} - q^{7} - q^{9} - 4 q^{11} + 4 q^{13} - 3 q^{17} + 8 q^{21} + 3 q^{23} + 8 q^{27} - 12 q^{29} - 9 q^{31} + 8 q^{33} + 4 q^{39} + 10 q^{41} + 12 q^{43} + 9 q^{47} - 13 q^{49} + 6 q^{51} - 6 q^{53} - 8 q^{59} - 8 q^{61} + 5 q^{63} + 14 q^{67} + 12 q^{69} + 22 q^{71} - 2 q^{73} - 16 q^{77} - 9 q^{79} + 11 q^{81} + 12 q^{83} - 12 q^{87} - 11 q^{89} - 2 q^{91} + 18 q^{93} + 22 q^{97} + 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times\).

\(n\) \(351\) \(701\) \(801\) \(1177\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(3\) 1.00000 1.73205i 0.577350 1.00000i −0.418432 0.908248i \(-0.637420\pi\)
0.995782 0.0917517i \(-0.0292466\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −0.500000 + 2.59808i −0.188982 + 0.981981i
\(8\) 0 0
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) −2.00000 + 3.46410i −0.603023 + 1.04447i 0.389338 + 0.921095i \(0.372704\pi\)
−0.992361 + 0.123371i \(0.960630\pi\)
\(12\) 0 0
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.50000 + 2.59808i −0.363803 + 0.630126i −0.988583 0.150675i \(-0.951855\pi\)
0.624780 + 0.780801i \(0.285189\pi\)
\(18\) 0 0
\(19\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(20\) 0 0
\(21\) 4.00000 + 3.46410i 0.872872 + 0.755929i
\(22\) 0 0
\(23\) 1.50000 + 2.59808i 0.312772 + 0.541736i 0.978961 0.204046i \(-0.0654092\pi\)
−0.666190 + 0.745782i \(0.732076\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 4.00000 0.769800
\(28\) 0 0
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) 0 0
\(31\) −4.50000 + 7.79423i −0.808224 + 1.39988i 0.105869 + 0.994380i \(0.466238\pi\)
−0.914093 + 0.405505i \(0.867096\pi\)
\(32\) 0 0
\(33\) 4.00000 + 6.92820i 0.696311 + 1.20605i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(38\) 0 0
\(39\) 2.00000 3.46410i 0.320256 0.554700i
\(40\) 0 0
\(41\) 5.00000 0.780869 0.390434 0.920631i \(-0.372325\pi\)
0.390434 + 0.920631i \(0.372325\pi\)
\(42\) 0 0
\(43\) 6.00000 0.914991 0.457496 0.889212i \(-0.348747\pi\)
0.457496 + 0.889212i \(0.348747\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 4.50000 + 7.79423i 0.656392 + 1.13691i 0.981543 + 0.191243i \(0.0612518\pi\)
−0.325150 + 0.945662i \(0.605415\pi\)
\(48\) 0 0
\(49\) −6.50000 2.59808i −0.928571 0.371154i
\(50\) 0 0
\(51\) 3.00000 + 5.19615i 0.420084 + 0.727607i
\(52\) 0 0
\(53\) −3.00000 + 5.19615i −0.412082 + 0.713746i −0.995117 0.0987002i \(-0.968532\pi\)
0.583036 + 0.812447i \(0.301865\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −4.00000 + 6.92820i −0.520756 + 0.901975i 0.478953 + 0.877841i \(0.341016\pi\)
−0.999709 + 0.0241347i \(0.992317\pi\)
\(60\) 0 0
\(61\) −4.00000 6.92820i −0.512148 0.887066i −0.999901 0.0140840i \(-0.995517\pi\)
0.487753 0.872982i \(-0.337817\pi\)
\(62\) 0 0
\(63\) 2.50000 0.866025i 0.314970 0.109109i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 7.00000 12.1244i 0.855186 1.48123i −0.0212861 0.999773i \(-0.506776\pi\)
0.876472 0.481452i \(-0.159891\pi\)
\(68\) 0 0
\(69\) 6.00000 0.722315
\(70\) 0 0
\(71\) 11.0000 1.30546 0.652730 0.757591i \(-0.273624\pi\)
0.652730 + 0.757591i \(0.273624\pi\)
\(72\) 0 0
\(73\) −1.00000 + 1.73205i −0.117041 + 0.202721i −0.918594 0.395203i \(-0.870674\pi\)
0.801553 + 0.597924i \(0.204008\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −8.00000 6.92820i −0.911685 0.789542i
\(78\) 0 0
\(79\) −4.50000 7.79423i −0.506290 0.876919i −0.999974 0.00727784i \(-0.997683\pi\)
0.493684 0.869641i \(-0.335650\pi\)
\(80\) 0 0
\(81\) 5.50000 9.52628i 0.611111 1.05848i
\(82\) 0 0
\(83\) 6.00000 0.658586 0.329293 0.944228i \(-0.393190\pi\)
