Properties

Label 1170.2.bj.c.199.4
Level $1170$
Weight $2$
Character 1170.199
Analytic conductor $9.342$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1170.bj (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.34249703649\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 2 x^{11} - 8 x^{10} + 34 x^{9} + 8 x^{8} - 134 x^{7} + 98 x^{6} + 154 x^{5} + 104 x^{4} + 190 x^{3} - 1196 x^{2} - 338 x + 2197\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 390)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 199.4
Root \(-1.44229 - 0.433312i\) of defining polynomial
Character \(\chi\) \(=\) 1170.199
Dual form 1170.2.bj.c.829.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.230377 + 2.22417i) q^{5} +(-0.432713 - 0.749482i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.230377 + 2.22417i) q^{5} +(-0.432713 - 0.749482i) q^{7} +1.00000 q^{8} +(-1.81100 - 1.31160i) q^{10} +(-0.151430 - 0.0874279i) q^{11} +(-1.35486 - 3.34131i) q^{13} +0.865427 q^{14} +(-0.500000 + 0.866025i) q^{16} +(7.08339 - 4.08960i) q^{17} +(5.20843 - 3.00709i) q^{19} +(2.04138 - 0.912572i) q^{20} +(0.151430 - 0.0874279i) q^{22} +(2.52211 + 1.45614i) q^{23} +(-4.89385 - 1.02479i) q^{25} +(3.57109 + 0.497314i) q^{26} +(-0.432713 + 0.749482i) q^{28} +(-3.24491 + 5.62035i) q^{29} +6.95057i q^{31} +(-0.500000 - 0.866025i) q^{32} +8.17919i q^{34} +(1.76666 - 0.789764i) q^{35} +(0.879573 - 1.52347i) q^{37} +6.01418i q^{38} +(-0.230377 + 2.22417i) q^{40} +(7.08339 + 4.08960i) q^{41} +(7.94476 - 4.58691i) q^{43} +0.174856i q^{44} +(-2.52211 + 1.45614i) q^{46} -11.9021 q^{47} +(3.12552 - 5.41356i) q^{49} +(3.33442 - 3.72580i) q^{50} +(-2.21623 + 2.84400i) q^{52} +2.48735i q^{53} +(0.229340 - 0.316664i) q^{55} +(-0.432713 - 0.749482i) q^{56} +(-3.24491 - 5.62035i) q^{58} +(6.09393 - 3.51833i) q^{59} +(3.98695 + 6.90559i) q^{61} +(-6.01937 - 3.47529i) q^{62} +1.00000 q^{64} +(7.74377 - 2.24367i) q^{65} +(-1.36766 + 2.36886i) q^{67} +(-7.08339 - 4.08960i) q^{68} +(-0.199374 + 1.92486i) q^{70} +(-12.2677 + 7.08275i) q^{71} +12.8706 q^{73} +(0.879573 + 1.52347i) q^{74} +(-5.20843 - 3.00709i) q^{76} +0.151325i q^{77} +9.48961 q^{79} +(-1.81100 - 1.31160i) q^{80} +(-7.08339 + 4.08960i) q^{82} +0.139544 q^{83} +(7.46410 + 16.6968i) q^{85} +9.17382i q^{86} +(-0.151430 - 0.0874279i) q^{88} +(11.3790 + 6.56966i) q^{89} +(-1.91799 + 2.46127i) q^{91} -2.91228i q^{92} +(5.95105 - 10.3075i) q^{94} +(5.48837 + 12.2772i) q^{95} +(4.32411 + 7.48957i) q^{97} +(3.12552 + 5.41356i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 6 q^{2} - 6 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8} + O(q^{10}) \) \( 12 q - 6 q^{2} - 6 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8} + 4 q^{10} - 6 q^{11} + 8 q^{13} - 4 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} - 2 q^{20} + 6 q^{22} + 6 q^{23} - 10 q^{25} + 2 q^{26} + 2 q^{28} - 14 q^{29} - 6 q^{32} + 22 q^{35} + 12 q^{37} - 2 q^{40} + 18 q^{41} + 36 q^{43} - 6 q^{46} + 16 q^{47} + 8 q^{49} + 20 q^{50} - 10 q^{52} + 8 q^{55} + 2 q^{56} - 14 q^{58} + 36 q^{59} + 10 q^{61} + 6 q^{62} + 12 q^{64} + 44 q^{65} - 4 q^{67} - 18 q^{68} + 4 q^{70} + 12 q^{71} - 28 q^{73} + 12 q^{74} + 6 q^{76} + 4 q^{79} + 4 q^{80} - 18 q^{82} + 72 q^{83} + 48 q^{85} - 6 q^{88} - 18 q^{89} + 2 q^{91} - 8 q^{94} - 18 q^{95} + 48 q^{97} + 8 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).

