Properties

Label 1134.2.h.s.541.2
Level $1134$
Weight $2$
Character 1134.541
Analytic conductor $9.055$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1134.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.05503558921\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 541.2
Root \(-0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 1134.541
Dual form 1134.2.h.s.109.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.00000 + 2.44949i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.00000 + 2.44949i) q^{7} -1.00000 q^{8} +4.24264 q^{11} +(1.12132 + 1.94218i) q^{13} +(-1.62132 + 2.09077i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.12132 - 1.94218i) q^{19} +(2.12132 + 3.67423i) q^{22} +1.24264 q^{23} -5.00000 q^{25} +(-1.12132 + 1.94218i) q^{26} +(-2.62132 - 0.358719i) q^{28} +(2.12132 - 3.67423i) q^{29} +(-4.62132 + 8.00436i) q^{31} +(0.500000 - 0.866025i) q^{32} +(2.00000 - 3.46410i) q^{37} +2.24264 q^{38} +(5.74264 + 9.94655i) q^{41} +(-5.24264 + 9.08052i) q^{43} +(-2.12132 + 3.67423i) q^{44} +(0.621320 + 1.07616i) q^{46} +(2.37868 + 4.11999i) q^{47} +(-5.00000 + 4.89898i) q^{49} +(-2.50000 - 4.33013i) q^{50} -2.24264 q^{52} +(-2.12132 - 3.67423i) q^{53} +(-1.00000 - 2.44949i) q^{56} +4.24264 q^{58} +(1.12132 + 1.94218i) q^{61} -9.24264 q^{62} +1.00000 q^{64} +(-0.121320 + 0.210133i) q^{67} -1.24264 q^{71} +(3.50000 + 6.06218i) q^{73} +4.00000 q^{74} +(1.12132 + 1.94218i) q^{76} +(4.24264 + 10.3923i) q^{77} +(-0.378680 - 0.655892i) q^{79} +(-5.74264 + 9.94655i) q^{82} +(8.12132 - 14.0665i) q^{83} -10.4853 q^{86} -4.24264 q^{88} +(5.74264 - 9.94655i) q^{89} +(-3.63604 + 4.68885i) q^{91} +(-0.621320 + 1.07616i) q^{92} +(-2.37868 + 4.11999i) q^{94} +(-2.24264 + 3.88437i) q^{97} +(-6.74264 - 1.88064i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{2} - 2q^{4} + 4q^{7} - 4q^{8} + O(q^{10}) \) \( 4q + 2q^{2} - 2q^{4} + 4q^{7} - 4q^{8} - 4q^{13} + 2q^{14} - 2q^{16} - 4q^{19} - 12q^{23} - 20q^{25} + 4q^{26} - 2q^{28} - 10q^{31} + 2q^{32} + 8q^{37} - 8q^{38} + 6q^{41} - 4q^{43} - 6q^{46} + 18q^{47} - 20q^{49} - 10q^{50} + 8q^{52} - 4q^{56} - 4q^{61} - 20q^{62} + 4q^{64} + 8q^{67} + 12q^{71} + 14q^{73} + 16q^{74} - 4q^{76} - 10q^{79} - 6q^{82} + 24q^{83} - 8q^{86} + 6q^{89} - 40q^{91} + 6q^{92} - 18q^{94} + 8q^{97} - 10q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) 0 0
\(7\) 1.00000 + 2.44949i 0.377964 + 0.925820i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 0 0
\(11\) 4.24264 1.27920 0.639602 0.768706i \(-0.279099\pi\)
0.639602 + 0.768706i \(0.279099\pi\)
\(12\) 0 0
\(13\) 1.12132 + 1.94218i 0.310998 + 0.538665i 0.978579 0.205873i \(-0.0660033\pi\)
−0.667580 + 0.744538i \(0.732670\pi\)
\(14\) −1.62132 + 2.09077i −0.433316 + 0.558782i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(18\) 0 0
\(19\) 1.12132 1.94218i 0.257249 0.445568i −0.708255 0.705956i \(-0.750517\pi\)
0.965504 + 0.260389i \(0.0838508\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 2.12132 + 3.67423i 0.452267 + 0.783349i
\(23\) 1.24264 0.259108 0.129554 0.991572i \(-0.458645\pi\)
0.129554 + 0.991572i \(0.458645\pi\)
\(24\) 0 0
\(25\) −5.00000 −1.00000
\(26\) −1.12132 + 1.94218i −0.219909 + 0.380894i
\(27\) 0 0
\(28\) −2.62132 0.358719i −0.495383 0.0677916i
\(29\) 2.12132 3.67423i 0.393919 0.682288i −0.599043 0.800717i \(-0.704452\pi\)
0.992963 + 0.118428i \(0.0377856\pi\)
\(30\) 0 0
\(31\) −4.62132 + 8.00436i −0.830014 + 1.43763i 0.0680129 + 0.997684i \(0.478334\pi\)
−0.898027 + 0.439941i \(0.854999\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 2.00000 3.46410i 0.328798 0.569495i −0.653476 0.756948i \(-0.726690\pi\)
0.982274 + 0.187453i \(0.0600231\pi\)
\(38\) 2.24264 0.363804
\(39\) 0 0
\(40\) 0 0
\(41\) 5.74264 + 9.94655i 0.896850 + 1.55339i 0.831498 + 0.555527i \(0.187483\pi\)
0.0653514 + 0.997862i \(0.479183\pi\)
\(42\) 0 0
\(43\) −5.24264 + 9.08052i −0.799495 + 1.38477i 0.120450 + 0.992719i \(0.461566\pi\)
−0.919945 + 0.392047i \(0.871767\pi\)
\(44\) −2.12132 + 3.67423i −0.319801 + 0.553912i
\(45\) 0 0
\(46\) 0.621320 + 1.07616i 0.0916087 + 0.158671i
\(47\) 2.37868 + 4.11999i 0.346966 + 0.600963i 0.985709 0.168457i \(-0.0538786\pi\)
−0.638743 + 0.769420i \(0.720545\pi\)
\(48\) 0 0
\(49\) −5.00000 + 4.89898i −0.714286 + 0.699854i