0.329293 + 0.944228i \(0.393190\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −6.00000 + 10.3923i −0.643268 + 1.11417i
\(88\) 0 0
\(89\) −5.50000 9.52628i −0.582999 1.00978i −0.995122 0.0986553i \(-0.968546\pi\)
0.412123 0.911128i \(-0.364787\pi\)
\(90\) 0 0
\(91\) −1.00000 + 5.19615i −0.104828 + 0.544705i
\(92\) 0 0
\(93\) 9.00000 + 15.5885i 0.933257 + 1.61645i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 11.0000 1.11688 0.558440 0.829545i \(-0.311400\pi\)
0.558440 + 0.829545i \(0.311400\pi\)
\(98\) 0 0
\(99\) 4.00000 0.402015
\(100\) 0 0
\(101\) 4.00000 6.92820i 0.398015 0.689382i −0.595466 0.803380i \(-0.703033\pi\)
0.993481 + 0.113998i \(0.0363659\pi\)
\(102\) 0 0
\(103\) 7.50000 + 12.9904i 0.738997 + 1.27998i 0.952947 + 0.303136i \(0.0980336\pi\)
−0.213950 + 0.976845i \(0.568633\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 4.00000 + 6.92820i 0.386695 + 0.669775i 0.992003 0.126217i \(-0.0402834\pi\)
−0.605308 + 0.795991i \(0.706950\pi\)
\(108\) 0 0
\(109\) 7.00000 12.1244i 0.670478 1.16130i −0.307290 0.951616i \(-0.599422\pi\)
0.977769 0.209687i \(-0.0672444\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −15.0000 −1.41108 −0.705541 0.708669i \(-0.749296\pi\)
−0.705541 + 0.708669i \(0.749296\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −1.00000 1.73205i −0.0924500 0.160128i
\(118\) 0 0
\(119\) −6.00000 5.19615i −0.550019 0.476331i
\(120\) 0 0
\(121\) −2.50000 4.33013i −0.227273 0.393648i
\(122\) 0 0
\(123\) 5.00000 8.66025i 0.450835 0.780869i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −8.00000 −0.709885 −0.354943 0.934888i \(-0.615500\pi\)
−0.354943 + 0.934888i \(0.615500\pi\)
\(128\) 0 0
\(129\) 6.00000 10.3923i 0.528271 0.914991i
\(130\) 0 0
\(131\) −6.00000 10.3923i −0.524222 0.907980i −0.999602 0.0281993i \(-0.991023\pi\)
0.475380 0.879781i \(-0.342311\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 8.50000 14.7224i 0.726204 1.25782i −0.232273 0.972651i \(-0.574616\pi\)
0.958477 0.285171i \(-0.0920506\pi\)
\(138\) 0 0
\(139\) −6.00000 −0.508913 −0.254457 0.967084i \(-0.581897\pi\)
−0.254457 + 0.967084i \(0.581897\pi\)
\(140\) 0 0
\(141\) 18.0000 1.51587
\(142\) 0 0
\(143\) −4.00000 + 6.92820i −0.334497 + 0.579365i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −11.0000 + 8.66025i −0.907265 + 0.714286i
\(148\) 0 0
\(149\) 10.0000 + 17.3205i 0.819232 + 1.41895i 0.906249 + 0.422744i \(0.138933\pi\)
−0.0870170 + 0.996207i \(0.527733\pi\)
\(150\) 0 0
\(151\) −10.0000 + 17.3205i −0.813788 + 1.40952i 0.0964061 + 0.995342i \(0.469265\pi\)
−0.910195 + 0.414181i \(0.864068\pi\)
\(152\) 0 0
\(153\) 3.00000 0.242536
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 5.00000 8.66025i 0.399043 0.691164i −0.594565 0.804048i \(-0.702676\pi\)
0.993608 + 0.112884i \(0.0360089\pi\)
\(158\) 0 0
\(159\) 6.00000 + 10.3923i 0.475831 + 0.824163i
\(160\) 0 0
\(161\) −7.50000 + 2.59808i −0.591083 + 0.204757i
\(162\) 0 0
\(163\) −12.0000 20.7846i −0.939913 1.62798i −0.765631 0.643280i \(-0.777573\pi\)
−0.174282 0.984696i \(-0.555760\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 8.00000 + 13.8564i 0.608229 + 1.05348i 0.991532 + 0.129861i \(0.0414530\pi\)
−0.383304 + 0.923622i \(0.625214\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 8.00000 + 13.8564i 0.601317 + 1.04151i
\(178\) 0 0
\(179\) −2.00000 + 3.46410i −0.149487 + 0.258919i −0.931038 0.364922i \(-0.881096\pi\)
0.781551 + 0.623841i \(0.214429\pi\)
\(180\) 0 0
\(181\) −8.00000 −0.594635 −0.297318 0.954779i \(-0.596092\pi\)
−0.297318 + 0.954779i \(0.596092\pi\)
\(182\) 0 0
