Properties

Label 1400.2.q.b.401.1
Level $1400$
Weight $2$
Character 1400.401
Analytic conductor $11.179$
Analytic rank $1$
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: \(1\)
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 401.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1400.401
Dual form 1400.2.q.b.1201.1

$q$-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 \(\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times\).

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

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 −0.995782 0.0917517i \(-0.970753\pi\)
0.418432 0.908248i \(-0.362580\pi\)
\(4\) 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 −0.992361 0.123371i \(-0.960630\pi\)
0.389338 0.921095i \(-0.372704\pi\)
\(12\) 0 0
\(13\) −2.00000 −0.554700 −0.277350 0.960769i \(-0.589456\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.50000 + 2.59808i 0.363803 + 0.630126i 0.988583 0.150675i \(-0.0481447\pi\)
−0.624780 + 0.780801i \(0.714811\pi\)
\(18\) 0 0
\(19\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(20\) 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 \(-0.934591\pi\)
0.666190 + 0.745782i \(0.267924\pi\)
\(24\) 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 −0.914093 0.405505i \(-0.867096\pi\)
0.105869 0.994380i \(-0.466238\pi\)
\(32\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(38\) 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 \(-0.651253\pi\)
−0.457496 + 0.889212i \(0.651253\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −4.50000 + 7.79423i −0.656392 + 1.13691i 0.325150 + 0.945662i \(0.394585\pi\)
−0.981543 + 0.191243i \(0.938748\pi\)
\(48\) 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 \(-0.0314685\pi\)
−0.583036 + 0.812447i \(0.698135\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −4.00000 6.92820i −0.520756 0.901975i −0.999709 0.0241347i \(-0.992317\pi\)
0.478953 0.877841i \(-0.341016\pi\)
\(60\) 0 0
\(61\) −4.00000 + 6.92820i −0.512148 + 0.887066i 0.487753 + 0.872982i \(0.337817\pi\)
−0.999901 + 0.0140840i \(0.995517\pi\)
\(62\) 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 −0.876472 0.481452i \(-0.840109\pi\)
0.0212861 0.999773i \(-0.493224\pi\)
\(68\) 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 \(-0.129326\pi\)
−0.801553 + 0.597924i \(0.795992\pi\)
\(74\) 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 0.493684 + 0.869641i \(0.335650\pi\)
−0.999974 + 0.00727784i \(0.997683\pi\)
\(80\) 0 0
\(81\) 5.50000 + 9.52628i 0.611111 + 1.05848i
\(82\) 0 0
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) 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 0.412123 + 0.911128i \(0.364787\pi\)
−0.995122 + 0.0986553i \(0.968546\pi\)
\(90\) 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 \(-0.688600\pi\)
−0.558440 + 0.829545i \(0.688600\pi\)
\(98\) 0 0
\(99\) 4.00000 0.402015
\(100\) 0 0
\(101\) 4.00000 + 6.92820i 0.398015 + 0.689382i 0.993481 0.113998i \(-0.0363659\pi\)
−0.595466 + 0.803380i \(0.703033\pi\)
\(102\) 0 0
\(103\) −7.50000 + 12.9904i −0.738997 + 1.27998i 0.213950 + 0.976845i \(0.431367\pi\)
−0.952947 + 0.303136i \(0.901966\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −4.00000 + 6.92820i −0.386695 + 0.669775i −0.992003 0.126217i \(-0.959717\pi\)
0.605308 + 0.795991i \(0.293050\pi\)
\(108\) 0 0
\(109\) 7.00000 + 12.1244i 0.670478 + 1.16130i 0.977769 + 0.209687i \(0.0672444\pi\)
−0.307290 + 0.951616i \(0.599422\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 15.0000 1.41108 0.705541 0.708669i \(-0.250704\pi\)
0.705541 + 0.708669i \(0.250704\pi\)
\(114\) 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 \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) 0 0
\(129\) 6.00000 + 10.3923i 0.528271 + 0.914991i
\(130\) 0 0
\(131\) −6.00000 + 10.3923i −0.524222 + 0.907980i 0.475380 + 0.879781i \(0.342311\pi\)