\(50\) −2.50000 4.33013i −0.353553 0.612372i
\(51\) 0 0
\(52\) −2.24264 −0.310998
\(53\) −2.12132 3.67423i −0.291386 0.504695i 0.682752 0.730650i \(-0.260783\pi\)
−0.974138 + 0.225955i \(0.927450\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −1.00000 2.44949i −0.133631 0.327327i
\(57\) 0 0
\(58\) 4.24264 0.557086
\(59\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(60\) 0 0
\(61\) 1.12132 + 1.94218i 0.143570 + 0.248671i 0.928839 0.370484i \(-0.120808\pi\)
−0.785268 + 0.619156i \(0.787475\pi\)
\(62\) −9.24264 −1.17382
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −0.121320 + 0.210133i −0.0148216 + 0.0256718i −0.873341 0.487109i \(-0.838051\pi\)
0.858519 + 0.512781i \(0.171385\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −1.24264 −0.147474 −0.0737372 0.997278i \(-0.523493\pi\)
−0.0737372 + 0.997278i \(0.523493\pi\)
\(72\) 0 0
\(73\) 3.50000 + 6.06218i 0.409644 + 0.709524i 0.994850 0.101361i \(-0.0323196\pi\)
−0.585206 + 0.810885i \(0.698986\pi\)
\(74\) 4.00000 0.464991
\(75\) 0 0
\(76\) 1.12132 + 1.94218i 0.128624 + 0.222784i
\(77\) 4.24264 + 10.3923i 0.483494 + 1.18431i
\(78\) 0 0
\(79\) −0.378680 0.655892i −0.0426048 0.0737937i 0.843937 0.536443i \(-0.180232\pi\)
−0.886541 + 0.462649i \(0.846899\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −5.74264 + 9.94655i −0.634169 + 1.09841i
\(83\) 8.12132 14.0665i 0.891431 1.54400i 0.0532699 0.998580i \(-0.483036\pi\)
0.838161 0.545423i \(-0.183631\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −10.4853 −1.13066
\(87\) 0 0
\(88\) −4.24264 −0.452267
\(89\) 5.74264 9.94655i 0.608719 1.05433i −0.382733 0.923859i \(-0.625017\pi\)
0.991452 0.130473i \(-0.0416495\pi\)
\(90\) 0 0
\(91\) −3.63604 + 4.68885i −0.381160 + 0.491525i
\(92\) −0.621320 + 1.07616i −0.0647771 + 0.112197i
\(93\) 0 0
\(94\) −2.37868 + 4.11999i −0.245342 + 0.424945i
\(95\) 0 0
\(96\) 0 0
\(97\) −2.24264 + 3.88437i −0.227706 + 0.394398i −0.957128 0.289666i \(-0.906456\pi\)
0.729422 + 0.684064i \(0.239789\pi\)
\(98\) −6.74264 1.88064i −0.681110 0.189973i
\(99\) 0 0
\(100\) 2.50000 4.33013i 0.250000 0.433013i
\(101\) −16.2426 −1.61620 −0.808102 0.589043i \(-0.799505\pi\)
−0.808102 + 0.589043i \(0.799505\pi\)
\(102\) 0 0
\(103\) 9.24264 0.910704 0.455352 0.890311i \(-0.349513\pi\)
0.455352 + 0.890311i \(0.349513\pi\)
\(104\) −1.12132 1.94218i −0.109955 0.190447i
\(105\) 0 0
\(106\) 2.12132 3.67423i 0.206041 0.356873i
\(107\) 7.24264 12.5446i 0.700173 1.21273i −0.268233 0.963354i \(-0.586440\pi\)
0.968406 0.249380i \(-0.0802269\pi\)
\(108\) 0 0
\(109\) −3.12132 5.40629i −0.298968 0.517828i 0.676932 0.736046i \(-0.263309\pi\)
−0.975900 + 0.218217i \(0.929976\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 1.62132 2.09077i 0.153200 0.197559i
\(113\) −1.75736 3.04384i −0.165318 0.286340i 0.771450 0.636290i \(-0.219532\pi\)
−0.936768 + 0.349950i \(0.886199\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 2.12132 + 3.67423i 0.196960 + 0.341144i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 7.00000 0.636364
\(122\) −1.12132 + 1.94218i −0.101520 + 0.175837i
\(123\) 0 0
\(124\) −4.62132 8.00436i −0.415007 0.718813i
\(125\) 0 0
\(126\) 0 0
\(127\) 15.2426 1.35257 0.676283 0.736642i \(-0.263590\pi\)
0.676283 + 0.736642i \(0.263590\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 0 0
\(131\) 16.2426 1.41913 0.709563 0.704642i \(-0.248892\pi\)
0.709563 + 0.704642i \(0.248892\pi\)
\(132\) 0 0
\(133\) 5.87868 + 0.804479i 0.509746 + 0.0697572i
\(134\) −0.242641 −0.0209610
\(135\) 0 0
\(136\) 0 0
\(137\) −13.9706 −1.19359 −0.596793 0.802395i \(-0.703559\pi\)
−0.596793 + 0.802395i \(0.703559\pi\)
\(138\) 0 0
\(139\) −10.3640 17.9509i −0.879060 1.52258i −0.852374 0.522932i \(-0.824838\pi\)
−0.0266854 0.999644i \(-0.508495\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −0.621320 1.07616i −0.0521400 0.0903092i
\(143\) 4.75736 + 8.23999i 0.397830 + 0.689062i
\(144\) 0 0
\(145\) 0 0
\(146\) −3.50000 + 6.06218i −0.289662 + 0.501709i
\(147\) 0 0
\(148\) 2.00000 + 3.46410i 0.164399 + 0.284747i
\(149\) −7.75736 −0.635508 −0.317754 0.948173i \(-0.602929\pi\)
−0.317754 + 0.948173i \(0.602929\pi\)
\(150\) 0 0
\(151\) −11.2426 −0.914913 −0.457457 0.889232i \(-0.651239\pi\)
−0.457457 + 0.889232i \(0.651239\pi\)