\(n\) \(911\) \(937\) \(1081\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{6}\right)\)

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
\(5\) −0.230377 + 2.22417i −0.103028 + 0.994678i
\(6\) 0 0
\(7\) −0.432713 0.749482i −0.163550 0.283277i 0.772589 0.634906i \(-0.218961\pi\)
−0.936140 + 0.351629i \(0.885628\pi\)
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) −1.81100 1.31160i −0.572688 0.414763i
\(11\) −0.151430 0.0874279i −0.0456577 0.0263605i 0.476997 0.878905i \(-0.341725\pi\)
−0.522655 + 0.852544i \(0.675058\pi\)
\(12\) 0 0
\(13\) −1.35486 3.34131i −0.375770 0.926713i
\(14\) 0.865427 0.231295
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 7.08339 4.08960i 1.71797 0.991873i 0.795370 0.606125i \(-0.207277\pi\)
0.922604 0.385748i \(-0.126057\pi\)
\(18\) 0 0
\(19\) 5.20843 3.00709i 1.19490 0.689873i 0.235483 0.971879i \(-0.424333\pi\)
0.959413 + 0.282005i \(0.0909996\pi\)
\(20\) 2.04138 0.912572i 0.456465 0.204057i
\(21\) 0 0
\(22\) 0.151430 0.0874279i 0.0322849 0.0186397i
\(23\) 2.52211 + 1.45614i 0.525896 + 0.303626i 0.739344 0.673328i \(-0.235136\pi\)
−0.213448 + 0.976954i \(0.568469\pi\)
\(24\) 0 0
\(25\) −4.89385 1.02479i −0.978771 0.204959i
\(26\) 3.57109 + 0.497314i 0.700348 + 0.0975312i
\(27\) 0 0
\(28\) −0.432713 + 0.749482i −0.0817752 + 0.141639i
\(29\) −3.24491 + 5.62035i −0.602564 + 1.04367i 0.389867 + 0.920871i \(0.372521\pi\)
−0.992431 + 0.122801i \(0.960812\pi\)
\(30\) 0 0
\(31\) 6.95057i 1.24836i 0.781281 + 0.624180i \(0.214567\pi\)
−0.781281 + 0.624180i \(0.785433\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0 0
\(34\) 8.17919i 1.40272i
\(35\) 1.76666 0.789764i 0.298620 0.133495i
\(36\) 0 0
\(37\) 0.879573 1.52347i 0.144601 0.250456i −0.784623 0.619973i \(-0.787144\pi\)
0.929224 + 0.369517i \(0.120477\pi\)
\(38\) 6.01418i 0.975628i
\(39\) 0 0
\(40\) −0.230377 + 2.22417i −0.0364258 + 0.351672i
\(41\) 7.08339 + 4.08960i 1.10624 + 0.638688i 0.937853 0.347034i \(-0.112811\pi\)
0.168387 + 0.985721i \(0.446144\pi\)
\(42\) 0 0
\(43\) 7.94476 4.58691i 1.21156 0.699497i 0.248465 0.968641i \(-0.420074\pi\)
0.963100 + 0.269144i \(0.0867407\pi\)
\(44\) 0.174856i 0.0263605i
\(45\) 0 0
\(46\) −2.52211 + 1.45614i −0.371865 + 0.214696i
\(47\) −11.9021 −1.73610 −0.868050 0.496478i \(-0.834627\pi\)
−0.868050 + 0.496478i \(0.834627\pi\)
\(48\) 0 0
\(49\) 3.12552 5.41356i 0.446503 0.773365i
\(50\) 3.33442 3.72580i 0.471559 0.526908i
\(51\) 0 0
\(52\) −2.21623 + 2.84400i −0.307336 + 0.394391i
\(53\) 2.48735i 0.341663i 0.985300 + 0.170832i \(0.0546454\pi\)