\(183\) −16.0000 −1.18275
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −6.00000 10.3923i −0.438763 0.759961i
\(188\) 0 0
\(189\) −2.00000 + 10.3923i −0.145479 + 0.755929i
\(190\) 0 0
\(191\) 6.50000 + 11.2583i 0.470323 + 0.814624i 0.999424 0.0339349i \(-0.0108039\pi\)
−0.529101 + 0.848559i \(0.677471\pi\)
\(192\) 0 0
\(193\) 2.50000 4.33013i 0.179954 0.311689i −0.761911 0.647682i \(-0.775738\pi\)
0.941865 + 0.335993i \(0.109072\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 0 0
\(199\) −10.5000 + 18.1865i −0.744325 + 1.28921i 0.206184 + 0.978513i \(0.433895\pi\)
−0.950509 + 0.310696i \(0.899438\pi\)
\(200\) 0 0
\(201\) −14.0000 24.2487i −0.987484 1.71037i
\(202\) 0 0
\(203\) 3.00000 15.5885i 0.210559 1.09410i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 1.50000 2.59808i 0.104257 0.180579i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 22.0000 1.51454 0.757271 0.653101i \(-0.226532\pi\)
0.757271 + 0.653101i \(0.226532\pi\)
\(212\) 0 0
\(213\) 11.0000 19.0526i 0.753708 1.30546i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −18.0000 15.5885i −1.22192 1.05821i
\(218\) 0 0
\(219\) 2.00000 + 3.46410i 0.135147 + 0.234082i
\(220\) 0 0
\(221\) −3.00000 + 5.19615i −0.201802 + 0.349531i
\(222\) 0 0
\(223\) −11.0000 −0.736614 −0.368307 0.929704i \(-0.620063\pi\)
−0.368307 + 0.929704i \(0.620063\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −11.0000 + 19.0526i −0.730096 + 1.26456i 0.226746 + 0.973954i \(0.427191\pi\)
−0.956842 + 0.290609i \(0.906142\pi\)
\(228\) 0 0
\(229\) 4.00000 + 6.92820i 0.264327 + 0.457829i 0.967387 0.253302i \(-0.0815167\pi\)
−0.703060 + 0.711131i \(0.748183\pi\)
\(230\) 0 0
\(231\) −20.0000 + 6.92820i −1.31590 + 0.455842i
\(232\) 0 0
\(233\) −11.0000 19.0526i −0.720634 1.24817i −0.960746 0.277429i \(-0.910518\pi\)
0.240112 0.970745i \(-0.422816\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −18.0000 −1.16923
\(238\) 0 0
\(239\) 11.0000 0.711531 0.355765 0.934575i \(-0.384220\pi\)
0.355765 + 0.934575i \(0.384220\pi\)
\(240\) 0 0
\(241\) −9.00000 + 15.5885i −0.579741 + 1.00414i 0.415768 + 0.909471i \(0.363513\pi\)
−0.995509 + 0.0946700i \(0.969820\pi\)
\(242\) 0 0
\(243\) −5.00000 8.66025i −0.320750 0.555556i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 6.00000 10.3923i 0.380235 0.658586i
\(250\) 0 0
\(251\) −16.0000 −1.00991 −0.504956 0.863145i \(-0.668491\pi\)
−0.504956 + 0.863145i \(0.668491\pi\)
\(252\) 0 0
\(253\) −12.0000 −0.754434
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 9.00000 + 15.5885i 0.561405 + 0.972381i 0.997374 + 0.0724199i \(0.0230722\pi\)
−0.435970 + 0.899961i \(0.643595\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 3.00000 + 5.19615i 0.185695 + 0.321634i
\(262\) 0 0
\(263\) −1.50000 + 2.59808i −0.0924940 + 0.160204i −0.908560 0.417755i \(-0.862817\pi\)
0.816066 + 0.577959i \(0.196151\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −22.0000 −1.34638
\(268\) 0 0
\(269\) 1.00000 1.73205i 0.0609711 0.105605i −0.833929 0.551872i \(-0.813914\pi\)
0.894900 + 0.446267i \(0.147247\pi\)
\(270\) 0 0
\(271\) −3.50000 6.06218i −0.212610 0.368251i 0.739921 0.672694i \(-0.234863\pi\)
−0.952531 + 0.304443i \(0.901530\pi\)
\(272\) 0 0
\(273\) 8.00000 + 6.92820i 0.484182 + 0.419314i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 4.00000 6.92820i 0.240337 0.416275i −0.720473 0.693482i \(-0.756075\pi\)
0.960810 + 0.277207i \(0.0894088\pi\)
\(278\) 0 0
\(279\) 9.00000 0.538816
\(280\) 0 0
\(281\) −13.0000 −0.775515 −0.387757 0.921761i \(-0.626750\pi\)
−0.387757 + 0.921761i \(0.626750\pi\)