\(152\) −1.12132 + 1.94218i −0.0909511 + 0.157532i
\(153\) 0 0
\(154\) −6.87868 + 8.87039i −0.554300 + 0.714796i
\(155\) 0 0
\(156\) 0 0
\(157\) −7.00000 + 12.1244i −0.558661 + 0.967629i 0.438948 + 0.898513i \(0.355351\pi\)
−0.997609 + 0.0691164i \(0.977982\pi\)
\(158\) 0.378680 0.655892i 0.0301261 0.0521800i
\(159\) 0 0
\(160\) 0 0
\(161\) 1.24264 + 3.04384i 0.0979338 + 0.239888i
\(162\) 0 0
\(163\) 10.1213 17.5306i 0.792763 1.37311i −0.131487 0.991318i \(-0.541975\pi\)
0.924250 0.381788i \(-0.124692\pi\)
\(164\) −11.4853 −0.896850
\(165\) 0 0
\(166\) 16.2426 1.26067
\(167\) −9.10660 15.7731i −0.704690 1.22056i −0.966803 0.255522i \(-0.917753\pi\)
0.262113 0.965037i \(-0.415581\pi\)
\(168\) 0 0
\(169\) 3.98528 6.90271i 0.306560 0.530978i
\(170\) 0 0
\(171\) 0 0
\(172\) −5.24264 9.08052i −0.399748 0.692383i
\(173\) 11.4853 + 19.8931i 0.873210 + 1.51244i 0.858658 + 0.512550i \(0.171299\pi\)
0.0145521 + 0.999894i \(0.495368\pi\)
\(174\) 0 0
\(175\) −5.00000 12.2474i −0.377964 0.925820i
\(176\) −2.12132 3.67423i −0.159901 0.276956i
\(177\) 0 0
\(178\) 11.4853 0.860858
\(179\) −3.87868 6.71807i −0.289906 0.502132i 0.683881 0.729594i \(-0.260291\pi\)
−0.973787 + 0.227461i \(0.926957\pi\)
\(180\) 0 0
\(181\) −11.7574 −0.873918 −0.436959 0.899482i \(-0.643944\pi\)
−0.436959 + 0.899482i \(0.643944\pi\)
\(182\) −5.87868 0.804479i −0.435757 0.0596319i
\(183\) 0 0
\(184\) −1.24264 −0.0916087
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) −4.75736 −0.346966
\(189\) 0 0
\(190\) 0 0
\(191\) −4.24264 7.34847i −0.306987 0.531717i 0.670715 0.741715i \(-0.265987\pi\)
−0.977702 + 0.209999i \(0.932654\pi\)
\(192\) 0 0
\(193\) 10.7426 18.6068i 0.773272 1.33935i −0.162488 0.986710i \(-0.551952\pi\)
0.935760 0.352636i \(-0.114715\pi\)
\(194\) −4.48528 −0.322024
\(195\) 0 0
\(196\) −1.74264 6.77962i −0.124474 0.484258i
\(197\) 16.9706 1.20910 0.604551 0.796566i \(-0.293352\pi\)
0.604551 + 0.796566i \(0.293352\pi\)
\(198\) 0 0
\(199\) 11.6213 + 20.1287i 0.823814 + 1.42689i 0.902823 + 0.430013i \(0.141491\pi\)
−0.0790091 + 0.996874i \(0.525176\pi\)
\(200\) 5.00000 0.353553
\(201\) 0 0
\(202\) −8.12132 14.0665i −0.571414 0.989718i
\(203\) 11.1213 + 1.52192i 0.780564 + 0.106818i
\(204\) 0 0
\(205\) 0 0
\(206\) 4.62132 + 8.00436i 0.321983 + 0.557690i
\(207\) 0 0
\(208\) 1.12132 1.94218i 0.0777496 0.134666i
\(209\) 4.75736 8.23999i 0.329073 0.569972i
\(210\) 0 0
\(211\) −5.24264 9.08052i −0.360918 0.625129i 0.627194 0.778863i \(-0.284203\pi\)
−0.988112 + 0.153734i \(0.950870\pi\)
\(212\) 4.24264 0.291386
\(213\) 0 0
\(214\) 14.4853 0.990193
\(215\) 0 0
\(216\) 0 0
\(217\) −24.2279 3.31552i −1.64470 0.225072i
\(218\) 3.12132 5.40629i 0.211402 0.366160i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 6.86396 11.8887i 0.459645 0.796128i −0.539297 0.842116i \(-0.681310\pi\)
0.998942 + 0.0459873i \(0.0146434\pi\)
\(224\) 2.62132 + 0.358719i 0.175144 + 0.0239680i
\(225\) 0 0
\(226\) 1.75736 3.04384i 0.116898 0.202473i
\(227\) −9.51472 −0.631514 −0.315757 0.948840i \(-0.602258\pi\)
−0.315757 + 0.948840i \(0.602258\pi\)
\(228\) 0 0
\(229\) −8.97056 −0.592791 −0.296396 0.955065i \(-0.595785\pi\)
−0.296396 + 0.955065i \(0.595785\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −2.12132 + 3.67423i −0.139272 + 0.241225i
\(233\) 1.75736 3.04384i 0.115128 0.199408i −0.802703 0.596379i \(-0.796605\pi\)
0.917831 + 0.396971i \(0.129939\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −10.8640 18.8169i −0.702731 1.21717i −0.967504 0.252855i \(-0.918630\pi\)
0.264773 0.964311i \(-0.414703\pi\)
\(240\) 0 0
\(241\) 25.4853 1.64165 0.820826 0.571179i \(-0.193514\pi\)
0.820826 + 0.571179i \(0.193514\pi\)
\(242\) 3.50000 + 6.06218i 0.224989 + 0.389692i
\(243\) 0 0
\(244\) −2.24264 −0.143570
\(245\) 0 0
\(246\) 0 0
\(247\) 5.02944 0.320015
\(248\) 4.62132 8.00436i 0.293454 0.508277i
\(249\) 0 0
\(250\) 0 0
\(251\) 6.72792 0.424663 0.212331 0.977198i \(-0.431894\pi\)
0.212331 + 0.977198i \(0.431894\pi\)
\(252\) 0 0
\(253\) 5.27208 0.331453
\(254\) 7.62132 + 13.2005i 0.478204 + 0.828274i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 11.4853 0.716432 0.358216 0.933639i \(-0.383385\pi\)
0.358216 + 0.933639i \(0.383385\pi\)
\(258\) 0 0
\(259\) 10.4853 + 1.43488i 0.651524 + 0.0891590i
\(260\) 0 0
\(261\) 0 0
