Properties

Label 1456.2.s.h.113.1
Level $1456$
Weight $2$
Character 1456.113
Analytic conductor $11.626$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1456.s (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.6262185343\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{5})\)
Defining polynomial: \(x^{4} - x^{3} + 2 x^{2} + x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 113.1
Root \(0.809017 - 1.40126i\) of defining polynomial
Character \(\chi\) \(=\) 1456.113
Dual form 1456.2.s.h.1121.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.30902 + 2.26728i) q^{3} +2.61803 q^{5} +(0.500000 + 0.866025i) q^{7} +(-1.92705 - 3.33775i) q^{9} +O(q^{10})\) \(q+(-1.30902 + 2.26728i) q^{3} +2.61803 q^{5} +(0.500000 + 0.866025i) q^{7} +(-1.92705 - 3.33775i) q^{9} +(0.927051 - 1.60570i) q^{11} +(-2.50000 + 2.59808i) q^{13} +(-3.42705 + 5.93583i) q^{15} +(0.736068 + 1.27491i) q^{17} +(-0.927051 - 1.60570i) q^{19} -2.61803 q^{21} +(-2.23607 + 3.87298i) q^{23} +1.85410 q^{25} +2.23607 q^{27} +(-3.54508 + 6.14027i) q^{29} +4.70820 q^{31} +(2.42705 + 4.20378i) q^{33} +(1.30902 + 2.26728i) q^{35} +(-2.00000 + 3.46410i) q^{37} +(-2.61803 - 9.06914i) q^{39} +(-0.381966 + 0.661585i) q^{41} +(6.28115 + 10.8793i) q^{43} +(-5.04508 - 8.73834i) q^{45} +2.23607 q^{47} +(-0.500000 + 0.866025i) q^{49} -3.85410 q^{51} +3.76393 q^{53} +(2.42705 - 4.20378i) q^{55} +4.85410 q^{57} +(-1.11803 - 1.93649i) q^{59} +(3.00000 + 5.19615i) q^{61} +(1.92705 - 3.33775i) q^{63} +(-6.54508 + 6.80185i) q^{65} +(-6.35410 + 11.0056i) q^{67} +(-5.85410 - 10.1396i) q^{69} +(-7.09017 - 12.2805i) q^{71} -2.00000 q^{73} +(-2.42705 + 4.20378i) q^{75} +1.85410 q^{77} -4.00000 q^{79} +(2.85410 - 4.94345i) q^{81} -6.70820 q^{83} +(1.92705 + 3.33775i) q^{85} +(-9.28115 - 16.0754i) q^{87} +(-2.45492 + 4.25204i) q^{89} +(-3.50000 - 0.866025i) q^{91} +(-6.16312 + 10.6748i) q^{93} +(-2.42705 - 4.20378i) q^{95} +(-9.42705 - 16.3281i) q^{97} -7.14590 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 3 q^{3} + 6 q^{5} + 2 q^{7} - q^{9} + O(q^{10}) \) \( 4 q - 3 q^{3} + 6 q^{5} + 2 q^{7} - q^{9} - 3 q^{11} - 10 q^{13} - 7 q^{15} - 6 q^{17} + 3 q^{19} - 6 q^{21} - 6 q^{25} - 3 q^{29} - 8 q^{31} + 3 q^{33} + 3 q^{35} - 8 q^{37} - 6 q^{39} - 6 q^{41} + 5 q^{43} - 9 q^{45} - 2 q^{49} - 2 q^{51} + 24 q^{53} + 3 q^{55} + 6 q^{57} + 12 q^{61} + q^{63} - 15 q^{65} - 12 q^{67} - 10 q^{69} - 6 q^{71} - 8 q^{73} - 3 q^{75} - 6 q^{77} - 16 q^{79} - 2 q^{81} + q^{85} - 17 q^{87} - 21 q^{89} - 14 q^{91} - 9 q^{93} - 3 q^{95} - 31 q^{97} - 42 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times\).

\(n\) \(561\) \(911\) \(1093\) \(1249\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\) \(1\)

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
\(3\) −1.30902 + 2.26728i −0.755761 + 1.30902i 0.189234 + 0.981932i \(0.439400\pi\)
−0.944995 + 0.327085i \(0.893934\pi\)
\(4\) 0 0
\(5\) 2.61803 1.17082 0.585410 0.810737i \(-0.300933\pi\)
0.585410 + 0.810737i \(0.300933\pi\)
\(6\) 0 0
\(7\) 0.500000 + 0.866025i 0.188982 + 0.327327i
\(8\) 0 0
\(9\) −1.92705 3.33775i −0.642350 1.11258i
\(10\) 0 0
\(11\) 0.927051 1.60570i 0.279516 0.484137i −0.691748 0.722139i \(-0.743159\pi\)
0.971265 + 0.238002i \(0.0764925\pi\)
\(12\) 0 0
\(13\) −2.50000 + 2.59808i −0.693375 + 0.720577i
\(14\) 0 0
\(15\) −3.42705 + 5.93583i −0.884861 + 1.53262i
\(16\) 0 0
\(17\) 0.736068 + 1.27491i 0.178523 + 0.309210i 0.941375 0.337363i \(-0.109535\pi\)
−0.762852 + 0.646573i \(0.776202\pi\)
\(18\) 0 0
\(19\) −0.927051 1.60570i −0.212680 0.368373i 0.739872 0.672747i \(-0.234886\pi\)
−0.952552 + 0.304375i \(0.901553\pi\)
\(20\) 0 0
\(21\) −2.61803 −0.571302
\(22\) 0 0
\(23\) −2.23607 + 3.87298i −0.466252 + 0.807573i −0.999257 0.0385394i \(-0.987729\pi\)
0.533005 + 0.846112i \(0.321063\pi\)
\(24\) 0 0
\(25\) 1.85410 0.370820
\(26\) 0 0
\(27\) 2.23607 0.430331
\(28\) 0 0
\(29\) −3.54508 + 6.14027i −0.658306 + 1.14022i 0.322748 + 0.946485i \(0.395393\pi\)
−0.981054 + 0.193734i \(0.937940\pi\)
\(30\) 0 0
\(31\) 4.70820 0.845618 0.422809 0.906219i \(-0.361044\pi\)
0.422809 + 0.906219i \(0.361044\pi\)
\(32\) 0 0
\(33\) 2.42705 + 4.20378i 0.422495 + 0.731783i
\(34\) 0 0
\(35\) 1.30902 + 2.26728i 0.221264 + 0.383241i