\(282\) 0 0
\(283\) 1.00000 1.73205i 0.0594438 0.102960i −0.834772 0.550596i \(-0.814401\pi\)
0.894216 + 0.447636i \(0.147734\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −2.50000 + 12.9904i −0.147570 + 0.766798i
\(288\) 0 0
\(289\) 4.00000 + 6.92820i 0.235294 + 0.407541i
\(290\) 0 0
\(291\) 11.0000 19.0526i 0.644831 1.11688i
\(292\) 0 0
\(293\) −14.0000 −0.817889 −0.408944 0.912559i \(-0.634103\pi\)
−0.408944 + 0.912559i \(0.634103\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −8.00000 + 13.8564i −0.464207 + 0.804030i
\(298\) 0 0
\(299\) 3.00000 + 5.19615i 0.173494 + 0.300501i
\(300\) 0 0
\(301\) −3.00000 + 15.5885i −0.172917 + 0.898504i
\(302\) 0 0
\(303\) −8.00000 13.8564i −0.459588 0.796030i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 24.0000 1.36975 0.684876 0.728659i \(-0.259856\pi\)
0.684876 + 0.728659i \(0.259856\pi\)
\(308\) 0 0
\(309\) 30.0000 1.70664
\(310\) 0 0
\(311\) −0.500000 + 0.866025i −0.0283524 + 0.0491078i −0.879853 0.475245i \(-0.842359\pi\)
0.851501 + 0.524353i \(0.175693\pi\)
\(312\) 0 0
\(313\) −15.5000 26.8468i −0.876112 1.51747i −0.855574 0.517681i \(-0.826795\pi\)
−0.0205381 0.999789i \(-0.506538\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −6.00000 10.3923i −0.336994 0.583690i 0.646872 0.762598i \(-0.276077\pi\)
−0.983866 + 0.178908i \(0.942743\pi\)
\(318\) 0 0
\(319\) 12.0000 20.7846i 0.671871 1.16371i
\(320\) 0 0
\(321\) 16.0000 0.893033
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −14.0000 24.2487i −0.774202 1.34096i
\(328\) 0 0
\(329\) −22.5000 + 7.79423i −1.24047 + 0.429710i
\(330\) 0 0
\(331\) 1.00000 + 1.73205i 0.0549650 + 0.0952021i 0.892199 0.451643i \(-0.149162\pi\)
−0.837234 + 0.546845i \(0.815829\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 29.0000 1.57973 0.789865 0.613280i \(-0.210150\pi\)
0.789865 + 0.613280i \(0.210150\pi\)
\(338\) 0 0
\(339\) −15.0000 + 25.9808i −0.814688 + 1.41108i
\(340\) 0 0
\(341\) −18.0000 31.1769i −0.974755 1.68832i
\(342\) 0 0
\(343\) 10.0000 15.5885i 0.539949 0.841698i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1.00000 1.73205i 0.0536828 0.0929814i −0.837935 0.545770i \(-0.816237\pi\)
0.891618 + 0.452788i \(0.149571\pi\)
\(348\) 0 0
\(349\) 14.0000 0.749403 0.374701 0.927146i \(-0.377745\pi\)
0.374701 + 0.927146i \(0.377745\pi\)
\(350\) 0 0
\(351\) 8.00000 0.427008
\(352\) 0 0
\(353\) 7.50000 12.9904i 0.399185 0.691408i −0.594441 0.804139i \(-0.702627\pi\)
0.993626 + 0.112731i \(0.0359599\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −15.0000 + 5.19615i −0.793884 + 0.275010i
\(358\) 0 0
\(359\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(360\) 0 0
\(361\) 9.50000 16.4545i 0.500000 0.866025i
\(362\) 0 0
\(363\) −10.0000 −0.524864
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 8.00000 13.8564i 0.417597 0.723299i −0.578101 0.815966i \(-0.696206\pi\)
0.995697 + 0.0926670i \(0.0295392\pi\)
\(368\) 0 0
\(369\) −2.50000 4.33013i −0.130145 0.225417i
\(370\) 0 0
\(371\) −12.0000 10.3923i −0.623009 0.539542i
\(372\) 0 0
\(373\) 3.00000 + 5.19615i 0.155334 + 0.269047i 0.933181 0.359408i \(-0.117021\pi\)
−0.777847 + 0.628454i \(0.783688\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −12.0000 −0.618031
\(378\) 0 0
\(379\) 4.00000 0.205466 0.102733 0.994709i \(-0.467241\pi\)
0.102733 + 0.994709i \(0.467241\pi\)
\(380\) 0 0
\(381\) −8.00000 + 13.8564i −0.409852 + 0.709885i
\(382\) 0 0
\(383\) 10.5000 + 18.1865i 0.536525 + 0.929288i 0.999088 + 0.0427020i \(0.0135966\pi\)
−0.462563 + 0.886586i \(0.653070\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −3.00000 5.19615i −0.152499 0.264135i