\(262\) 8.12132 + 14.0665i 0.501737 + 0.869034i
\(263\) 10.9706 0.676474 0.338237 0.941061i \(-0.390169\pi\)
0.338237 + 0.941061i \(0.390169\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 2.24264 + 5.49333i 0.137505 + 0.336817i
\(267\) 0 0
\(268\) −0.121320 0.210133i −0.00741082 0.0128359i
\(269\) 11.4853 + 19.8931i 0.700270 + 1.21290i 0.968372 + 0.249513i \(0.0802704\pi\)
−0.268102 + 0.963391i \(0.586396\pi\)
\(270\) 0 0
\(271\) −2.24264 + 3.88437i −0.136231 + 0.235959i −0.926067 0.377359i \(-0.876832\pi\)
0.789836 + 0.613318i \(0.210166\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) −6.98528 12.0989i −0.421996 0.730919i
\(275\) −21.2132 −1.27920
\(276\) 0 0
\(277\) 23.2132 1.39475 0.697373 0.716708i \(-0.254352\pi\)
0.697373 + 0.716708i \(0.254352\pi\)
\(278\) 10.3640 17.9509i 0.621589 1.07662i
\(279\) 0 0
\(280\) 0 0
\(281\) −14.2279 + 24.6435i −0.848767 + 1.47011i 0.0335428 + 0.999437i \(0.489321\pi\)
−0.882309 + 0.470670i \(0.844012\pi\)
\(282\) 0 0
\(283\) 4.48528 7.76874i 0.266622 0.461803i −0.701365 0.712802i \(-0.747426\pi\)
0.967987 + 0.250999i \(0.0807590\pi\)
\(284\) 0.621320 1.07616i 0.0368686 0.0638583i
\(285\) 0 0
\(286\) −4.75736 + 8.23999i −0.281309 + 0.487241i
\(287\) −18.6213 + 24.0131i −1.09918 + 1.41745i
\(288\) 0 0
\(289\) 8.50000 14.7224i 0.500000 0.866025i
\(290\) 0 0
\(291\) 0 0
\(292\) −7.00000 −0.409644
\(293\) 11.4853 + 19.8931i 0.670977 + 1.16217i 0.977627 + 0.210344i \(0.0674585\pi\)
−0.306650 + 0.951822i \(0.599208\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −2.00000 + 3.46410i −0.116248 + 0.201347i
\(297\) 0 0
\(298\) −3.87868 6.71807i −0.224686 0.389167i
\(299\) 1.39340 + 2.41344i 0.0805823 + 0.139573i
\(300\) 0 0
\(301\) −27.4853 3.76127i −1.58423 0.216796i
\(302\) −5.62132 9.73641i −0.323471 0.560268i
\(303\) 0 0
\(304\) −2.24264 −0.128624
\(305\) 0 0
\(306\) 0 0
\(307\) −28.0000 −1.59804 −0.799022 0.601302i \(-0.794649\pi\)
−0.799022 + 0.601302i \(0.794649\pi\)
\(308\) −11.1213 1.52192i −0.633696 0.0867193i
\(309\) 0 0
\(310\) 0 0
\(311\) 11.4853 19.8931i 0.651271 1.12803i −0.331544 0.943440i \(-0.607570\pi\)
0.982815 0.184594i \(-0.0590970\pi\)
\(312\) 0 0
\(313\) −7.98528 13.8309i −0.451355 0.781769i 0.547116 0.837057i \(-0.315726\pi\)
−0.998470 + 0.0552876i \(0.982392\pi\)
\(314\) −14.0000 −0.790066
\(315\) 0 0
\(316\) 0.757359 0.0426048
\(317\) 8.48528 + 14.6969i 0.476581 + 0.825462i 0.999640 0.0268342i \(-0.00854260\pi\)
−0.523059 + 0.852296i \(0.675209\pi\)
\(318\) 0 0
\(319\) 9.00000 15.5885i 0.503903 0.872786i
\(320\) 0 0
\(321\) 0 0
\(322\) −2.01472 + 2.59808i −0.112276 + 0.144785i
\(323\) 0 0
\(324\) 0 0
\(325\) −5.60660 9.71092i −0.310998 0.538665i
\(326\) 20.2426 1.12114
\(327\) 0 0
\(328\) −5.74264 9.94655i −0.317084 0.549206i
\(329\) −7.71320 + 9.94655i −0.425243 + 0.548371i
\(330\) 0 0
\(331\) 0.757359 + 1.31178i 0.0416282 + 0.0721022i 0.886089 0.463515i \(-0.153412\pi\)
−0.844461 + 0.535618i \(0.820079\pi\)
\(332\) 8.12132 + 14.0665i 0.445715 + 0.772002i
\(333\) 0 0
\(334\) 9.10660 15.7731i 0.498291 0.863065i
\(335\) 0 0
\(336\) 0 0
\(337\) 6.24264 + 10.8126i 0.340058 + 0.588998i 0.984443 0.175703i \(-0.0562199\pi\)
−0.644385 + 0.764701i \(0.722887\pi\)
\(338\) 7.97056 0.433541
\(339\) 0 0
\(340\) 0 0
\(341\) −19.6066 + 33.9596i −1.06176 + 1.83902i
\(342\) 0 0
\(343\) −17.0000 7.34847i −0.917914 0.396780i
\(344\) 5.24264 9.08052i 0.282664 0.489589i
\(345\) 0 0
\(346\) −11.4853 + 19.8931i −0.617453 + 1.06946i
\(347\) 9.36396 16.2189i 0.502684 0.870674i −0.497311 0.867572i \(-0.665679\pi\)
0.999995 0.00310172i \(-0.000987311\pi\)
\(348\) 0 0
\(349\) 4.48528 7.76874i 0.240092 0.415851i −0.720649 0.693301i \(-0.756156\pi\)
0.960740 + 0.277450i \(0.0894892\pi\)
\(350\) 8.10660 10.4539i 0.433316 0.558782i
\(351\) 0 0
\(352\) 2.12132 3.67423i 0.113067 0.195837i
\(353\) −21.0000 −1.11772 −0.558859 0.829263i \(-0.688761\pi\)
−0.558859 + 0.829263i \(0.688761\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 5.74264 + 9.94655i 0.304359 + 0.527166i
\(357\) 0 0
\(358\) 3.87868 6.71807i 0.204995 0.355061i
\(359\) 9.62132 16.6646i 0.507794 0.879525i −0.492165 0.870502i \(-0.663794\pi\)
0.999959 0.00902308i \(-0.00287218\pi\)
\(360\) 0 0
\(361\) 6.98528 + 12.0989i 0.367646 + 0.636782i
\(362\) −5.87868 10.1822i −0.308977 0.535163i