\(36\) 0 0
\(37\) −2.00000 + 3.46410i −0.328798 + 0.569495i −0.982274 0.187453i \(-0.939977\pi\)
0.653476 + 0.756948i \(0.273310\pi\)
\(38\) 0 0
\(39\) −2.61803 9.06914i −0.419221 1.45222i
\(40\) 0 0
\(41\) −0.381966 + 0.661585i −0.0596531 + 0.103322i −0.894310 0.447449i \(-0.852333\pi\)
0.834657 + 0.550771i \(0.185666\pi\)
\(42\) 0 0
\(43\) 6.28115 + 10.8793i 0.957867 + 1.65907i 0.727667 + 0.685931i \(0.240605\pi\)
0.230200 + 0.973143i \(0.426062\pi\)
\(44\) 0 0
\(45\) −5.04508 8.73834i −0.752077 1.30264i
\(46\) 0 0
\(47\) 2.23607 0.326164 0.163082 0.986613i \(-0.447856\pi\)
0.163082 + 0.986613i \(0.447856\pi\)
\(48\) 0 0
\(49\) −0.500000 + 0.866025i −0.0714286 + 0.123718i
\(50\) 0 0
\(51\) −3.85410 −0.539682
\(52\) 0 0
\(53\) 3.76393 0.517016 0.258508 0.966009i \(-0.416769\pi\)
0.258508 + 0.966009i \(0.416769\pi\)
\(54\) 0 0
\(55\) 2.42705 4.20378i 0.327263 0.566837i
\(56\) 0 0
\(57\) 4.85410 0.642942
\(58\) 0 0
\(59\) −1.11803 1.93649i −0.145556 0.252110i 0.784024 0.620730i \(-0.213164\pi\)
−0.929580 + 0.368620i \(0.879830\pi\)
\(60\) 0 0
\(61\) 3.00000 + 5.19615i 0.384111 + 0.665299i 0.991645 0.128994i \(-0.0411748\pi\)
−0.607535 + 0.794293i \(0.707841\pi\)
\(62\) 0 0
\(63\) 1.92705 3.33775i 0.242786 0.420517i
\(64\) 0 0
\(65\) −6.54508 + 6.80185i −0.811818 + 0.843666i
\(66\) 0 0
\(67\) −6.35410 + 11.0056i −0.776277 + 1.34455i 0.157797 + 0.987472i \(0.449561\pi\)
−0.934074 + 0.357080i \(0.883772\pi\)
\(68\) 0 0
\(69\) −5.85410 10.1396i −0.704751 1.22066i
\(70\) 0 0
\(71\) −7.09017 12.2805i −0.841448 1.45743i −0.888670 0.458547i \(-0.848370\pi\)
0.0472218 0.998884i \(-0.484963\pi\)
\(72\) 0 0
\(73\) −2.00000 −0.234082 −0.117041 0.993127i \(-0.537341\pi\)
−0.117041 + 0.993127i \(0.537341\pi\)
\(74\) 0 0
\(75\) −2.42705 + 4.20378i −0.280252 + 0.485410i
\(76\) 0 0
\(77\) 1.85410 0.211295
\(78\) 0 0
\(79\) −4.00000 −0.450035 −0.225018 0.974355i \(-0.572244\pi\)
−0.225018 + 0.974355i \(0.572244\pi\)
\(80\) 0 0
\(81\) 2.85410 4.94345i 0.317122 0.549272i
\(82\) 0 0
\(83\) −6.70820 −0.736321 −0.368161 0.929762i \(-0.620012\pi\)
−0.368161 + 0.929762i \(0.620012\pi\)
\(84\) 0 0
\(85\) 1.92705 + 3.33775i 0.209018 + 0.362030i
\(86\) 0 0
\(87\) −9.28115 16.0754i −0.995044 1.72347i
\(88\) 0 0
\(89\) −2.45492 + 4.25204i −0.260220 + 0.450715i −0.966300 0.257417i \(-0.917129\pi\)
0.706080 + 0.708132i \(0.250462\pi\)
\(90\) 0 0
\(91\) −3.50000 0.866025i −0.366900 0.0907841i
\(92\) 0 0
\(93\) −6.16312 + 10.6748i −0.639086 + 1.10693i
\(94\) 0 0
\(95\) −2.42705 4.20378i −0.249010 0.431298i
\(96\) 0 0
\(97\) −9.42705 16.3281i −0.957172 1.65787i −0.729318 0.684175i \(-0.760162\pi\)
−0.227854 0.973695i \(-0.573171\pi\)
\(98\) 0 0
\(99\) −7.14590 −0.718190
\(100\) 0 0
\(101\) 5.78115 10.0133i 0.575246 0.996356i −0.420769 0.907168i \(-0.638240\pi\)
0.996015 0.0891877i \(-0.0284271\pi\)
\(102\) 0 0
\(103\) 8.70820 0.858045 0.429022 0.903294i \(-0.358858\pi\)
0.429022 + 0.903294i \(0.358858\pi\)
\(104\) 0 0
\(105\) −6.85410 −0.668892
\(106\) 0 0
\(107\) −1.69098 + 2.92887i −0.163473 + 0.283144i −0.936112 0.351702i \(-0.885603\pi\)
0.772639 + 0.634846i \(0.218936\pi\)
\(108\) 0 0
\(109\) −2.70820 −0.259399 −0.129699 0.991553i \(-0.541401\pi\)
−0.129699 + 0.991553i \(0.541401\pi\)
\(110\) 0 0
\(111\) −5.23607 9.06914i −0.496986 0.860804i
\(112\) 0 0
\(113\) −0.736068 1.27491i −0.0692435 0.119933i 0.829325 0.558766i \(-0.188725\pi\)
−0.898568 + 0.438833i \(0.855392\pi\)
\(114\) 0 0
\(115\) −5.85410 + 10.1396i −0.545898 + 0.945523i
\(116\) 0 0
\(117\) 13.4894 + 3.33775i 1.24709 + 0.308575i
\(118\) 0 0
\(119\) −0.736068 + 1.27491i −0.0674752 + 0.116871i
\(120\) 0 0
\(121\) 3.78115 + 6.54915i 0.343741 + 0.595377i
\(122\) 0 0
\(123\) −1.00000 1.73205i −0.0901670 0.156174i
\(124\) 0 0
\(125\) −8.23607 −0.736656
\(126\) 0 0
\(127\) −10.4271 + 18.0602i −0.925251 + 1.60258i −0.134094 + 0.990969i \(0.542813\pi\)
−0.791157 + 0.611613i \(0.790521\pi\)
\(128\) 0 0
\(129\) −32.8885 −2.89567
\(130\) 0 0
\(131\) 15.3262 1.33906 0.669530 0.742785i \(-0.266496\pi\)
0.669530 + 0.742785i \(0.266496\pi\)
\(132\) 0 0
\(133\) 0.927051 1.60570i 0.0803855 0.139232i
\(134\) 0 0
\(135\) 5.85410 0.503841
\(136\) 0 0
\(137\) 1.30902 + 2.26728i 0.111837 + 0.193707i 0.916511 0.400010i \(-0.130993\pi\)