\(388\) 0 0
\(389\) −17.0000 + 29.4449i −0.861934 + 1.49291i 0.00812520 + 0.999967i \(0.497414\pi\)
−0.870059 + 0.492947i \(0.835920\pi\)
\(390\) 0 0
\(391\) −9.00000 −0.455150
\(392\) 0 0
\(393\) −24.0000 −1.21064
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −19.0000 32.9090i −0.953583 1.65165i −0.737579 0.675261i \(-0.764031\pi\)
−0.216004 0.976392i \(-0.569302\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −9.00000 15.5885i −0.449439 0.778450i 0.548911 0.835881i \(-0.315043\pi\)
−0.998350 + 0.0574304i \(0.981709\pi\)
\(402\) 0 0
\(403\) −9.00000 + 15.5885i −0.448322 + 0.776516i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 15.5000 26.8468i 0.766426 1.32749i −0.173064 0.984911i \(-0.555367\pi\)
0.939490 0.342578i \(-0.111300\pi\)
\(410\) 0 0
\(411\) −17.0000 29.4449i −0.838548 1.45241i
\(412\) 0 0
\(413\) −16.0000 13.8564i −0.787309 0.681829i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −6.00000 + 10.3923i −0.293821 + 0.508913i
\(418\) 0 0
\(419\) 30.0000 1.46560 0.732798 0.680446i \(-0.238214\pi\)
0.732798 + 0.680446i \(0.238214\pi\)
\(420\) 0 0
\(421\) 20.0000 0.974740 0.487370 0.873195i \(-0.337956\pi\)
0.487370 + 0.873195i \(0.337956\pi\)
\(422\) 0 0
\(423\) 4.50000 7.79423i 0.218797 0.378968i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 20.0000 6.92820i 0.967868 0.335279i
\(428\) 0 0
\(429\) 8.00000 + 13.8564i 0.386244 + 0.668994i
\(430\) 0 0
\(431\) 15.5000 26.8468i 0.746609 1.29316i −0.202831 0.979214i \(-0.565014\pi\)
0.949439 0.313950i \(-0.101653\pi\)
\(432\) 0 0
\(433\) −21.0000 −1.00920 −0.504598 0.863355i \(-0.668359\pi\)
−0.504598 + 0.863355i \(0.668359\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −17.5000 30.3109i −0.835229 1.44666i −0.893843 0.448379i \(-0.852001\pi\)
0.0586141 0.998281i \(-0.481332\pi\)
\(440\) 0 0
\(441\) 1.00000 + 6.92820i 0.0476190 + 0.329914i
\(442\) 0 0
\(443\) 6.00000 + 10.3923i 0.285069 + 0.493753i 0.972626 0.232377i \(-0.0746503\pi\)
−0.687557 + 0.726130i \(0.741317\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 40.0000 1.89194
\(448\) 0 0
\(449\) −27.0000 −1.27421 −0.637104 0.770778i \(-0.719868\pi\)
−0.637104 + 0.770778i \(0.719868\pi\)
\(450\) 0 0
\(451\) −10.0000 + 17.3205i −0.470882 + 0.815591i
\(452\) 0 0
\(453\) 20.0000 + 34.6410i 0.939682 + 1.62758i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 1.00000 + 1.73205i 0.0467780 + 0.0810219i 0.888466 0.458942i \(-0.151771\pi\)
−0.841688 + 0.539964i \(0.818438\pi\)
\(458\) 0 0
\(459\) −6.00000 + 10.3923i −0.280056 + 0.485071i
\(460\) 0 0
\(461\) 24.0000 1.11779 0.558896 0.829238i \(-0.311225\pi\)
0.558896 + 0.829238i \(0.311225\pi\)
\(462\) 0 0
\(463\) −11.0000 −0.511213 −0.255607 0.966781i \(-0.582275\pi\)
−0.255607 + 0.966781i \(0.582275\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −15.0000 25.9808i −0.694117 1.20225i −0.970477 0.241192i \(-0.922462\pi\)
0.276360 0.961054i \(-0.410872\pi\)
\(468\) 0 0
\(469\) 28.0000 + 24.2487i 1.29292 + 1.11970i
\(470\) 0 0
\(471\) −10.0000 17.3205i −0.460776 0.798087i
\(472\) 0 0
\(473\) −12.0000 + 20.7846i −0.551761 + 0.955677i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 6.00000 0.274721
\(478\) 0 0
\(479\) −4.50000 + 7.79423i −0.205610 + 0.356127i −0.950327 0.311253i \(-0.899251\pi\)
0.744717 + 0.667381i \(0.232585\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) −3.00000 + 15.5885i −0.136505 + 0.709299i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 11.5000 19.9186i 0.521115 0.902597i −0.478584 0.878042i \(-0.658850\pi\)