−0.999602 + 0.0281993i \(0.991023\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −8.50000 14.7224i −0.726204 1.25782i −0.958477 0.285171i \(-0.907949\pi\)
0.232273 0.972651i \(-0.425384\pi\)
\(138\) 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 −0.0870170 0.996207i \(-0.527733\pi\)
0.906249 0.422744i \(-0.138933\pi\)
\(150\) 0 0
\(151\) −10.0000 17.3205i −0.813788 1.40952i −0.910195 0.414181i \(-0.864068\pi\)
0.0964061 0.995342i \(-0.469265\pi\)
\(152\) 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 \(-0.297324\pi\)
−0.993608 + 0.112884i \(0.963991\pi\)
\(158\) 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 0.174282 0.984696i \(-0.444240\pi\)
0.765631 0.643280i \(-0.222427\pi\)
\(164\) 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 0.383304 + 0.923622i \(0.374786\pi\)
−0.991532 + 0.129861i \(0.958547\pi\)
\(174\) 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 0.781551 0.623841i \(-0.214429\pi\)
−0.931038 + 0.364922i \(0.881096\pi\)
\(180\) 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 −0.529101 0.848559i \(-0.677471\pi\)
0.999424 + 0.0339349i \(0.0108039\pi\)
\(192\) 0 0
\(193\) −2.50000 4.33013i −0.179954 0.311689i 0.761911 0.647682i \(-0.224262\pi\)
−0.941865 + 0.335993i \(0.890928\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) 0 0
\(199\) −10.5000 18.1865i −0.744325 1.28921i −0.950509 0.310696i \(-0.899438\pi\)
0.206184 0.978513i \(-0.433895\pi\)
\(200\) 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 \(-0.379937\pi\)
0.368307 + 0.929704i \(0.379937\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 11.0000 + 19.0526i 0.730096 + 1.26456i 0.956842 + 0.290609i \(0.0938578\pi\)
−0.226746 + 0.973954i \(0.572809\pi\)
\(228\) 0 0
\(229\) 4.00000 6.92820i 0.264327 0.457829i −0.703060 0.711131i \(-0.748183\pi\)
0.967387 + 0.253302i \(0.0815167\pi\)
\(230\) 0 0
\(231\) −20.0000 6.92820i −1.31590 0.455842i
\(232\) 0 0
\(233\) 11.0000 19.0526i 0.720634 1.24817i −0.240112 0.970745i \(-0.577184\pi\)
0.960746 0.277429i \(-0.0894825\pi\)
\(234\) 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 −0.995509 0.0946700i \(-0.969820\pi\)
0.415768 0.909471i \(-0.363513\pi\)
\(242\) 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 0.435970 + 0.899961i \(0.356405\pi\)
−0.997374 + 0.0724199i \(0.976928\pi\)
\(258\) 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 \(-0.137183\pi\)
−0.816066 + 0.577959i \(0.803849\pi\)
\(264\) 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 0.894900 0.446267i \(-0.147247\pi\)
−0.833929 + 0.551872i \(0.813914\pi\)
\(270\) 0 0
\(271\) −3.50000 + 6.06218i −0.212610 + 0.368251i −0.952531 0.304443i \(-0.901530\pi\)
0.739921 + 0.672694i \(0.234863\pi\)
\(272\) 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 \(-0.243925\pi\)
−0.960810 + 0.277207i \(0.910591\pi\)
\(278\) 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 \(-0.185599\pi\)
−0.894216 + 0.447636i \(0.852266\pi\)
\(284\) 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 \(-0.365897\pi\)
0.408944 + 0.912559i \(0.365897\pi\)
\(294\) 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 \(-0.740144\pi\)
−0.684876 + 0.728659i \(0.740144\pi\)
\(308\) 0 0
\(309\) 30.0000 1.70664
\(310\) 0 0
\(311\) −0.500000 0.866025i −0.0283524 0.0491078i 0.851501 0.524353i \(-0.175693\pi\)
−0.879853 + 0.475245i \(0.842359\pi\)
\(312\) 0 0
\(313\) 15.5000 26.8468i 0.876112 1.51747i 0.0205381 0.999789i \(-0.493462\pi\)
0.855574 0.517681i \(-0.173205\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 6.00000 10.3923i 0.336994 0.583690i −0.646872 0.762598i \(-0.723923\pi\)
0.983866 + 0.178908i \(0.0572566\pi\)
\(318\) 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 −0.837234 0.546845i \(-0.815829\pi\)
0.892199 + 0.451643i \(0.149162\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −29.0000 −1.57973 −0.789865 0.613280i \(-0.789850\pi\)
−0.789865 + 0.613280i \(0.789850\pi\)