−0.804674 + 0.593717i \(0.797660\pi\)
\(138\) 0 0
\(139\) 2.28115 + 3.95107i 0.193485 + 0.335126i 0.946403 0.322989i \(-0.104688\pi\)
−0.752918 + 0.658114i \(0.771354\pi\)
\(140\) 0 0
\(141\) −2.92705 + 5.06980i −0.246502 + 0.426954i
\(142\) 0 0
\(143\) 1.85410 + 6.42280i 0.155048 + 0.537101i
\(144\) 0 0
\(145\) −9.28115 + 16.0754i −0.770758 + 1.33499i
\(146\) 0 0
\(147\) −1.30902 2.26728i −0.107966 0.187002i
\(148\) 0 0
\(149\) −0.927051 1.60570i −0.0759470 0.131544i 0.825551 0.564328i \(-0.190865\pi\)
−0.901498 + 0.432784i \(0.857531\pi\)
\(150\) 0 0
\(151\) 1.29180 0.105125 0.0525624 0.998618i \(-0.483261\pi\)
0.0525624 + 0.998618i \(0.483261\pi\)
\(152\) 0 0
\(153\) 2.83688 4.91362i 0.229348 0.397243i
\(154\) 0 0
\(155\) 12.3262 0.990067
\(156\) 0 0
\(157\) 14.8541 1.18549 0.592743 0.805392i \(-0.298045\pi\)
0.592743 + 0.805392i \(0.298045\pi\)
\(158\) 0 0
\(159\) −4.92705 + 8.53390i −0.390741 + 0.676783i
\(160\) 0 0
\(161\) −4.47214 −0.352454
\(162\) 0 0
\(163\) −1.85410 3.21140i −0.145224 0.251536i 0.784232 0.620467i \(-0.213057\pi\)
−0.929457 + 0.368931i \(0.879724\pi\)
\(164\) 0 0
\(165\) 6.35410 + 11.0056i 0.494666 + 0.856787i
\(166\) 0 0
\(167\) 7.11803 12.3288i 0.550810 0.954031i −0.447406 0.894331i \(-0.647652\pi\)
0.998216 0.0597001i \(-0.0190144\pi\)
\(168\) 0 0
\(169\) −0.500000 12.9904i −0.0384615 0.999260i
\(170\) 0 0
\(171\) −3.57295 + 6.18853i −0.273230 + 0.473249i
\(172\) 0 0
\(173\) 4.50000 + 7.79423i 0.342129 + 0.592584i 0.984828 0.173534i \(-0.0555188\pi\)
−0.642699 + 0.766119i \(0.722185\pi\)
\(174\) 0 0
\(175\) 0.927051 + 1.60570i 0.0700785 + 0.121379i
\(176\) 0 0
\(177\) 5.85410 0.440021
\(178\) 0 0
\(179\) −4.50000 + 7.79423i −0.336346 + 0.582568i −0.983742 0.179585i \(-0.942524\pi\)
0.647397 + 0.762153i \(0.275858\pi\)
\(180\) 0 0
\(181\) 9.70820 0.721605 0.360803 0.932642i \(-0.382503\pi\)
0.360803 + 0.932642i \(0.382503\pi\)
\(182\) 0 0
\(183\) −15.7082 −1.16118
\(184\) 0 0
\(185\) −5.23607 + 9.06914i −0.384963 + 0.666776i
\(186\) 0 0
\(187\) 2.72949 0.199600
\(188\) 0 0
\(189\) 1.11803 + 1.93649i 0.0813250 + 0.140859i
\(190\) 0 0
\(191\) 10.6910 + 18.5173i 0.773572 + 1.33987i 0.935593 + 0.353079i \(0.114865\pi\)
−0.162021 + 0.986787i \(0.551801\pi\)
\(192\) 0 0
\(193\) 3.00000 5.19615i 0.215945 0.374027i −0.737620 0.675216i \(-0.764050\pi\)
0.953564 + 0.301189i \(0.0973836\pi\)
\(194\) 0 0
\(195\) −6.85410 23.7433i −0.490832 1.70029i
\(196\) 0 0
\(197\) 8.39919 14.5478i 0.598417 1.03649i −0.394638 0.918837i \(-0.629130\pi\)
0.993055 0.117652i \(-0.0375368\pi\)
\(198\) 0 0
\(199\) −12.2082 21.1452i −0.865417 1.49895i −0.866633 0.498946i \(-0.833720\pi\)
0.00121626 0.999999i \(-0.499613\pi\)
\(200\) 0 0
\(201\) −16.6353 28.8131i −1.17336 2.03232i
\(202\) 0 0
\(203\) −7.09017 −0.497632
\(204\) 0 0
\(205\) −1.00000 + 1.73205i −0.0698430 + 0.120972i
\(206\) 0 0
\(207\) 17.2361 1.19799
\(208\) 0 0
\(209\) −3.43769 −0.237790
\(210\) 0 0
\(211\) 2.35410 4.07742i 0.162063 0.280701i −0.773545 0.633741i \(-0.781519\pi\)
0.935608 + 0.353039i \(0.114852\pi\)
\(212\) 0 0
\(213\) 37.1246 2.54374
\(214\) 0 0
\(215\) 16.4443 + 28.4823i 1.12149 + 1.94248i
\(216\) 0 0
\(217\) 2.35410 + 4.07742i 0.159807 + 0.276794i
\(218\) 0 0
\(219\) 2.61803 4.53457i 0.176910 0.306418i
\(220\) 0 0
\(221\) −5.15248 1.27491i −0.346593 0.0857595i
\(222\) 0 0
\(223\) 10.1353 17.5548i 0.678707 1.17555i −0.296664 0.954982i \(-0.595874\pi\)
0.975371 0.220573i \(-0.0707926\pi\)
\(224\) 0 0
\(225\) −3.57295 6.18853i −0.238197 0.412569i
\(226\) 0 0
\(227\) 0.736068 + 1.27491i 0.0488545 + 0.0846186i 0.889419 0.457094i \(-0.151110\pi\)
−0.840564 + 0.541712i \(0.817776\pi\)
\(228\) 0 0
\(229\) −13.1246 −0.867299 −0.433649 0.901082i \(-0.642774\pi\)
−0.433649 + 0.901082i \(0.642774\pi\)
\(230\) 0 0
\(231\) −2.42705 + 4.20378i −0.159688 + 0.276588i
\(232\) 0 0
\(233\) 2.61803 0.171513 0.0857566 0.996316i \(-0.472669\pi\)
0.0857566 + 0.996316i \(0.472669\pi\)
\(234\) 0 0
\(235\) 5.85410 0.381880
\(236\) 0 0
\(237\) 5.23607 9.06914i 0.340119 0.589104i
\(238\) 0 0
\(239\) 24.7082 1.59824 0.799120 0.601171i \(-0.205299\pi\)
0.799120 + 0.601171i \(0.205299\pi\)
\(240\) 0 0
\(241\) −12.2812 21.2716i −0.791099 1.37022i −0.925287 0.379267i \(-0.876176\pi\)