0.999698 0.0245553i \(-0.00781698\pi\)
\(488\) 0 0
\(489\) −48.0000 −2.17064
\(490\) 0 0
\(491\) 30.0000 1.35388 0.676941 0.736038i \(-0.263305\pi\)
0.676941 + 0.736038i \(0.263305\pi\)
\(492\) 0 0
\(493\) 9.00000 15.5885i 0.405340 0.702069i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −5.50000 + 28.5788i −0.246709 + 1.28194i
\(498\) 0 0
\(499\) −19.0000 32.9090i −0.850557 1.47321i −0.880707 0.473662i \(-0.842932\pi\)
0.0301498 0.999545i \(-0.490402\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 16.0000 0.713405 0.356702 0.934218i \(-0.383901\pi\)
0.356702 + 0.934218i \(0.383901\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −9.00000 + 15.5885i −0.399704 + 0.692308i
\(508\) 0 0
\(509\) −6.00000 10.3923i −0.265945 0.460631i 0.701866 0.712309i \(-0.252351\pi\)
−0.967811 + 0.251679i \(0.919017\pi\)
\(510\) 0 0
\(511\) −4.00000 3.46410i −0.176950 0.153243i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −36.0000 −1.58328
\(518\) 0 0
\(519\) 32.0000 1.40464
\(520\) 0 0
\(521\) −22.5000 + 38.9711i −0.985743 + 1.70736i −0.347155 + 0.937808i \(0.612852\pi\)
−0.638588 + 0.769549i \(0.720481\pi\)
\(522\) 0 0
\(523\) 11.0000 + 19.0526i 0.480996 + 0.833110i 0.999762 0.0218062i \(-0.00694167\pi\)
−0.518766 + 0.854916i \(0.673608\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −13.5000 23.3827i −0.588069 1.01857i
\(528\) 0 0
\(529\) 7.00000 12.1244i 0.304348 0.527146i
\(530\) 0 0
\(531\) 8.00000 0.347170
\(532\) 0 0
\(533\) 10.0000 0.433148
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 4.00000 + 6.92820i 0.172613 + 0.298974i
\(538\) 0 0
\(539\) 22.0000 17.3205i 0.947607 0.746047i
\(540\) 0 0
\(541\) 15.0000 + 25.9808i 0.644900 + 1.11700i 0.984325 + 0.176367i \(0.0564345\pi\)
−0.339424 + 0.940633i \(0.610232\pi\)
\(542\) 0 0
\(543\) −8.00000 + 13.8564i −0.343313 + 0.594635i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 40.0000 1.71028 0.855138 0.518400i \(-0.173472\pi\)
0.855138 + 0.518400i \(0.173472\pi\)
\(548\) 0 0
\(549\) −4.00000 + 6.92820i −0.170716 + 0.295689i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 22.5000 7.79423i 0.956797 0.331444i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −18.0000 + 31.1769i −0.762684 + 1.32101i 0.178778 + 0.983890i \(0.442786\pi\)
−0.941462 + 0.337119i \(0.890548\pi\)
\(558\) 0 0
\(559\) 12.0000 0.507546
\(560\) 0 0
\(561\) −24.0000 −1.01328
\(562\) 0 0
\(563\) −13.0000 + 22.5167i −0.547885 + 0.948964i 0.450535 + 0.892759i \(0.351233\pi\)
−0.998419 + 0.0562051i \(0.982100\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 22.0000 + 19.0526i 0.923913 + 0.800132i
\(568\) 0 0
\(569\) 5.50000 + 9.52628i 0.230572 + 0.399362i 0.957977 0.286846i \(-0.0926069\pi\)
−0.727405 + 0.686209i \(0.759274\pi\)
\(570\) 0 0
\(571\) 6.00000 10.3923i 0.251092 0.434904i −0.712735 0.701434i \(-0.752544\pi\)
0.963827 + 0.266529i \(0.0858769\pi\)
\(572\) 0 0
\(573\) 26.0000 1.08617
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 7.00000 12.1244i 0.291414 0.504744i −0.682730 0.730670i \(-0.739208\pi\)
0.974144 + 0.225927i \(0.0725410\pi\)
\(578\) 0 0
\(579\) −5.00000 8.66025i −0.207793 0.359908i
\(580\) 0 0
\(581\) −3.00000 + 15.5885i −0.124461 + 0.646718i
\(582\) 0 0
\(583\) −12.0000 20.7846i −0.496989 0.860811i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −8.00000 −0.330195 −0.165098 0.986277i \(-0.552794\pi\)
−0.165098 + 0.986277i \(0.552794\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 18.0000 31.1769i 0.740421 1.28245i
\(592\) 0 0
\(593\) −6.50000 11.2583i −0.266923 0.462324i 0.701143 0.713021i \(-0.252674\pi\)