−0.985300 + 0.170832i \(0.945355\pi\)
\(54\) 0 0
\(55\) 0.229340 0.316664i 0.0309242 0.0426989i
\(56\) −0.432713 0.749482i −0.0578238 0.100154i
\(57\) 0 0
\(58\) −3.24491 5.62035i −0.426077 0.737988i
\(59\) 6.09393 3.51833i 0.793363 0.458048i −0.0477824 0.998858i \(-0.515215\pi\)
0.841145 + 0.540810i \(0.181882\pi\)
\(60\) 0 0
\(61\) 3.98695 + 6.90559i 0.510476 + 0.884171i 0.999926 + 0.0121394i \(0.00386418\pi\)
−0.489450 + 0.872031i \(0.662802\pi\)
\(62\) −6.01937 3.47529i −0.764461 0.441362i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 7.74377 2.24367i 0.960496 0.278293i
\(66\) 0 0
\(67\) −1.36766 + 2.36886i −0.167086 + 0.289402i −0.937394 0.348270i \(-0.886769\pi\)
0.770308 + 0.637672i \(0.220103\pi\)
\(68\) −7.08339 4.08960i −0.858987 0.495936i
\(69\) 0 0
\(70\) −0.199374 + 1.92486i −0.0238298 + 0.230064i
\(71\) −12.2677 + 7.08275i −1.45591 + 0.840568i −0.998806 0.0488476i \(-0.984445\pi\)
−0.457100 + 0.889415i \(0.651112\pi\)
\(72\) 0 0
\(73\) 12.8706 1.50639 0.753193 0.657800i \(-0.228513\pi\)
0.753193 + 0.657800i \(0.228513\pi\)
\(74\) 0.879573 + 1.52347i 0.102248 + 0.177099i
\(75\) 0 0
\(76\) −5.20843 3.00709i −0.597448 0.344937i
\(77\) 0.151325i 0.0172451i
\(78\) 0 0
\(79\) 9.48961 1.06766 0.533832 0.845590i \(-0.320751\pi\)
0.533832 + 0.845590i \(0.320751\pi\)
\(80\) −1.81100 1.31160i −0.202476 0.146641i
\(81\) 0 0
\(82\) −7.08339 + 4.08960i −0.782229 + 0.451620i
\(83\) 0.139544 0.0153169 0.00765845 0.999971i \(-0.497562\pi\)
0.00765845 + 0.999971i \(0.497562\pi\)
\(84\) 0 0
\(85\) 7.46410 + 16.6968i 0.809595 + 1.81102i
\(86\) 9.17382i 0.989238i
\(87\) 0 0
\(88\) −0.151430 0.0874279i −0.0161424 0.00931985i
\(89\) 11.3790 + 6.56966i 1.20617 + 0.696382i 0.961920 0.273330i \(-0.0881253\pi\)
0.244249 + 0.969713i \(0.421459\pi\)
\(90\) 0 0
\(91\) −1.91799 + 2.46127i −0.201060 + 0.258011i
\(92\) 2.91228i 0.303626i
\(93\) 0 0
\(94\) 5.95105 10.3075i 0.613804 1.06314i
\(95\) 5.48837 + 12.2772i 0.563095 + 1.25961i
\(96\) 0 0
\(97\) 4.32411 + 7.48957i 0.439047 + 0.760451i 0.997616 0.0690066i \(-0.0219830\pi\)
−0.558570 + 0.829458i \(0.688650\pi\)
\(98\) 3.12552 + 5.41356i 0.315725 + 0.546852i
\(99\) 0 0
\(100\) 1.55943 + 4.75060i 0.155943 + 0.475060i
\(101\) 5.28276 9.15001i 0.525654 0.910460i −0.473899 0.880579i \(-0.657154\pi\)
0.999553 0.0298810i \(-0.00951284\pi\)
\(102\) 0 0
\(103\) 8.93568i 0.880459i −0.897885 0.440230i \(-0.854897\pi\)
0.897885 0.440230i \(-0.145103\pi\)
\(104\) −1.35486 3.34131i −0.132855 0.327642i
\(105\) 0 0
\(106\) −2.15410 1.24367i −0.209225 0.120796i