\(338\) 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 \(-0.183763\pi\)
−0.891618 + 0.452788i \(0.850429\pi\)
\(348\) 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 \(-0.297373\pi\)
−0.993626 + 0.112731i \(0.964040\pi\)
\(354\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(360\) 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 \(-0.303794\pi\)
−0.995697 + 0.0926670i \(0.970461\pi\)
\(368\) 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 \(-0.882979\pi\)
0.777847 + 0.628454i \(0.216312\pi\)
\(374\) 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 0.462563 + 0.886586i \(0.346930\pi\)
−0.999088 + 0.0427020i \(0.986403\pi\)
\(384\) 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 −0.870059 0.492947i \(-0.835920\pi\)
0.00812520 0.999967i \(-0.497414\pi\)
\(390\) 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 0.216004 0.976392i \(-0.430698\pi\)
0.737579 0.675261i \(-0.235969\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −9.00000 + 15.5885i −0.449439 + 0.778450i −0.998350 0.0574304i \(-0.981709\pi\)
0.548911 + 0.835881i \(0.315043\pi\)
\(402\) 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 0.939490 + 0.342578i \(0.111300\pi\)
−0.173064 + 0.984911i \(0.555367\pi\)
\(410\) 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 0.949439 + 0.313950i \(0.101653\pi\)
−0.202831 + 0.979214i \(0.565014\pi\)
\(432\) 0 0
\(433\) 21.0000 1.00920 0.504598 0.863355i \(-0.331641\pi\)
0.504598 + 0.863355i \(0.331641\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −17.5000 + 30.3109i −0.835229 + 1.44666i 0.0586141 + 0.998281i \(0.481332\pi\)
−0.893843 + 0.448379i \(0.852001\pi\)
\(440\) 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 \(-0.925350\pi\)
0.687557 + 0.726130i \(0.258683\pi\)
\(444\) 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 \(-0.848229\pi\)
0.841688 + 0.539964i \(0.181562\pi\)
\(458\) 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 \(-0.417725\pi\)
0.255607 + 0.966781i \(0.417725\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 15.0000 25.9808i 0.694117 1.20225i −0.276360 0.961054i \(-0.589128\pi\)
0.970477 0.241192i \(-0.0775384\pi\)
\(468\) 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 0.744717 0.667381i \(-0.232585\pi\)
−0.950327 + 0.311253i \(0.899251\pi\)
\(480\) 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 −0.999698 0.0245553i \(-0.992183\pi\)
0.478584 0.878042i \(-0.341150\pi\)
\(488\) 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 0.0301498 + 0.999545i \(0.490402\pi\)
−0.880707 + 0.473662i \(0.842932\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −16.0000 −0.713405 −0.356702 0.934218i \(-0.616099\pi\)
−0.356702 + 0.934218i \(0.616099\pi\)
\(504\) 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 −0.967811 0.251679i \(-0.919017\pi\)
0.701866 + 0.712309i \(0.252351\pi\)
\(510\) 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 −0.638588 0.769549i \(-0.720481\pi\)
−0.347155 0.937808i \(-0.612852\pi\)
\(522\) 0 0
\(523\) −11.0000 + 19.0526i −0.480996 + 0.833110i −0.999762 0.0218062i \(-0.993058\pi\)
0.518766 + 0.854916i \(0.326392\pi\)
\(524\) 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 −0.339424 0.940633i \(-0.610232\pi\)
0.984325 0.176367i \(-0.0564345\pi\)
\(542\) 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 \(-0.826528\pi\)
−0.855138 + 0.518400i \(0.826528\pi\)
\(548\) 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 0.941462 + 0.337119i \(0.109452\pi\)
−0.178778 + 0.983890i \(0.557214\pi\)
\(558\) 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 0.998419 + 0.0562051i \(0.0179001\pi\)
−0.450535 + 0.892759i \(0.648767\pi\)
\(564\) 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 −0.727405 0.686209i \(-0.759274\pi\)
0.957977 + 0.286846i \(0.0926069\pi\)
\(570\) 0 0
\(571\) 6.00000 + 10.3923i 0.251092 + 0.434904i 0.963827 0.266529i \(-0.0858769\pi\)