−0.968066 + 0.250697i \(0.919340\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 21.0000 + 36.3731i 0.859473 + 1.48865i
\(598\) 0 0
\(599\) −4.50000 + 7.79423i −0.183865 + 0.318464i −0.943193 0.332244i \(-0.892194\pi\)
0.759328 + 0.650708i \(0.225528\pi\)
\(600\) 0 0
\(601\) 26.0000 1.06056 0.530281 0.847822i \(-0.322086\pi\)
0.530281 + 0.847822i \(0.322086\pi\)
\(602\) 0 0
\(603\) −14.0000 −0.570124
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −6.50000 11.2583i −0.263827 0.456962i 0.703429 0.710766i \(-0.251651\pi\)
−0.967256 + 0.253804i \(0.918318\pi\)
\(608\) 0 0
\(609\) −24.0000 20.7846i −0.972529 0.842235i
\(610\) 0 0
\(611\) 9.00000 + 15.5885i 0.364101 + 0.630641i
\(612\) 0 0
\(613\) 13.0000 22.5167i 0.525065 0.909439i −0.474509 0.880251i \(-0.657374\pi\)
0.999574 0.0291886i \(-0.00929235\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 17.0000 0.684394 0.342197 0.939628i \(-0.388829\pi\)
0.342197 + 0.939628i \(0.388829\pi\)
\(618\) 0 0
\(619\) 5.00000 8.66025i 0.200967 0.348085i −0.747873 0.663842i \(-0.768925\pi\)
0.948840 + 0.315757i \(0.102258\pi\)
\(620\) 0 0
\(621\) 6.00000 + 10.3923i 0.240772 + 0.417029i
\(622\) 0 0
\(623\) 27.5000 9.52628i 1.10176 0.381662i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) −15.0000 −0.597141 −0.298570 0.954388i \(-0.596510\pi\)
−0.298570 + 0.954388i \(0.596510\pi\)
\(632\) 0 0
\(633\) 22.0000 38.1051i 0.874421 1.51454i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −13.0000 5.19615i −0.515079 0.205879i
\(638\) 0 0
\(639\) −5.50000 9.52628i −0.217577 0.376854i
\(640\) 0 0
\(641\) 17.5000 30.3109i 0.691208 1.19721i −0.280234 0.959932i \(-0.590412\pi\)
0.971442 0.237276i \(-0.0762547\pi\)
\(642\) 0 0
\(643\) 16.0000 0.630978 0.315489 0.948929i \(-0.397831\pi\)
0.315489 + 0.948929i \(0.397831\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −24.0000 + 41.5692i −0.943537 + 1.63425i −0.184884 + 0.982760i \(0.559191\pi\)
−0.758654 + 0.651494i \(0.774142\pi\)
\(648\) 0 0
\(649\) −16.0000 27.7128i −0.628055 1.08782i
\(650\) 0 0
\(651\) −45.0000 + 15.5885i −1.76369 + 0.610960i
\(652\) 0 0
\(653\) 15.0000 + 25.9808i 0.586995 + 1.01671i 0.994623 + 0.103558i \(0.0330227\pi\)
−0.407628 + 0.913148i \(0.633644\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 2.00000 0.0780274
\(658\) 0 0
\(659\) 14.0000 0.545363 0.272681 0.962104i \(-0.412090\pi\)
0.272681 + 0.962104i \(0.412090\pi\)
\(660\) 0 0
\(661\) −22.0000 + 38.1051i −0.855701 + 1.48212i 0.0202925 + 0.999794i \(0.493540\pi\)
−0.875993 + 0.482323i \(0.839793\pi\)
\(662\) 0 0
\(663\) 6.00000 + 10.3923i 0.233021 + 0.403604i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −9.00000 15.5885i −0.348481 0.603587i
\(668\) 0 0
\(669\) −11.0000 + 19.0526i −0.425285 + 0.736614i
\(670\) 0 0
\(671\) 32.0000 1.23535
\(672\) 0 0
\(673\) 43.0000 1.65753 0.828764 0.559598i \(-0.189045\pi\)
0.828764 + 0.559598i \(0.189045\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −3.00000 5.19615i −0.115299 0.199704i 0.802600 0.596518i \(-0.203449\pi\)
−0.917899 + 0.396813i \(0.870116\pi\)
\(678\) 0 0
\(679\) −5.50000 + 28.5788i −0.211071 + 1.09676i
\(680\) 0 0
\(681\) 22.0000 + 38.1051i 0.843042 + 1.46019i
\(682\) 0 0
\(683\) −7.00000 + 12.1244i −0.267848 + 0.463926i −0.968306 0.249768i \(-0.919646\pi\)
0.700458 + 0.713693i \(0.252979\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 16.0000 0.610438
\(688\) 0 0
\(689\) −6.00000 + 10.3923i −0.228582 + 0.395915i
\(690\) 0 0
\(691\) 11.0000 + 19.0526i 0.418460 + 0.724793i 0.995785 0.0917209i \(-0.0292368\pi\)