\(107\) −0.745455 0.430389i −0.0720658 0.0416072i 0.463534 0.886079i \(-0.346581\pi\)
−0.535600 + 0.844472i \(0.679914\pi\)
\(108\) 0 0
\(109\) 5.45336i 0.522337i −0.965293 0.261168i \(-0.915892\pi\)
0.965293 0.261168i \(-0.0841078\pi\)
\(110\) 0.159569 + 0.356946i 0.0152143 + 0.0340335i
\(111\) 0 0
\(112\) 0.865427 0.0817752
\(113\) −10.2036 + 5.89106i −0.959876 + 0.554184i −0.896135 0.443782i \(-0.853636\pi\)
−0.0637409 + 0.997966i \(0.520303\pi\)
\(114\) 0 0
\(115\) −3.81974 + 5.27413i −0.356192 + 0.491815i
\(116\) 6.48982 0.602564
\(117\) 0 0
\(118\) 7.03667i 0.647778i
\(119\) −6.13015 3.53925i −0.561950 0.324442i
\(120\) 0 0
\(121\) −5.48471 9.49980i −0.498610 0.863618i
\(122\) −7.97389 −0.721922
\(123\) 0 0
\(124\) 6.01937 3.47529i 0.540555 0.312090i
\(125\) 3.40675 10.6487i 0.304709 0.952446i
\(126\) 0 0
\(127\) −6.01228 3.47119i −0.533503 0.308018i 0.208939 0.977929i \(-0.432999\pi\)
−0.742442 + 0.669911i \(0.766332\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −1.92881 + 7.82814i −0.169167 + 0.686573i
\(131\) −2.27133 −0.198447 −0.0992235 0.995065i \(-0.531636\pi\)
−0.0992235 + 0.995065i \(0.531636\pi\)
\(132\) 0 0
\(133\) −4.50751 2.60241i −0.390851 0.225658i
\(134\) −1.36766 2.36886i −0.118148 0.204638i
\(135\) 0 0
\(136\) 7.08339 4.08960i 0.607395 0.350680i
\(137\) 3.68809 + 6.38795i 0.315094 + 0.545760i 0.979458 0.201650i \(-0.0646305\pi\)
−0.664363 + 0.747410i \(0.731297\pi\)
\(138\) 0 0
\(139\) 0.410380 + 0.710798i 0.0348079 + 0.0602891i 0.882905 0.469552i \(-0.155585\pi\)
−0.848097 + 0.529842i \(0.822251\pi\)
\(140\) −1.56729 1.13509i −0.132460 0.0959327i
\(141\) 0 0
\(142\) 14.1655i 1.18874i
\(143\) −0.0869582 + 0.624426i −0.00727181 + 0.0522171i
\(144\) 0 0
\(145\) −11.7530 8.51202i −0.976037 0.706885i
\(146\) −6.43528 + 11.1462i −0.532588 + 0.922469i
\(147\) 0 0
\(148\) −1.75915 −0.144601
\(149\) 8.90766 5.14284i 0.729744 0.421318i −0.0885845 0.996069i \(-0.528234\pi\)
0.818329 + 0.574751i \(0.194901\pi\)
\(150\) 0 0
\(151\) 11.7419i 0.955544i 0.878484 + 0.477772i \(0.158555\pi\)
−0.878484 + 0.477772i \(0.841445\pi\)
\(152\) 5.20843 3.00709i 0.422459 0.243907i
\(153\) 0 0
\(154\) −0.131051 0.0756625i −0.0105604 0.00609706i
\(155\) −15.4592 1.60125i −1.24172 0.128616i
\(156\) 0 0
\(157\) 6.76034i 0.539534i 0.962926 + 0.269767i \(0.0869467\pi\)
−0.962926 + 0.269767i \(0.913053\pi\)
\(158\) −4.74480 + 8.21824i −0.377476 + 0.653808i
\(159\) 0 0
\(160\) 2.04138 0.912572i 0.161385 0.0721452i
\(161\) 2.52036i 0.198633i
\(162\) 0 0
\(163\) 0.713746 + 1.23624i 0.0559049 + 0.0968301i 0.892623 0.450803i \(-0.148862\pi\)