\(363\) 0 0
\(364\) −2.24264 5.49333i −0.117546 0.287928i
\(365\) 0 0
\(366\) 0 0
\(367\) −13.7279 −0.716592 −0.358296 0.933608i \(-0.616642\pi\)
−0.358296 + 0.933608i \(0.616642\pi\)
\(368\) −0.621320 1.07616i −0.0323886 0.0560986i
\(369\) 0 0
\(370\) 0 0
\(371\) 6.87868 8.87039i 0.357123 0.460528i
\(372\) 0 0
\(373\) 35.2132 1.82327 0.911635 0.411000i \(-0.134820\pi\)
0.911635 + 0.411000i \(0.134820\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −2.37868 4.11999i −0.122671 0.212472i
\(377\) 9.51472 0.490033
\(378\) 0 0
\(379\) 26.7279 1.37292 0.686461 0.727167i \(-0.259163\pi\)
0.686461 + 0.727167i \(0.259163\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 4.24264 7.34847i 0.217072 0.375980i
\(383\) −18.2132 −0.930651 −0.465326 0.885140i \(-0.654063\pi\)
−0.465326 + 0.885140i \(0.654063\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 21.4853 1.09357
\(387\) 0 0
\(388\) −2.24264 3.88437i −0.113853 0.197199i
\(389\) −1.75736 −0.0891017 −0.0445508 0.999007i \(-0.514186\pi\)
−0.0445508 + 0.999007i \(0.514186\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 5.00000 4.89898i 0.252538 0.247436i
\(393\) 0 0
\(394\) 8.48528 + 14.6969i 0.427482 + 0.740421i
\(395\) 0 0
\(396\) 0 0
\(397\) 5.87868 10.1822i 0.295042 0.511029i −0.679952 0.733256i \(-0.738000\pi\)
0.974995 + 0.222228i \(0.0713329\pi\)
\(398\) −11.6213 + 20.1287i −0.582524 + 1.00896i
\(399\) 0 0
\(400\) 2.50000 + 4.33013i 0.125000 + 0.216506i
\(401\) −12.5147 −0.624955 −0.312478 0.949925i \(-0.601159\pi\)
−0.312478 + 0.949925i \(0.601159\pi\)
\(402\) 0 0
\(403\) −20.7279 −1.03253
\(404\) 8.12132 14.0665i 0.404051 0.699836i
\(405\) 0 0
\(406\) 4.24264 + 10.3923i 0.210559 + 0.515761i
\(407\) 8.48528 14.6969i 0.420600 0.728500i
\(408\) 0 0
\(409\) −17.5000 + 30.3109i −0.865319 + 1.49878i 0.00141047 + 0.999999i \(0.499551\pi\)
−0.866730 + 0.498778i \(0.833782\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −4.62132 + 8.00436i −0.227676 + 0.394347i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 2.24264 0.109955
\(417\) 0 0
\(418\) 9.51472 0.465380
\(419\) −8.12132 14.0665i −0.396752 0.687195i 0.596571 0.802561i \(-0.296530\pi\)
−0.993323 + 0.115365i \(0.963196\pi\)
\(420\) 0 0
\(421\) 2.87868 4.98602i 0.140298 0.243004i −0.787311 0.616557i \(-0.788527\pi\)
0.927609 + 0.373553i \(0.121861\pi\)
\(422\) 5.24264 9.08052i 0.255208 0.442033i
\(423\) 0 0
\(424\) 2.12132 + 3.67423i 0.103020 + 0.178437i
\(425\) 0 0
\(426\) 0 0
\(427\) −3.63604 + 4.68885i −0.175960 + 0.226909i
\(428\) 7.24264 + 12.5446i 0.350086 + 0.606367i
\(429\) 0 0
\(430\) 0 0
\(431\) −14.3787 24.9046i −0.692597 1.19961i −0.970984 0.239144i \(-0.923133\pi\)
0.278388 0.960469i \(-0.410200\pi\)
\(432\) 0 0
\(433\) −29.9706 −1.44029 −0.720147 0.693822i \(-0.755926\pi\)
−0.720147 + 0.693822i \(0.755926\pi\)
\(434\) −9.24264 22.6398i −0.443661 1.08674i
\(435\) 0 0
\(436\) 6.24264 0.298968
\(437\) 1.39340 2.41344i 0.0666553 0.115450i
\(438\) 0 0
\(439\) 6.86396 + 11.8887i 0.327599 + 0.567418i 0.982035 0.188699i \(-0.0604272\pi\)
−0.654436 + 0.756117i \(0.727094\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 13.2426 + 22.9369i 0.629177 + 1.08977i 0.987717 + 0.156252i \(0.0499412\pi\)
−0.358540 + 0.933514i \(0.616725\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 13.7279 0.650036
\(447\) 0 0
\(448\) 1.00000 + 2.44949i 0.0472456 + 0.115728i
\(449\) −28.9706 −1.36721 −0.683603 0.729854i \(-0.739588\pi\)
−0.683603 + 0.729854i \(0.739588\pi\)
\(450\) 0 0
\(451\) 24.3640 + 42.1996i 1.14725 + 1.98710i
\(452\) 3.51472 0.165318
\(453\) 0 0
\(454\) −4.75736 8.23999i −0.223274 0.386722i
\(455\) 0 0
\(456\) 0 0
\(457\) −14.2426 24.6690i −0.666243 1.15397i −0.978947 0.204116i \(-0.934568\pi\)
0.312704 0.949851i \(-0.398765\pi\)
\(458\) −4.48528 7.76874i −0.209583 0.363009i
\(459\) 0 0
\(460\) 0 0
\(461\) 12.8787 22.3065i 0.599820 1.03892i −0.393027 0.919527i \(-0.628572\pi\)
0.992847 0.119392i \(-0.0380944\pi\)
\(462\) 0 0
\(463\) 8.62132 + 14.9326i 0.400667 + 0.693975i 0.993807 0.111124i \(-0.0354452\pi\)
−0.593140 + 0.805100i \(0.702112\pi\)
\(464\) −4.24264 −0.196960
\(465\) 0 0
\(466\) 3.51472 0.162816
\(467\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(468\) 0 0