−0.577325 + 0.816514i \(0.695903\pi\)
\(692\) 0 0
\(693\) −2.00000 + 10.3923i −0.0759737 + 0.394771i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −7.50000 + 12.9904i −0.284083 + 0.492046i
\(698\) 0 0
\(699\) −44.0000 −1.66423
\(700\) 0 0
\(701\) 12.0000 0.453234 0.226617 0.973984i \(-0.427233\pi\)
0.226617 + 0.973984i \(0.427233\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 16.0000 + 13.8564i 0.601742 + 0.521124i
\(708\) 0 0
\(709\) 4.00000 + 6.92820i 0.150223 + 0.260194i 0.931309 0.364229i \(-0.118667\pi\)
−0.781086 + 0.624423i \(0.785334\pi\)
\(710\) 0 0
\(711\) −4.50000 + 7.79423i −0.168763 + 0.292306i
\(712\) 0 0
\(713\) −27.0000 −1.01116
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 11.0000 19.0526i 0.410803 0.711531i
\(718\) 0 0
\(719\) −14.5000 25.1147i −0.540759 0.936622i −0.998861 0.0477220i \(-0.984804\pi\)
0.458102 0.888900i \(-0.348529\pi\)
\(720\) 0 0
\(721\) −37.5000 + 12.9904i −1.39657 + 0.483787i
\(722\) 0 0
\(723\) 18.0000 + 31.1769i 0.669427 + 1.15948i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −29.0000 −1.07555 −0.537775 0.843088i \(-0.680735\pi\)
−0.537775 + 0.843088i \(0.680735\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) −9.00000 + 15.5885i −0.332877 + 0.576560i
\(732\) 0 0
\(733\) 7.00000 + 12.1244i 0.258551 + 0.447823i 0.965854 0.259087i \(-0.0834217\pi\)
−0.707303 + 0.706910i \(0.750088\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 28.0000 + 48.4974i 1.03139 + 1.78643i
\(738\) 0 0
\(739\) 8.00000 13.8564i 0.294285 0.509716i −0.680534 0.732717i \(-0.738252\pi\)
0.974818 + 0.223001i \(0.0715853\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 27.0000 0.990534 0.495267 0.868741i \(-0.335070\pi\)
0.495267 + 0.868741i \(0.335070\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −3.00000 5.19615i −0.109764 0.190117i
\(748\) 0 0
\(749\) −20.0000 + 6.92820i −0.730784 + 0.253151i
\(750\) 0 0
\(751\) 16.0000 + 27.7128i 0.583848 + 1.01125i 0.995018 + 0.0996961i \(0.0317870\pi\)
−0.411170 + 0.911559i \(0.634880\pi\)
\(752\) 0 0
\(753\) −16.0000 + 27.7128i −0.583072 + 1.00991i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 34.0000 1.23575 0.617876 0.786276i \(-0.287994\pi\)
0.617876 + 0.786276i \(0.287994\pi\)
\(758\) 0 0
\(759\) −12.0000 + 20.7846i −0.435572 + 0.754434i
\(760\) 0 0
\(761\) 21.5000 + 37.2391i 0.779374 + 1.34992i 0.932303 + 0.361679i \(0.117796\pi\)
−0.152928 + 0.988237i \(0.548870\pi\)
\(762\) 0 0
\(763\) 28.0000 + 24.2487i 1.01367 + 0.877862i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −8.00000 + 13.8564i −0.288863 + 0.500326i
\(768\) 0 0
\(769\) 14.0000 0.504853 0.252426 0.967616i \(-0.418771\pi\)
0.252426 + 0.967616i \(0.418771\pi\)
\(770\) 0 0
\(771\) 36.0000 1.29651
\(772\) 0 0
\(773\) −10.0000 + 17.3205i −0.359675 + 0.622975i −0.987906 0.155051i \(-0.950446\pi\)
0.628231 + 0.778027i \(0.283779\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) −22.0000 + 38.1051i −0.787222 + 1.36351i
\(782\) 0 0
\(783\) −24.0000 −0.857690
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 4.00000 6.92820i 0.142585 0.246964i −0.785885 0.618373i \(-0.787792\pi\)
0.928469 + 0.371409i \(0.121125\pi\)
\(788\) 0 0
\(789\) 3.00000 + 5.19615i 0.106803 + 0.184988i
\(790\) 0 0
\(791\) 7.50000 38.9711i 0.266669 1.38565i
\(792\) 0 0
\(793\) −8.00000 13.8564i −0.284088 0.492055i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −8.00000 −0.283375 −0.141687 0.989911i \(-0.545253\pi\)
−0.141687 + 0.989911i \(0.545253\pi\)
\(798\) 0 0
\(799\) −27.0000 −0.955191
\(800\) 0 0