0.134189 0.990956i \(-0.457157\pi\)
\(242\) 0 0
\(243\) 10.8262 + 18.7516i 0.694503 + 1.20292i
\(244\) 0 0
\(245\) −1.30902 + 2.26728i −0.0836300 + 0.144851i
\(246\) 0 0
\(247\) 6.48936 + 1.60570i 0.412908 + 0.102168i
\(248\) 0 0
\(249\) 8.78115 15.2094i 0.556483 0.963857i
\(250\) 0 0
\(251\) 0.381966 + 0.661585i 0.0241095 + 0.0417588i 0.877828 0.478975i \(-0.158992\pi\)
−0.853719 + 0.520734i \(0.825658\pi\)
\(252\) 0 0
\(253\) 4.14590 + 7.18091i 0.260650 + 0.451460i
\(254\) 0 0
\(255\) −10.0902 −0.631871
\(256\) 0 0
\(257\) −8.37132 + 14.4996i −0.522189 + 0.904457i 0.477478 + 0.878644i \(0.341551\pi\)
−0.999667 + 0.0258138i \(0.991782\pi\)
\(258\) 0 0
\(259\) −4.00000 −0.248548
\(260\) 0 0
\(261\) 27.3262 1.69145
\(262\) 0 0
\(263\) 4.50000 7.79423i 0.277482 0.480613i −0.693276 0.720672i \(-0.743833\pi\)
0.970758 + 0.240059i \(0.0771668\pi\)
\(264\) 0 0
\(265\) 9.85410 0.605333
\(266\) 0 0
\(267\) −6.42705 11.1320i −0.393329 0.681266i
\(268\) 0 0
\(269\) 14.3713 + 24.8919i 0.876235 + 1.51768i 0.855441 + 0.517900i \(0.173286\pi\)
0.0207937 + 0.999784i \(0.493381\pi\)
\(270\) 0 0
\(271\) −4.20820 + 7.28882i −0.255630 + 0.442764i −0.965066 0.262005i \(-0.915616\pi\)
0.709436 + 0.704770i \(0.248950\pi\)
\(272\) 0 0
\(273\) 6.54508 6.80185i 0.396127 0.411667i
\(274\) 0 0
\(275\) 1.71885 2.97713i 0.103650 0.179528i
\(276\) 0 0
\(277\) 2.50000 + 4.33013i 0.150210 + 0.260172i 0.931305 0.364241i \(-0.118672\pi\)
−0.781094 + 0.624413i \(0.785338\pi\)
\(278\) 0 0
\(279\) −9.07295 15.7148i −0.543183 0.940821i
\(280\) 0 0
\(281\) 20.1803 1.20386 0.601929 0.798550i \(-0.294399\pi\)
0.601929 + 0.798550i \(0.294399\pi\)
\(282\) 0 0
\(283\) 6.70820 11.6190i 0.398761 0.690675i −0.594812 0.803865i \(-0.702774\pi\)
0.993573 + 0.113190i \(0.0361069\pi\)
\(284\) 0 0
\(285\) 12.7082 0.752769
\(286\) 0 0
\(287\) −0.763932 −0.0450935
\(288\) 0 0
\(289\) 7.41641 12.8456i 0.436259 0.755623i
\(290\) 0 0
\(291\) 49.3607 2.89357
\(292\) 0 0
\(293\) 3.38197 + 5.85774i 0.197577 + 0.342213i 0.947742 0.319037i \(-0.103360\pi\)
−0.750166 + 0.661250i \(0.770026\pi\)
\(294\) 0 0
\(295\) −2.92705 5.06980i −0.170419 0.295175i
\(296\) 0 0
\(297\) 2.07295 3.59045i 0.120285 0.208339i
\(298\) 0 0
\(299\) −4.47214 15.4919i −0.258630 0.895922i
\(300\) 0 0
\(301\) −6.28115 + 10.8793i −0.362040 + 0.627071i
\(302\) 0 0
\(303\) 15.1353 + 26.2150i 0.869498 + 1.50601i
\(304\) 0 0
\(305\) 7.85410 + 13.6037i 0.449725 + 0.778946i
\(306\) 0 0
\(307\) 4.85410 0.277038 0.138519 0.990360i \(-0.455766\pi\)
0.138519 + 0.990360i \(0.455766\pi\)
\(308\) 0 0
\(309\) −11.3992 + 19.7440i −0.648477 + 1.12320i
\(310\) 0 0
\(311\) −3.32624 −0.188614 −0.0943068 0.995543i \(-0.530063\pi\)
−0.0943068 + 0.995543i \(0.530063\pi\)
\(312\) 0 0
\(313\) 25.1246 1.42013 0.710064 0.704138i \(-0.248666\pi\)
0.710064 + 0.704138i \(0.248666\pi\)
\(314\) 0 0
\(315\) 5.04508 8.73834i 0.284258 0.492350i
\(316\) 0 0
\(317\) 26.2361 1.47356 0.736782 0.676130i \(-0.236344\pi\)
0.736782 + 0.676130i \(0.236344\pi\)
\(318\) 0 0
\(319\) 6.57295 + 11.3847i 0.368014 + 0.637420i
\(320\) 0 0
\(321\) −4.42705 7.66788i −0.247094 0.427979i
\(322\) 0 0
\(323\) 1.36475 2.36381i 0.0759364 0.131526i
\(324\) 0 0
\(325\) −4.63525 + 4.81710i −0.257118 + 0.267205i
\(326\) 0 0
\(327\) 3.54508 6.14027i 0.196044 0.339558i
\(328\) 0 0
\(329\) 1.11803 + 1.93649i 0.0616392 + 0.106762i
\(330\) 0 0
\(331\) −5.07295 8.78661i −0.278834 0.482956i 0.692261 0.721647i \(-0.256615\pi\)
−0.971095 + 0.238692i \(0.923281\pi\)
\(332\) 0 0
\(333\) 15.4164 0.844814
\(334\) 0 0
\(335\) −16.6353 + 28.8131i −0.908881 + 1.57423i
\(336\) 0 0
\(337\) −11.5623 −0.629839 −0.314919 0.949118i \(-0.601978\pi\)
−0.314919 + 0.949118i \(0.601978\pi\)
\(338\) 0 0
\(339\) 3.85410 0.209326
\(340\) 0 0
\(341\) 4.36475 7.55996i 0.236364 0.409395i
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) −15.3262 26.5458i −0.825137 1.42918i
\(346\) 0 0
\(347\) 15.3820 + 26.6423i 0.825747 + 1.43024i 0.901347 + 0.433098i \(0.142580\pi\)
−0.0755997 + 0.997138i \(0.524087\pi\)
\(348\) 0 0
\(349\) −10.3541 + 17.9338i −0.554242 + 0.959976i 0.443720 + 0.896166i \(0.353659\pi\)
−0.997962 + 0.0638103i \(0.979675\pi\)
\(350\) 0 0