\(469\) −0.636039 0.0870399i −0.0293696 0.00401913i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −22.2426 + 38.5254i −1.02272 + 1.77140i
\(474\) 0 0
\(475\) −5.60660 + 9.71092i −0.257249 + 0.445568i
\(476\) 0 0
\(477\) 0 0
\(478\) 10.8640 18.8169i 0.496906 0.860666i
\(479\) 4.75736 0.217369 0.108685 0.994076i \(-0.465336\pi\)
0.108685 + 0.994076i \(0.465336\pi\)
\(480\) 0 0
\(481\) 8.97056 0.409022
\(482\) 12.7426 + 22.0709i 0.580411 + 1.00530i
\(483\) 0 0
\(484\) −3.50000 + 6.06218i −0.159091 + 0.275554i
\(485\) 0 0
\(486\) 0 0
\(487\) 5.62132 + 9.73641i 0.254726 + 0.441199i 0.964821 0.262907i \(-0.0846813\pi\)
−0.710095 + 0.704106i \(0.751348\pi\)
\(488\) −1.12132 1.94218i −0.0507598 0.0879185i
\(489\) 0 0
\(490\) 0 0
\(491\) −9.36396 16.2189i −0.422590 0.731947i 0.573602 0.819134i \(-0.305546\pi\)
−0.996192 + 0.0871872i \(0.972212\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 2.51472 + 4.35562i 0.113143 + 0.195969i
\(495\) 0 0
\(496\) 9.24264 0.415007
\(497\) −1.24264 3.04384i −0.0557401 0.136535i
\(498\) 0 0
\(499\) 14.7279 0.659312 0.329656 0.944101i \(-0.393067\pi\)
0.329656 + 0.944101i \(0.393067\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 3.36396 + 5.82655i 0.150141 + 0.260052i
\(503\) −18.2132 −0.812087 −0.406043 0.913854i \(-0.633092\pi\)
−0.406043 + 0.913854i \(0.633092\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 2.63604 + 4.56575i 0.117186 + 0.202972i
\(507\) 0 0
\(508\) −7.62132 + 13.2005i −0.338141 + 0.585678i
\(509\) −16.2426 −0.719942 −0.359971 0.932963i \(-0.617213\pi\)
−0.359971 + 0.932963i \(0.617213\pi\)
\(510\) 0 0
\(511\) −11.3492 + 14.6354i −0.502061 + 0.647432i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 5.74264 + 9.94655i 0.253297 + 0.438723i
\(515\) 0 0
\(516\) 0 0
\(517\) 10.0919 + 17.4797i 0.443841 + 0.768754i
\(518\) 4.00000 + 9.79796i 0.175750 + 0.430498i
\(519\) 0 0
\(520\) 0 0
\(521\) −17.2279 29.8396i −0.754769 1.30730i −0.945489 0.325654i \(-0.894416\pi\)
0.190720 0.981644i \(-0.438918\pi\)
\(522\) 0 0
\(523\) 5.87868 10.1822i 0.257057 0.445235i −0.708395 0.705816i \(-0.750581\pi\)
0.965452 + 0.260581i \(0.0839139\pi\)
\(524\) −8.12132 + 14.0665i −0.354782 + 0.614500i
\(525\) 0 0
\(526\) 5.48528 + 9.50079i 0.239170 + 0.414254i
\(527\) 0 0
\(528\) 0 0
\(529\) −21.4558 −0.932863
\(530\) 0 0
\(531\) 0 0
\(532\) −3.63604 + 4.68885i −0.157642 + 0.203287i
\(533\) −12.8787 + 22.3065i −0.557838 + 0.966203i
\(534\) 0 0
\(535\) 0 0
\(536\) 0.121320 0.210133i 0.00524024 0.00907636i
\(537\) 0 0
\(538\) −11.4853 + 19.8931i −0.495166 + 0.857652i
\(539\) −21.2132 + 20.7846i −0.913717 + 0.895257i
\(540\) 0 0
\(541\) −9.48528 + 16.4290i −0.407804 + 0.706337i −0.994643 0.103366i \(-0.967039\pi\)
0.586839 + 0.809703i \(0.300372\pi\)
\(542\) −4.48528 −0.192659
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −5.24264 + 9.08052i −0.224159 + 0.388255i −0.956067 0.293149i \(-0.905297\pi\)
0.731908 + 0.681404i \(0.238630\pi\)
\(548\) 6.98528 12.0989i 0.298396 0.516838i
\(549\) 0 0
\(550\) −10.6066 18.3712i −0.452267 0.783349i
\(551\) −4.75736 8.23999i −0.202670 0.351035i
\(552\) 0 0
\(553\) 1.22792 1.58346i 0.0522166 0.0673358i
\(554\) 11.6066 + 20.1032i 0.493117 + 0.854104i
\(555\) 0 0
\(556\) 20.7279 0.879060
\(557\) −3.51472 6.08767i −0.148923 0.257943i 0.781906 0.623396i \(-0.214247\pi\)
−0.930830 + 0.365453i \(0.880914\pi\)
\(558\) 0 0
\(559\) −23.5147 −0.994567
\(560\) 0 0
\(561\) 0 0
\(562\) −28.4558 −1.20034
\(563\) −3.36396 + 5.82655i −0.141774 + 0.245560i −0.928165 0.372170i \(-0.878614\pi\)
0.786391 + 0.617729i \(0.211947\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 8.97056 0.377061
\(567\) 0 0
\(568\) 1.24264 0.0521400
\(569\) −21.4706 37.1881i −0.900093 1.55901i −0.827372 0.561654i \(-0.810165\pi\)
−0.0727207 0.997352i \(-0.523168\pi\)
\(570\) 0 0
\(571\) −6.48528 + 11.2328i −0.271401 + 0.470080i −0.969221 0.246193i \(-0.920820\pi\)
0.697820 + 0.716273i \(0.254153\pi\)
\(572\) −9.51472 −0.397830
\(573\) 0 0
\(574\) −30.1066 4.11999i −1.25663 0.171965i
\(575\) −6.21320 −0.259108
\(576\) 0 0
\(577\) 15.9706 + 27.6618i 0.664863 + 1.15158i 0.979322 + 0.202306i \(0.0648435\pi\)
−0.314459 + 0.949271i \(0.601823\pi\)
\(578\) 17.0000 0.707107
\(579\) 0 0
\(580\) 0 0
\(581\) 42.5772 + 5.82655i 1.76640 + 0.241726i
\(582\) 0 0