−0.836719 + 0.547633i \(0.815529\pi\)
\(164\) 8.17919i 0.638688i
\(165\) 0 0
\(166\) −0.0697718 + 0.120848i −0.00541534 + 0.00937964i
\(167\) 2.93528 5.08406i 0.227139 0.393416i −0.729820 0.683639i \(-0.760396\pi\)
0.956959 + 0.290223i \(0.0937295\pi\)
\(168\) 0 0
\(169\) −9.32872 + 9.05401i −0.717594 + 0.696462i
\(170\) −18.1919 1.88430i −1.39526 0.144519i
\(171\) 0 0
\(172\) −7.94476 4.58691i −0.605782 0.349749i
\(173\) 11.8669 6.85138i 0.902226 0.520901i 0.0243045 0.999705i \(-0.492263\pi\)
0.877922 + 0.478804i \(0.158930\pi\)
\(174\) 0 0
\(175\) 1.34957 + 4.11130i 0.102018 + 0.310785i
\(176\) 0.151430 0.0874279i 0.0114144 0.00659013i
\(177\) 0 0
\(178\) −11.3790 + 6.56966i −0.852890 + 0.492416i
\(179\) 7.09191 12.2835i 0.530074 0.918115i −0.469310 0.883033i \(-0.655497\pi\)
0.999384 0.0350821i \(-0.0111693\pi\)
\(180\) 0 0
\(181\) 13.7728 1.02373 0.511863 0.859067i \(-0.328956\pi\)
0.511863 + 0.859067i \(0.328956\pi\)
\(182\) −1.17253 2.89166i −0.0869138 0.214344i
\(183\) 0 0
\(184\) 2.52211 + 1.45614i 0.185932 + 0.107348i
\(185\) 3.18581 + 2.30729i 0.234225 + 0.169635i
\(186\) 0 0
\(187\) −1.43018 −0.104585
\(188\) 5.95105 + 10.3075i 0.434025 + 0.751753i
\(189\) 0 0
\(190\) −13.3765 1.38553i −0.970436 0.100517i
\(191\) −2.78821 4.82932i −0.201748 0.349437i 0.747344 0.664437i \(-0.231329\pi\)
−0.949092 + 0.315000i \(0.897995\pi\)
\(192\) 0 0
\(193\) 0.110405 0.191227i 0.00794712 0.0137648i −0.862024 0.506867i \(-0.830804\pi\)
0.869972 + 0.493102i \(0.164137\pi\)
\(194\) −8.64822 −0.620906
\(195\) 0 0
\(196\) −6.25104 −0.446503
\(197\) 0.861905 1.49286i 0.0614082 0.106362i −0.833687 0.552237i \(-0.813774\pi\)
0.895095 + 0.445875i \(0.147108\pi\)
\(198\) 0 0
\(199\) −3.97927 6.89229i −0.282083 0.488581i 0.689815 0.723986i \(-0.257692\pi\)
−0.971898 + 0.235404i \(0.924359\pi\)
\(200\) −4.89385 1.02479i −0.346048 0.0724639i
\(201\) 0 0
\(202\) 5.28276 + 9.15001i 0.371694 + 0.643793i
\(203\) 5.61646 0.394198
\(204\) 0 0
\(205\) −10.7278 + 14.8125i −0.749262 + 1.03455i
\(206\) 7.73853 + 4.46784i 0.539169 + 0.311289i
\(207\) 0 0
\(208\) 3.57109 + 0.497314i 0.247610 + 0.0344825i
\(209\) −1.05161 −0.0727416
\(210\) 0 0
\(211\) 2.10991 3.65448i 0.145252 0.251585i −0.784215 0.620490i \(-0.786934\pi\)
0.929467 + 0.368905i \(0.120267\pi\)
\(212\) 2.15410 1.24367i 0.147945 0.0854158i
\(213\) 0 0
\(214\) 0.745455 0.430389i 0.0509582 0.0294208i
\(215\) 8.37177 + 18.7272i 0.570950 + 1.27718i
\(216\) 0 0
\(217\) 5.20933 3.00761i 0.353632 0.204170i
\(218\) 4.72274 + 2.72668i 0.319865 + 0.184674i
\(219\) 0 0