\(351\) −5.59017 + 5.80948i −0.298381 + 0.310087i
\(352\) 0 0
\(353\) −11.0729 + 19.1789i −0.589354 + 1.02079i 0.404964 + 0.914333i \(0.367284\pi\)
−0.994317 + 0.106458i \(0.966049\pi\)
\(354\) 0 0
\(355\) −18.5623 32.1509i −0.985185 1.70639i
\(356\) 0 0
\(357\) −1.92705 3.33775i −0.101990 0.176652i
\(358\) 0 0
\(359\) 22.0902 1.16587 0.582937 0.812517i \(-0.301903\pi\)
0.582937 + 0.812517i \(0.301903\pi\)
\(360\) 0 0
\(361\) 7.78115 13.4774i 0.409534 0.709334i
\(362\) 0 0
\(363\) −19.7984 −1.03915
\(364\) 0 0
\(365\) −5.23607 −0.274068
\(366\) 0 0
\(367\) −0.708204 + 1.22665i −0.0369679 + 0.0640304i −0.883917 0.467643i \(-0.845103\pi\)
0.846949 + 0.531673i \(0.178437\pi\)
\(368\) 0 0
\(369\) 2.94427 0.153273
\(370\) 0 0
\(371\) 1.88197 + 3.25966i 0.0977068 + 0.169233i
\(372\) 0 0
\(373\) 10.2812 + 17.8075i 0.532338 + 0.922036i 0.999287 + 0.0377522i \(0.0120198\pi\)
−0.466949 + 0.884284i \(0.654647\pi\)
\(374\) 0 0
\(375\) 10.7812 18.6735i 0.556736 0.964296i
\(376\) 0 0
\(377\) −7.09017 24.5611i −0.365162 1.26496i
\(378\) 0 0
\(379\) −3.07295 + 5.32250i −0.157847 + 0.273399i −0.934092 0.357032i \(-0.883789\pi\)
0.776245 + 0.630431i \(0.217122\pi\)
\(380\) 0 0
\(381\) −27.2984 47.2822i −1.39854 2.42234i
\(382\) 0 0
\(383\) −10.9894 19.0341i −0.561530 0.972598i −0.997363 0.0725709i \(-0.976880\pi\)
0.435833 0.900027i \(-0.356454\pi\)
\(384\) 0 0
\(385\) 4.85410 0.247388
\(386\) 0 0
\(387\) 24.2082 41.9298i 1.23057 2.13141i
\(388\) 0 0
\(389\) −11.8885 −0.602773 −0.301387 0.953502i \(-0.597449\pi\)
−0.301387 + 0.953502i \(0.597449\pi\)
\(390\) 0 0
\(391\) −6.58359 −0.332947
\(392\) 0 0
\(393\) −20.0623 + 34.7489i −1.01201 + 1.75285i
\(394\) 0 0
\(395\) −10.4721 −0.526910
\(396\) 0 0
\(397\) −0.708204 1.22665i −0.0355437 0.0615636i 0.847706 0.530466i \(-0.177983\pi\)
−0.883250 + 0.468902i \(0.844650\pi\)
\(398\) 0 0
\(399\) 2.42705 + 4.20378i 0.121505 + 0.210452i
\(400\) 0 0
\(401\) −17.7254 + 30.7013i −0.885165 + 1.53315i −0.0396416 + 0.999214i \(0.512622\pi\)
−0.845524 + 0.533938i \(0.820712\pi\)
\(402\) 0 0
\(403\) −11.7705 + 12.2323i −0.586331 + 0.609333i
\(404\) 0 0
\(405\) 7.47214 12.9421i 0.371293 0.643099i
\(406\) 0 0
\(407\) 3.70820 + 6.42280i 0.183809 + 0.318366i
\(408\) 0 0
\(409\) −7.21885 12.5034i −0.356949 0.618254i 0.630500 0.776189i \(-0.282850\pi\)
−0.987450 + 0.157935i \(0.949516\pi\)
\(410\) 0 0
\(411\) −6.85410 −0.338088
\(412\) 0 0
\(413\) 1.11803 1.93649i 0.0550149 0.0952885i
\(414\) 0 0
\(415\) −17.5623 −0.862100
\(416\) 0 0
\(417\) −11.9443 −0.584914
\(418\) 0 0
\(419\) −5.97214 + 10.3440i −0.291758 + 0.505340i −0.974226 0.225576i \(-0.927574\pi\)
0.682468 + 0.730916i \(0.260907\pi\)
\(420\) 0 0
\(421\) 1.41641 0.0690315 0.0345157 0.999404i \(-0.489011\pi\)
0.0345157 + 0.999404i \(0.489011\pi\)
\(422\) 0 0
\(423\) −4.30902 7.46344i −0.209512 0.362885i
\(424\) 0 0
\(425\) 1.36475 + 2.36381i 0.0661999 + 0.114662i
\(426\) 0 0
\(427\) −3.00000 + 5.19615i −0.145180 + 0.251459i
\(428\) 0 0
\(429\) −16.9894 4.20378i −0.820254 0.202960i
\(430\) 0 0
\(431\) 3.89919 6.75359i 0.187817 0.325309i −0.756705 0.653756i \(-0.773192\pi\)
0.944522 + 0.328448i \(0.106525\pi\)
\(432\) 0 0
\(433\) −0.500000 0.866025i −0.0240285 0.0416185i 0.853761 0.520665i \(-0.174316\pi\)
−0.877790 + 0.479046i \(0.840983\pi\)
\(434\) 0 0
\(435\) −24.2984 42.0860i −1.16502 2.01787i
\(436\) 0 0
\(437\) 8.29180 0.396650
\(438\) 0 0
\(439\) 7.42705 12.8640i 0.354474 0.613967i −0.632554 0.774516i \(-0.717993\pi\)
0.987028 + 0.160550i \(0.0513267\pi\)
\(440\) 0 0
\(441\) 3.85410 0.183529
\(442\) 0 0
\(443\) 5.23607 0.248773 0.124387 0.992234i \(-0.460304\pi\)
0.124387 + 0.992234i \(0.460304\pi\)
\(444\) 0 0
\(445\) −6.42705 + 11.1320i −0.304671 + 0.527706i
\(446\) 0 0
\(447\) 4.85410 0.229591
\(448\) 0 0
\(449\) −9.76393 16.9116i −0.460788 0.798109i 0.538212 0.842809i \(-0.319100\pi\)
−0.999000 + 0.0447005i \(0.985767\pi\)
\(450\) 0 0
\(451\) 0.708204 + 1.22665i 0.0333480 + 0.0577605i
\(452\) 0 0
\(453\) −1.69098 + 2.92887i −0.0794493 + 0.137610i
\(454\) 0 0
\(455\) −9.16312 2.26728i −0.429574 0.106292i
\(456\) 0 0
\(457\) −7.70820 + 13.3510i −0.360575 + 0.624533i −0.988055 0.154098i \(-0.950753\pi\)
0.627481 + 0.778632i \(0.284086\pi\)
\(458\) 0 0