\(583\) −9.00000 15.5885i −0.372742 0.645608i
\(584\) −3.50000 6.06218i −0.144831 0.250855i
\(585\) 0 0
\(586\) −11.4853 + 19.8931i −0.474453 + 0.821776i
\(587\) 19.6066 33.9596i 0.809251 1.40166i −0.104132 0.994563i \(-0.533207\pi\)
0.913383 0.407100i \(-0.133460\pi\)
\(588\) 0 0
\(589\) 10.3640 + 17.9509i 0.427040 + 0.739654i
\(590\) 0 0
\(591\) 0 0
\(592\) −4.00000 −0.164399
\(593\) 5.74264 9.94655i 0.235822 0.408456i −0.723689 0.690126i \(-0.757555\pi\)
0.959511 + 0.281670i \(0.0908884\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 3.87868 6.71807i 0.158877 0.275183i
\(597\) 0 0
\(598\) −1.39340 + 2.41344i −0.0569803 + 0.0986928i
\(599\) −5.48528 + 9.50079i −0.224123 + 0.388192i −0.956056 0.293185i \(-0.905285\pi\)
0.731933 + 0.681376i \(0.238618\pi\)
\(600\) 0 0
\(601\) −7.98528 + 13.8309i −0.325726 + 0.564175i −0.981659 0.190645i \(-0.938942\pi\)
0.655933 + 0.754819i \(0.272276\pi\)
\(602\) −10.4853 25.6836i −0.427348 1.04678i
\(603\) 0 0
\(604\) 5.62132 9.73641i 0.228728 0.396169i
\(605\) 0 0
\(606\) 0 0
\(607\) −5.02944 −0.204139 −0.102069 0.994777i \(-0.532546\pi\)
−0.102069 + 0.994777i \(0.532546\pi\)
\(608\) −1.12132 1.94218i −0.0454755 0.0787660i
\(609\) 0 0
\(610\) 0 0
\(611\) −5.33452 + 9.23967i −0.215812 + 0.373797i
\(612\) 0 0
\(613\) −14.9706 25.9298i −0.604655 1.04729i −0.992106 0.125403i \(-0.959978\pi\)
0.387451 0.921891i \(-0.373356\pi\)
\(614\) −14.0000 24.2487i −0.564994 0.978598i
\(615\) 0 0
\(616\) −4.24264 10.3923i −0.170941 0.418718i
\(617\) 11.2279 + 19.4473i 0.452019 + 0.782920i 0.998511 0.0545441i \(-0.0173705\pi\)
−0.546492 + 0.837464i \(0.684037\pi\)
\(618\) 0 0
\(619\) −18.4853 −0.742986 −0.371493 0.928436i \(-0.621154\pi\)
−0.371493 + 0.928436i \(0.621154\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 22.9706 0.921036
\(623\) 30.1066 + 4.11999i 1.20620 + 0.165064i
\(624\) 0 0
\(625\) 25.0000 1.00000
\(626\) 7.98528 13.8309i 0.319156 0.552794i
\(627\) 0 0
\(628\) −7.00000 12.1244i −0.279330 0.483814i
\(629\) 0 0
\(630\) 0 0
\(631\) −7.51472 −0.299156 −0.149578 0.988750i \(-0.547792\pi\)
−0.149578 + 0.988750i \(0.547792\pi\)
\(632\) 0.378680 + 0.655892i 0.0150631 + 0.0260900i
\(633\) 0 0
\(634\) −8.48528 + 14.6969i −0.336994 + 0.583690i
\(635\) 0 0
\(636\) 0 0
\(637\) −15.1213 4.21759i −0.599129 0.167107i
\(638\) 18.0000 0.712627
\(639\) 0 0
\(640\) 0 0
\(641\) −46.4558 −1.83490 −0.917448 0.397856i \(-0.869754\pi\)
−0.917448 + 0.397856i \(0.869754\pi\)
\(642\) 0 0
\(643\) 10.6360 + 18.4222i 0.419444 + 0.726499i 0.995884 0.0906410i \(-0.0288916\pi\)
−0.576439 + 0.817140i \(0.695558\pi\)
\(644\) −3.25736 0.445759i −0.128358 0.0175654i
\(645\) 0 0
\(646\) 0 0
\(647\) 13.8640 + 24.0131i 0.545049 + 0.944052i 0.998604 + 0.0528236i \(0.0168221\pi\)
−0.453555 + 0.891228i \(0.649845\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 5.60660 9.71092i 0.219909 0.380894i
\(651\) 0 0
\(652\) 10.1213 + 17.5306i 0.396381 + 0.686553i
\(653\) −24.0000 −0.939193 −0.469596 0.882881i \(-0.655601\pi\)
−0.469596 + 0.882881i \(0.655601\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 5.74264 9.94655i 0.224212 0.388347i
\(657\) 0 0
\(658\) −12.4706 1.70656i −0.486153 0.0665285i
\(659\) 1.60660 2.78272i 0.0625843 0.108399i −0.833036 0.553219i \(-0.813399\pi\)
0.895620 + 0.444820i \(0.146732\pi\)
\(660\) 0 0
\(661\) −17.0919 + 29.6040i −0.664797 + 1.15146i 0.314543 + 0.949243i \(0.398149\pi\)
−0.979340 + 0.202219i \(0.935185\pi\)
\(662\) −0.757359 + 1.31178i −0.0294356 + 0.0509840i
\(663\) 0 0
\(664\) −8.12132 + 14.0665i −0.315168 + 0.545888i
\(665\) 0 0
\(666\) 0 0
\(667\) 2.63604 4.56575i 0.102068 0.176787i
\(668\) 18.2132 0.704690
\(669\) 0 0
\(670\) 0 0
\(671\) 4.75736 + 8.23999i 0.183656 + 0.318101i
\(672\) 0 0
\(673\) 5.25736 9.10601i 0.202656 0.351011i −0.746727 0.665130i \(-0.768376\pi\)
0.949383 + 0.314119i \(0.101709\pi\)
\(674\) −6.24264 + 10.8126i −0.240458 + 0.416485i
\(675\) 0 0
\(676\) 3.98528 + 6.90271i 0.153280 + 0.265489i
\(677\) 12.8787 + 22.3065i 0.494968 + 0.857309i 0.999983 0.00580089i \(-0.00184649\pi\)
−0.505015 + 0.863110i \(0.668513\pi\)
\(678\) 0 0
\(679\) −11.7574 1.60896i −0.451206 0.0617461i
\(680\) 0 0
\(681\) 0 0
\(682\) −39.2132 −1.50155
\(683\) −8.84924 15.3273i −0.338607 0.586484i 0.645564 0.763706i \(-0.276622\pi\)