\(220\) −0.388909 0.0402827i −0.0262202 0.00271586i
\(221\) −23.2616 18.1270i −1.56474 1.21935i
\(222\) 0 0
\(223\) −3.47638 + 6.02126i −0.232795 + 0.403214i −0.958630 0.284656i \(-0.908121\pi\)
0.725834 + 0.687870i \(0.241454\pi\)
\(224\) −0.432713 + 0.749482i −0.0289119 + 0.0500769i
\(225\) 0 0
\(226\) 11.7821i 0.783735i
\(227\) 1.44823 + 2.50840i 0.0961221 + 0.166488i 0.910076 0.414441i \(-0.136023\pi\)
−0.813954 + 0.580929i \(0.802689\pi\)
\(228\) 0 0
\(229\) 7.88800i 0.521254i −0.965440 0.260627i \(-0.916071\pi\)
0.965440 0.260627i \(-0.0839293\pi\)
\(230\) −2.65766 5.94505i −0.175241 0.392005i
\(231\) 0 0
\(232\) −3.24491 + 5.62035i −0.213039 + 0.368994i
\(233\) 1.42749i 0.0935181i −0.998906 0.0467590i \(-0.985111\pi\)
0.998906 0.0467590i \(-0.0148893\pi\)
\(234\) 0 0
\(235\) 2.74197 26.4723i 0.178866 1.72686i
\(236\) −6.09393 3.51833i −0.396681 0.229024i
\(237\) 0 0
\(238\) 6.13015 3.53925i 0.397359 0.229415i
\(239\) 10.9084i 0.705604i −0.935698 0.352802i \(-0.885229\pi\)
0.935698 0.352802i \(-0.114771\pi\)
\(240\) 0 0
\(241\) −25.4317 + 14.6830i −1.63820 + 0.945816i −0.656749 + 0.754109i \(0.728069\pi\)
−0.981452 + 0.191707i \(0.938598\pi\)
\(242\) 10.9694 0.705141
\(243\) 0 0
\(244\) 3.98695 6.90559i 0.255238 0.442085i
\(245\) 11.3206 + 8.19884i 0.723248 + 0.523805i
\(246\) 0 0
\(247\) −17.1043 13.3288i −1.08832 0.848091i
\(248\) 6.95057i 0.441362i
\(249\) 0 0
\(250\) 7.51864 + 8.27466i 0.475521 + 0.523336i
\(251\) −8.94708 15.4968i −0.564735 0.978150i −0.997074 0.0764387i \(-0.975645\pi\)
0.432339 0.901711i \(-0.357688\pi\)
\(252\) 0 0
\(253\) −0.254615 0.441005i −0.0160075 0.0277258i
\(254\) 6.01228 3.47119i 0.377244 0.217802i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −10.5472 6.08945i −0.657918 0.379849i 0.133565 0.991040i \(-0.457358\pi\)
−0.791483 + 0.611191i \(0.790691\pi\)
\(258\) 0 0
\(259\) −1.52241 −0.0945981
\(260\) −5.81496 5.58446i −0.360629 0.346334i
\(261\) 0 0
\(262\) 1.13567 1.96703i 0.0701616 0.121524i
\(263\) −18.3309 10.5834i −1.13033 0.652598i −0.186314 0.982490i \(-0.559654\pi\)
−0.944019 + 0.329892i \(0.892988\pi\)
\(264\) 0 0
\(265\) −5.53228 0.573027i −0.339845 0.0352008i
\(266\) 4.50751 2.60241i 0.276373 0.159564i
\(267\) 0 0
\(268\) 2.73532 0.167086
\(269\) 6.04371 + 10.4680i 0.368492 + 0.638246i 0.989330 0.145692i \(-0.0465410\pi\)
−0.620838 + 0.783939i \(0.713208\pi\)
\(270\) 0 0
\(271\) −12.7275 7.34824i −0.773142 0.446374i 0.0608525 0.998147i \(-0.480618\pi\)
−0.833994 + 0.551773i \(0.813951\pi\)
\(272\) 8.17919i 0.495936i
\(273\) 0 0
\(274\) −7.37617 −0.445611