−0.712735 + 0.701434i \(0.752544\pi\)
\(572\) 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 \(-0.260792\pi\)
−0.974144 + 0.225927i \(0.927459\pi\)
\(578\) 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 \(-0.447206\pi\)
0.165098 + 0.986277i \(0.447206\pi\)
\(588\) 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 \(-0.747326\pi\)
0.968066 + 0.250697i \(0.0806597\pi\)
\(594\) 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 0.759328 0.650708i \(-0.225528\pi\)
−0.943193 + 0.332244i \(0.892194\pi\)
\(600\) 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 \(-0.748349\pi\)
0.967256 + 0.253804i \(0.0816819\pi\)
\(608\) 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 −0.999574 0.0291886i \(-0.990708\pi\)
0.474509 0.880251i \(-0.342626\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −17.0000 −0.684394 −0.342197 0.939628i \(-0.611171\pi\)
−0.342197 + 0.939628i \(0.611171\pi\)
\(618\) 0 0
\(619\) 5.00000 + 8.66025i 0.200967 + 0.348085i 0.948840 0.315757i \(-0.102258\pi\)
−0.747873 + 0.663842i \(0.768925\pi\)
\(620\) 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 0.971442 + 0.237276i \(0.0762547\pi\)
−0.280234 + 0.959932i \(0.590412\pi\)
\(642\) 0 0
\(643\) −16.0000 −0.630978 −0.315489 0.948929i \(-0.602169\pi\)
−0.315489 + 0.948929i \(0.602169\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 24.0000 + 41.5692i 0.943537 + 1.63425i 0.758654 + 0.651494i \(0.225858\pi\)
0.184884 + 0.982760i \(0.440809\pi\)
\(648\) 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 0.407628 + 0.913148i \(0.366356\pi\)
−0.994623 + 0.103558i \(0.966977\pi\)
\(654\) 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 −0.875993 0.482323i \(-0.839793\pi\)
0.0202925 0.999794i \(-0.493540\pi\)
\(662\) 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 \(-0.810955\pi\)
−0.828764 + 0.559598i \(0.810955\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 3.00000 5.19615i 0.115299 0.199704i −0.802600 0.596518i \(-0.796551\pi\)
0.917899 + 0.396813i \(0.129884\pi\)
\(678\) 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 \(-0.0803543\pi\)
−0.700458 + 0.713693i \(0.747021\pi\)
\(684\) 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 −0.577325 0.816514i \(-0.695903\pi\)
0.995785 + 0.0917209i \(0.0292368\pi\)
\(692\) 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 −0.781086 0.624423i \(-0.785334\pi\)
0.931309 + 0.364229i \(0.118667\pi\)
\(710\) 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 0.458102 + 0.888900i \(0.348529\pi\)
−0.998861 + 0.0477220i \(0.984804\pi\)
\(720\) 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 \(-0.319265\pi\)
0.537775 + 0.843088i \(0.319265\pi\)
\(728\) 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 \(-0.916578\pi\)
0.707303 + 0.706910i \(0.249912\pi\)
\(734\) 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 0.974818 0.223001i \(-0.0715853\pi\)
−0.680534 + 0.732717i \(0.738252\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −27.0000 −0.990534 −0.495267 0.868741i \(-0.664930\pi\)
−0.495267 + 0.868741i \(0.664930\pi\)
\(744\) 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 −0.411170 0.911559i \(-0.634880\pi\)
0.995018 0.0996961i \(-0.0317870\pi\)
\(752\) 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 \(-0.712006\pi\)
−0.617876 + 0.786276i \(0.712006\pi\)
\(758\) 0 0
\(759\) −12.0000 20.7846i −0.435572 0.754434i
\(760\) 0 0
\(761\) 21.5000 37.2391i 0.779374 1.34992i −0.152928 0.988237i \(-0.548870\pi\)
0.932303 0.361679i \(-0.117796\pi\)
\(762\) 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 \(-0.0495542\pi\)
−0.628231 + 0.778027i \(0.716221\pi\)
\(774\) 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 \(-0.212208\pi\)
−0.928469 + 0.371409i \(0.878875\pi\)
\(788\) 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 \(-0.454747\pi\)
0.141687 + 0.989911i \(0.454747\pi\)
\(798\) 0 0
\(799\) −27.0000 −0.955191