\(459\) 1.64590 + 2.85078i 0.0768239 + 0.133063i
\(460\) 0 0
\(461\) 6.10739 + 10.5783i 0.284450 + 0.492681i 0.972476 0.233005i \(-0.0748558\pi\)
−0.688026 + 0.725686i \(0.741523\pi\)
\(462\) 0 0
\(463\) −6.70820 −0.311757 −0.155878 0.987776i \(-0.549821\pi\)
−0.155878 + 0.987776i \(0.549821\pi\)
\(464\) 0 0
\(465\) −16.1353 + 27.9471i −0.748255 + 1.29601i
\(466\) 0 0
\(467\) −2.34752 −0.108630 −0.0543152 0.998524i \(-0.517298\pi\)
−0.0543152 + 0.998524i \(0.517298\pi\)
\(468\) 0 0
\(469\) −12.7082 −0.586810
\(470\) 0 0
\(471\) −19.4443 + 33.6785i −0.895945 + 1.55182i
\(472\) 0 0
\(473\) 23.2918 1.07096
\(474\) 0 0
\(475\) −1.71885 2.97713i −0.0788661 0.136600i
\(476\) 0 0
\(477\) −7.25329 12.5631i −0.332105 0.575223i
\(478\) 0 0
\(479\) 12.4894 21.6322i 0.570653 0.988400i −0.425846 0.904796i \(-0.640023\pi\)
0.996499 0.0836047i \(-0.0266433\pi\)
\(480\) 0 0
\(481\) −4.00000 13.8564i −0.182384 0.631798i
\(482\) 0 0
\(483\) 5.85410 10.1396i 0.266371 0.461368i
\(484\) 0 0
\(485\) −24.6803 42.7476i −1.12068 1.94107i
\(486\) 0 0
\(487\) 14.9894 + 25.9623i 0.679233 + 1.17647i 0.975212 + 0.221271i \(0.0710206\pi\)
−0.295980 + 0.955194i \(0.595646\pi\)
\(488\) 0 0
\(489\) 9.70820 0.439020
\(490\) 0 0
\(491\) 6.19098 10.7231i 0.279395 0.483927i −0.691839 0.722051i \(-0.743199\pi\)
0.971235 + 0.238125i \(0.0765327\pi\)
\(492\) 0 0
\(493\) −10.4377 −0.470090
\(494\) 0 0
\(495\) −18.7082 −0.840871
\(496\) 0 0
\(497\) 7.09017 12.2805i 0.318038 0.550857i
\(498\) 0 0
\(499\) −14.8541 −0.664961 −0.332480 0.943110i \(-0.607886\pi\)
−0.332480 + 0.943110i \(0.607886\pi\)
\(500\) 0 0
\(501\) 18.6353 + 32.2772i 0.832562 + 1.44204i
\(502\) 0 0
\(503\) 13.3090 + 23.0519i 0.593420 + 1.02783i 0.993768 + 0.111470i \(0.0355559\pi\)
−0.400348 + 0.916363i \(0.631111\pi\)
\(504\) 0 0
\(505\) 15.1353 26.2150i 0.673510 1.16655i
\(506\) 0 0
\(507\) 30.1074 + 15.8710i 1.33712 + 0.704855i
\(508\) 0 0
\(509\) 9.29837 16.1053i 0.412143 0.713853i −0.582981 0.812486i \(-0.698114\pi\)
0.995124 + 0.0986331i \(0.0314470\pi\)
\(510\) 0 0
\(511\) −1.00000 1.73205i −0.0442374 0.0766214i
\(512\) 0 0
\(513\) −2.07295 3.59045i −0.0915229 0.158522i
\(514\) 0 0
\(515\) 22.7984 1.00462
\(516\) 0 0
\(517\) 2.07295 3.59045i 0.0911682 0.157908i
\(518\) 0 0
\(519\) −23.5623 −1.03427
\(520\) 0 0
\(521\) 18.6525 0.817180 0.408590 0.912718i \(-0.366021\pi\)
0.408590 + 0.912718i \(0.366021\pi\)
\(522\) 0 0
\(523\) 0.562306 0.973942i 0.0245879 0.0425875i −0.853470 0.521143i \(-0.825506\pi\)
0.878058 + 0.478555i \(0.158839\pi\)
\(524\) 0 0
\(525\) −4.85410 −0.211850
\(526\) 0 0
\(527\) 3.46556 + 6.00252i 0.150962 + 0.261474i
\(528\) 0 0
\(529\) 1.50000 + 2.59808i 0.0652174 + 0.112960i
\(530\) 0 0
\(531\) −4.30902 + 7.46344i −0.186995 + 0.323886i
\(532\) 0 0
\(533\) −0.763932 2.64634i −0.0330896 0.114626i
\(534\) 0 0
\(535\) −4.42705 + 7.66788i −0.191398 + 0.331511i
\(536\) 0 0
\(537\) −11.7812 20.4056i −0.508394 0.880565i
\(538\) 0 0
\(539\) 0.927051 + 1.60570i 0.0399309 + 0.0691624i
\(540\) 0 0
\(541\) 35.2705 1.51640 0.758199 0.652023i \(-0.226080\pi\)
0.758199 + 0.652023i \(0.226080\pi\)
\(542\) 0 0
\(543\) −12.7082 + 22.0113i −0.545361 + 0.944593i
\(544\) 0 0
\(545\) −7.09017 −0.303710
\(546\) 0 0
\(547\) 3.00000 0.128271 0.0641354 0.997941i \(-0.479571\pi\)
0.0641354 + 0.997941i \(0.479571\pi\)
\(548\) 0 0
\(549\) 11.5623 20.0265i 0.493467 0.854710i
\(550\) 0 0
\(551\) 13.1459 0.560034
\(552\) 0 0
\(553\) −2.00000 3.46410i −0.0850487 0.147309i
\(554\) 0 0
\(555\) −13.7082 23.7433i −0.581881 1.00785i
\(556\) 0 0
\(557\) 13.9894 24.2303i 0.592748 1.02667i −0.401112 0.916029i \(-0.631376\pi\)
0.993860 0.110641i \(-0.0352904\pi\)
\(558\) 0 0
\(559\) −43.9681 10.8793i −1.85965 0.460144i
\(560\) 0 0
\(561\) −3.57295 + 6.18853i −0.150850 + 0.261280i
\(562\) 0 0
\(563\) −10.5279 18.2348i −0.443697 0.768505i 0.554264 0.832341i \(-0.313000\pi\)
−0.997960 + 0.0638360i \(0.979667\pi\)
\(564\) 0 0
\(565\) −1.92705 3.33775i −0.0810716 0.140420i
\(566\) 0 0
\(567\) 5.70820 0.239722
\(568\) 0 0
\(569\) −7.47214 + 12.9421i −0.313248 + 0.542562i −0.979064 0.203555i \(-0.934751\pi\)
0.665815 + 0.746117i \(0.268084\pi\)
\(570\) 0 0
\(571\) −24.6869 −1.03312 −0.516558 0.856252i \(-0.672787\pi\)
−0.516558 + 0.856252i \(0.672787\pi\)