−0.984171 + 0.177222i \(0.943289\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −2.13604 18.3967i −0.0815543 0.702388i
\(687\) 0 0
\(688\) 10.4853 0.399748
\(689\) 4.75736 8.23999i 0.181241 0.313919i
\(690\) 0 0
\(691\) 1.12132 + 1.94218i 0.0426570 + 0.0738842i 0.886566 0.462603i \(-0.153084\pi\)
−0.843909 + 0.536487i \(0.819751\pi\)
\(692\) −22.9706 −0.873210
\(693\) 0 0
\(694\) 18.7279 0.710902
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 8.97056 0.339541
\(699\) 0 0
\(700\) 13.1066 + 1.79360i 0.495383 + 0.0677916i
\(701\) −22.2426 −0.840093 −0.420046 0.907503i \(-0.637986\pi\)
−0.420046 + 0.907503i \(0.637986\pi\)
\(702\) 0 0
\(703\) −4.48528 7.76874i −0.169166 0.293003i
\(704\) 4.24264 0.159901
\(705\) 0 0
\(706\) −10.5000 18.1865i −0.395173 0.684459i
\(707\) −16.2426 39.7862i −0.610867 1.49631i
\(708\) 0 0
\(709\) 16.8492 + 29.1837i 0.632787 + 1.09602i 0.986979 + 0.160846i \(0.0514223\pi\)
−0.354193 + 0.935172i \(0.615244\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −5.74264 + 9.94655i −0.215215 + 0.372763i
\(713\) −5.74264 + 9.94655i −0.215064 + 0.372501i
\(714\) 0 0
\(715\) 0 0
\(716\) 7.75736 0.289906
\(717\) 0 0
\(718\) 19.2426 0.718129
\(719\) −13.8640 + 24.0131i −0.517039 + 0.895537i 0.482766 + 0.875750i \(0.339632\pi\)
−0.999804 + 0.0197874i \(0.993701\pi\)
\(720\) 0 0
\(721\) 9.24264 + 22.6398i 0.344214 + 0.843148i
\(722\) −6.98528 + 12.0989i −0.259965 + 0.450273i
\(723\) 0 0
\(724\) 5.87868 10.1822i 0.218479 0.378417i
\(725\) −10.6066 + 18.3712i −0.393919 + 0.682288i
\(726\) 0 0
\(727\) 0.136039 0.235626i 0.00504541 0.00873890i −0.863492 0.504363i \(-0.831727\pi\)
0.868537 + 0.495624i \(0.165061\pi\)
\(728\) 3.63604 4.68885i 0.134761 0.173780i
\(729\) 0 0
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) −5.02944 −0.185767 −0.0928833 0.995677i \(-0.529608\pi\)
−0.0928833 + 0.995677i \(0.529608\pi\)
\(734\) −6.86396 11.8887i −0.253353 0.438821i
\(735\) 0 0
\(736\) 0.621320 1.07616i 0.0229022 0.0396677i
\(737\) −0.514719 + 0.891519i −0.0189599 + 0.0328395i
\(738\) 0 0
\(739\) 3.24264 + 5.61642i 0.119282 + 0.206603i 0.919484 0.393129i \(-0.128607\pi\)
−0.800201 + 0.599732i \(0.795274\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 11.1213 + 1.52192i 0.408277 + 0.0558714i
\(743\) 21.6213 + 37.4492i 0.793209 + 1.37388i 0.923970 + 0.382465i \(0.124925\pi\)
−0.130761 + 0.991414i \(0.541742\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 17.6066 + 30.4955i 0.644623 + 1.11652i
\(747\) 0 0
\(748\) 0 0
\(749\) 37.9706 + 5.19615i 1.38741 + 0.189863i
\(750\) 0 0
\(751\) −8.75736 −0.319561 −0.159780 0.987153i \(-0.551079\pi\)
−0.159780 + 0.987153i \(0.551079\pi\)
\(752\) 2.37868 4.11999i 0.0867415 0.150241i
\(753\) 0 0
\(754\) 4.75736 + 8.23999i 0.173253 + 0.300083i
\(755\) 0 0
\(756\) 0 0
\(757\) −20.9706 −0.762188 −0.381094 0.924536i \(-0.624453\pi\)
−0.381094 + 0.924536i \(0.624453\pi\)
\(758\) 13.3640 + 23.1471i 0.485401 + 0.840739i
\(759\) 0 0
\(760\) 0 0
\(761\) −21.0000 −0.761249 −0.380625 0.924730i \(-0.624291\pi\)
−0.380625 + 0.924730i \(0.624291\pi\)
\(762\) 0 0
\(763\) 10.1213 13.0519i 0.366416 0.472512i
\(764\) 8.48528 0.306987
\(765\) 0 0
\(766\) −9.10660 15.7731i −0.329035 0.569905i
\(767\) 0 0
\(768\) 0 0
\(769\) −2.24264 3.88437i −0.0808717 0.140074i 0.822753 0.568399i \(-0.192437\pi\)
−0.903625 + 0.428325i \(0.859104\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 10.7426 + 18.6068i 0.386636 + 0.669673i
\(773\) −1.39340 2.41344i −0.0501171 0.0868053i 0.839879 0.542774i \(-0.182626\pi\)
−0.889996 + 0.455969i \(0.849293\pi\)
\(774\) 0 0
\(775\) 23.1066 40.0218i 0.830014 1.43763i
\(776\) 2.24264 3.88437i 0.0805061 0.139441i
\(777\) 0 0
\(778\) −0.878680 1.52192i −0.0315022 0.0545634i
\(779\) 25.7574 0.922853
\(780\) 0 0
\(781\) −5.27208 −0.188650
\(782\) 0 0
\(783\) 0 0
\(784\) 6.74264 + 1.88064i 0.240809 + 0.0671656i
\(785\) 0 0
\(786\) 0 0
\(787\) −5.60660 + 9.71092i −0.199854 + 0.346157i −0.948481 0.316834i \(-0.897380\pi\)
0.748627 + 0.662991i \(0.230713\pi\)
\(788\) −8.48528 + 14.6969i −0.302276 + 0.523557i
\(789\) 0 0
\(790\) 0 0
\(791\) 5.69848 7.34847i 0.202615 0.261281i
\(792\) 0 0
\(793\) −2.51472 + 4.35562i −0.0893003 + 0.154673i
\(794\) 11.7574 0.417253
\(795\) 0 0
\(796\) −23.2426 −0.823814