\(572\) 0 0
\(573\) −55.9787 −2.33854
\(574\) 0 0
\(575\) −4.14590 + 7.18091i −0.172896 + 0.299464i
\(576\) 0 0
\(577\) −43.8328 −1.82478 −0.912392 0.409318i \(-0.865767\pi\)
−0.912392 + 0.409318i \(0.865767\pi\)
\(578\) 0 0
\(579\) 7.85410 + 13.6037i 0.326405 + 0.565351i
\(580\) 0 0
\(581\) −3.35410 5.80948i −0.139152 0.241018i
\(582\) 0 0
\(583\) 3.48936 6.04374i 0.144514 0.250306i
\(584\) 0 0
\(585\) 35.3156 + 8.73834i 1.46012 + 0.361286i
\(586\) 0 0
\(587\) −9.95492 + 17.2424i −0.410883 + 0.711671i −0.994987 0.100009i \(-0.968113\pi\)
0.584103 + 0.811679i \(0.301446\pi\)
\(588\) 0 0
\(589\) −4.36475 7.55996i −0.179846 0.311503i
\(590\) 0 0
\(591\) 21.9894 + 38.0867i 0.904521 + 1.56668i
\(592\) 0 0
\(593\) 43.7984 1.79858 0.899292 0.437349i \(-0.144083\pi\)
0.899292 + 0.437349i \(0.144083\pi\)
\(594\) 0 0
\(595\) −1.92705 + 3.33775i −0.0790014 + 0.136834i
\(596\) 0 0
\(597\) 63.9230 2.61619
\(598\) 0 0
\(599\) −29.5066 −1.20561 −0.602803 0.797890i \(-0.705950\pi\)
−0.602803 + 0.797890i \(0.705950\pi\)
\(600\) 0 0
\(601\) −20.1976 + 34.9832i −0.823876 + 1.42699i 0.0788998 + 0.996883i \(0.474859\pi\)
−0.902776 + 0.430112i \(0.858474\pi\)
\(602\) 0 0
\(603\) 48.9787 1.99457
\(604\) 0 0
\(605\) 9.89919 + 17.1459i 0.402459 + 0.697080i
\(606\) 0 0
\(607\) −11.5000 19.9186i −0.466771 0.808470i 0.532509 0.846424i \(-0.321249\pi\)
−0.999279 + 0.0379540i \(0.987916\pi\)
\(608\) 0 0
\(609\) 9.28115 16.0754i 0.376091 0.651409i
\(610\) 0 0
\(611\) −5.59017 + 5.80948i −0.226154 + 0.235026i
\(612\) 0 0
\(613\) −17.2812 + 29.9318i −0.697979 + 1.20894i 0.271187 + 0.962527i \(0.412584\pi\)
−0.969166 + 0.246409i \(0.920749\pi\)
\(614\) 0 0
\(615\) −2.61803 4.53457i −0.105569 0.182851i
\(616\) 0 0
\(617\) −0.0278640 0.0482619i −0.00112176 0.00194295i 0.865464 0.500971i \(-0.167024\pi\)
−0.866586 + 0.499028i \(0.833690\pi\)
\(618\) 0 0
\(619\) −9.41641 −0.378477 −0.189239 0.981931i \(-0.560602\pi\)
−0.189239 + 0.981931i \(0.560602\pi\)
\(620\) 0 0
\(621\) −5.00000 + 8.66025i −0.200643 + 0.347524i
\(622\) 0 0
\(623\) −4.90983 −0.196708
\(624\) 0 0
\(625\) −30.8328 −1.23331
\(626\) 0 0
\(627\) 4.50000 7.79423i 0.179713 0.311272i
\(628\) 0 0
\(629\) −5.88854 −0.234792
\(630\) 0 0
\(631\) 17.1976 + 29.7870i 0.684624 + 1.18580i 0.973555 + 0.228454i \(0.0733669\pi\)
−0.288931 + 0.957350i \(0.593300\pi\)
\(632\) 0 0
\(633\) 6.16312 + 10.6748i 0.244962 + 0.424287i
\(634\) 0 0
\(635\) −27.2984 + 47.2822i −1.08330 + 1.87634i
\(636\) 0 0
\(637\) −1.00000 3.46410i −0.0396214 0.137253i
\(638\) 0 0
\(639\) −27.3262 + 47.3304i −1.08101 + 1.87236i
\(640\) 0 0
\(641\) 23.7533 + 41.1419i 0.938199 + 1.62501i 0.768829 + 0.639455i \(0.220840\pi\)
0.169370 + 0.985553i \(0.445827\pi\)
\(642\) 0 0
\(643\) −3.50000 6.06218i −0.138027 0.239069i 0.788723 0.614749i \(-0.210743\pi\)
−0.926750 + 0.375680i \(0.877409\pi\)
\(644\) 0 0
\(645\) −86.1033 −3.39032
\(646\) 0 0
\(647\) 12.3820 21.4462i 0.486785 0.843137i −0.513099 0.858329i \(-0.671503\pi\)
0.999885 + 0.0151924i \(0.00483607\pi\)
\(648\) 0 0
\(649\) −4.14590 −0.162741
\(650\) 0 0
\(651\) −12.3262 −0.483103
\(652\) 0 0
\(653\) 0.190983 0.330792i 0.00747374 0.0129449i −0.862264 0.506458i \(-0.830954\pi\)
0.869738 + 0.493514i \(0.164288\pi\)
\(654\) 0 0
\(655\) 40.1246 1.56780
\(656\) 0 0
\(657\) 3.85410 + 6.67550i 0.150363 + 0.260436i
\(658\) 0 0
\(659\) −11.9443 20.6881i −0.465283 0.805893i 0.533931 0.845528i \(-0.320714\pi\)
−0.999214 + 0.0396343i \(0.987381\pi\)
\(660\) 0 0
\(661\) 24.2705 42.0378i 0.944013 1.63508i 0.186299 0.982493i \(-0.440351\pi\)
0.757715 0.652586i \(-0.226316\pi\)
\(662\) 0 0
\(663\) 9.63525 10.0133i 0.374202 0.388882i
\(664\) 0 0
\(665\) 2.42705 4.20378i 0.0941170 0.163015i
\(666\) 0 0
\(667\) −15.8541 27.4601i −0.613873 1.06326i
\(668\) 0 0
\(669\) 26.5344 + 45.9590i 1.02588 + 1.77688i
\(670\) 0 0
\(671\) 11.1246 0.429461
\(672\) 0 0
\(673\) 19.6246 33.9908i 0.756473 1.31025i −0.188165 0.982137i \(-0.560254\pi\)
0.944639 0.328113i \(-0.106413\pi\)
\(674\) 0 0
\(675\) 4.14590 0.159576
\(676\) 0 0
\(677\) 43.7426 1.68117 0.840583 0.541682i \(-0.182212\pi\)
0.840583 + 0.541682i \(0.182212\pi\)
\(678\) 0 0
\(679\) 9.42705 16.3281i 0.361777 0.626616i
\(680\) 0 0
\(681\) −3.85410 −0.147690
\(682\) 0 0
\(683\) 0.736068 + 1.27491i 0.0281649 + 0.0487830i 0.879764 0.475410i \(-0.157700\pi\)
−0.851599 + 0.524193i \(0.824367\pi\)
\(684\) 0 0
\(685\) 3.42705 + 5.93583i 0.130941 + 0.226796i
\(686\) 0 0
\(687\) 17.1803 29.7572i 0.655471 1.13531i
\(688\) 0 0
\(689\) −9.40983 + 9.77898i −0.358486 + 0.372550i
\(690\) 0 0
\(691\) −2.92705 + 5.06980i −0.111350 + 0.192864i −0.916315 0.400458i \(-0.868851\pi\)
0.804965 + 0.593323i \(0.202184\pi\)
\(692\) 0 0
\(693\) −3.57295 6.18853i −0.135725 0.235083i
\(694\) 0 0
\(695\) 5.97214 + 10.3440i 0.226536 + 0.392372i
\(696\) 0 0
\(697\) −1.12461 −0.0425977
\(698\) 0 0
\(699\) −3.42705 + 5.93583i −0.129623 + 0.224514i
\(700\) 0 0
\(701\) 11.2361 0.424380 0.212190 0.977228i \(-0.431940\pi\)
0.212190 + 0.977228i \(0.431940\pi\)
\(702\) 0 0
\(703\) 7.41641 0.279715
\(704\) 0 0
\(705\) −7.66312 + 13.2729i −0.288610 + 0.499887i
\(706\) 0 0
\(707\) 11.5623 0.434845
\(708\) 0 0
\(709\) −11.7812 20.4056i −0.442450 0.766347i 0.555420 0.831570i \(-0.312557\pi\)
−0.997871 + 0.0652231i \(0.979224\pi\)
\(710\) 0 0
\(711\) 7.70820 + 13.3510i 0.289080 + 0.500702i
\(712\) 0 0
\(713\) −10.5279 + 18.2348i −0.394272 + 0.682898i
\(714\) 0 0
\(715\) 4.85410 + 16.8151i 0.181533 + 0.628849i
\(716\) 0 0
\(717\) −32.3435 + 56.0205i −1.20789 + 2.09212i
\(718\) 0 0
\(719\) 4.06231 + 7.03612i 0.151498 + 0.262403i 0.931779 0.363027i \(-0.118257\pi\)
−0.780280 + 0.625430i \(0.784923\pi\)
\(720\) 0 0
\(721\) 4.35410 + 7.54153i 0.162155 + 0.280861i
\(722\) 0 0
\(723\) 64.3050 2.39153
\(724\) 0 0
\(725\) −6.57295 + 11.3847i −0.244113 + 0.422816i
\(726\) 0 0
\(727\) 30.7082 1.13890 0.569452 0.822025i \(-0.307155\pi\)
0.569452 + 0.822025i \(0.307155\pi\)
\(728\) 0 0
\(729\) −39.5623 −1.46527
\(730\) 0 0
\(731\) −9.24671 + 16.0158i −0.342002 + 0.592365i
\(732\) 0 0
\(733\) −32.2705 −1.19194 −0.595969 0.803007i \(-0.703232\pi\)
−0.595969 + 0.803007i \(0.703232\pi\)
\(734\) 0 0
\(735\) −3.42705 5.93583i −0.126409 0.218946i
\(736\) 0 0
\(737\) 11.7812 + 20.4056i 0.433964 + 0.751648i
\(738\) 0 0
\(739\) −3.43769 + 5.95426i −0.126458 + 0.219031i −0.922302 0.386470i \(-0.873694\pi\)
0.795844 + 0.605502i \(0.207027\pi\)
\(740\) 0 0
\(741\) −12.1353 + 12.6113i −0.445800 + 0.463289i
\(742\) 0 0
\(743\) 19.6631 34.0575i 0.721370 1.24945i −0.239081 0.971000i \(-0.576846\pi\)
0.960451 0.278450i \(-0.0898205\pi\)
\(744\) 0 0
\(745\) −2.42705 4.20378i −0.0889203 0.154014i
\(746\) 0 0
\(747\) 12.9271 + 22.3903i 0.472976 + 0.819219i
\(748\) 0 0
\(749\) −3.38197 −0.123574
\(750\) 0 0
\(751\) 11.3541 19.6659i 0.414317 0.717618i −0.581039 0.813875i \(-0.697354\pi\)
0.995356 + 0.0962572i \(0.0306871\pi\)
\(752\) 0 0
\(753\) −2.00000 −0.0728841
\(754\) 0 0
\(755\) 3.38197 0.123082
\(756\) 0 0
\(757\) −14.0000 + 24.2487i −0.508839 + 0.881334i 0.491109 + 0.871098i \(0.336592\pi\)
−0.999948 + 0.0102362i \(0.996742\pi\)
\(758\) 0 0
\(759\) −21.7082 −0.787958
\(760\) 0 0
\(761\) 14.4271 + 24.9884i 0.522980 + 0.905828i 0.999642 + 0.0267417i \(0.00851317\pi\)
−0.476662 + 0.879087i \(0.658154\pi\)
\(762\) 0 0
\(763\) −1.35410 2.34537i −0.0490218 0.0849082i
\(764\) 0 0
\(765\) 7.42705 12.8640i 0.268526 0.465100i
\(766\) 0 0
\(767\) 7.82624 + 1.93649i 0.282589 + 0.0699227i
\(768\) 0 0
\(769\) 9.20820 15.9491i 0.332056 0.575138i −0.650859 0.759199i \(-0.725591\pi\)
0.982915 + 0.184061i \(0.0589243\pi\)
\(770\) 0 0
\(771\) −21.9164 37.9603i −0.789300 1.36711i
\(772\) 0 0
\(773\) −12.6803 21.9630i −0.456080 0.789954i 0.542669 0.839946i \(-0.317414\pi\)
−0.998750 + 0.0499924i \(0.984080\pi\)
\(774\) 0 0
\(775\) 8.72949 0.313573
\(776\) 0 0
\(777\) 5.23607 9.06914i 0.187843 0.325353i
\(778\) 0 0
\(779\) 1.41641 0.0507481
\(780\) 0 0
\(781\) −26.2918 −0.940794
\(782\) 0 0
\(783\) −7.92705 + 13.7301i −0.283290 + 0.490672i
\(784\) 0 0
\(785\) 38.8885 1.38799
\(786\) 0 0
\(787\) 1.29180 + 2.23746i 0.0460476 + 0.0797567i 0.888131 0.459591i \(-0.152004\pi\)
−0.842083 + 0.539348i \(0.818671\pi\)
\(788\) 0 0
\(789\) 11.7812 + 20.4056i 0.419420 + 0.726457i
\(790\) 0 0
\(791\) 0.736068 1.27491i 0.0261716 0.0453305i
\(792\) 0 0
\(793\) −21.0000 5.19615i −0.745732 0.184521i
\(794\) 0 0
\(795\) −12.8992 + 22.3420i −0.457487 + 0.792391i
\(796\) 0 0