\(275\) 0.651479 + 0.583044i 0.0392856 + 0.0351588i
\(276\) 0 0
\(277\) 17.0717 9.85638i 1.02574 0.592212i 0.109980 0.993934i \(-0.464921\pi\)
0.915762 + 0.401722i \(0.131588\pi\)
\(278\) −0.820759 −0.0492259
\(279\) 0 0
\(280\) 1.76666 0.789764i 0.105578 0.0471975i
\(281\) 9.93073i 0.592418i 0.955123 + 0.296209i \(0.0957225\pi\)
−0.955123 + 0.296209i \(0.904278\pi\)
\(282\) 0 0
\(283\) −10.0790 5.81912i −0.599135 0.345911i 0.169566 0.985519i \(-0.445763\pi\)
−0.768701 + 0.639608i \(0.779097\pi\)
\(284\) 12.2677 + 7.08275i 0.727953 + 0.420284i
\(285\) 0 0
\(286\) −0.497290 0.387521i −0.0294053 0.0229146i
\(287\) 7.07849i 0.417830i
\(288\) 0 0
\(289\) 24.9496 43.2139i 1.46762 2.54200i
\(290\) 13.2482 5.92243i 0.777958 0.347777i
\(291\) 0 0
\(292\) −6.43528 11.1462i −0.376596 0.652284i
\(293\) 6.57636 + 11.3906i 0.384195 + 0.665445i 0.991657 0.128903i \(-0.0411457\pi\)
−0.607462 + 0.794349i \(0.707812\pi\)
\(294\) 0 0
\(295\) 6.42147 + 14.3645i 0.373872 + 0.836332i
\(296\) 0.879573 1.52347i 0.0511241 0.0885496i
\(297\) 0 0
\(298\) 10.2857i 0.595834i
\(299\) 1.44832 10.4000i 0.0837583 0.601448i
\(300\) 0 0
\(301\) −6.87561 3.96963i −0.396304 0.228806i
\(302\) −10.1688 5.87096i −0.585149 0.337836i
\(303\) 0 0
\(304\) 6.01418i 0.344937i
\(305\) −16.2777 + 7.27675i −0.932059 + 0.416666i
\(306\) 0 0
\(307\) 14.8609 0.848155 0.424077 0.905626i \(-0.360598\pi\)
0.424077 + 0.905626i \(0.360598\pi\)
\(308\) 0.131051 0.0756625i 0.00746734 0.00431127i
\(309\) 0 0
\(310\) 9.11635 12.5875i 0.517774 0.714920i
\(311\) −9.17666 −0.520361 −0.260180 0.965560i \(-0.583782\pi\)
−0.260180 + 0.965560i \(0.583782\pi\)
\(312\) 0 0
\(313\) 7.43905i 0.420480i 0.977650 + 0.210240i \(0.0674245\pi\)
−0.977650 + 0.210240i \(0.932576\pi\)
\(314\) −5.85463 3.38017i −0.330396 0.190754i
\(315\) 0 0
\(316\) −4.74480 8.21824i −0.266916 0.462312i
\(317\) −25.7510 −1.44632 −0.723161 0.690679i \(-0.757312\pi\)
−0.723161 + 0.690679i \(0.757312\pi\)
\(318\) 0 0
\(319\) 0.982750 0.567391i 0.0550235 0.0317678i
\(320\) −0.230377 + 2.22417i −0.0128785 + 0.124335i
\(321\) 0 0
\(322\) 2.18270 + 1.26018i 0.121637 + 0.0702272i
\(323\) 24.5955 42.6007i 1.36853 2.37037i
\(324\) 0 0
\(325\) 3.20632 + 17.7403i 0.177855 + 0.984057i
\(326\) −1.42749 −0.0790614
\(327\) 0 0
\(328\) 7.08339 + 4.08960i 0.391115 + 0.225810i
\(329\) 5.15020 + 8.92040i 0.283940 + 0.491798i
\(330\) 0 0
\(331\) 5.63295 3.25219i 0.309615 0.178756i −0.337139 0.941455i \(-0.609459\pi\)
0.646754 + 0.762699i \(0.276126\pi\)
\(332\) −0.0697718 0.120848i −0.00382922 0.00663241i
\(333\) 0 0
\(334\) 2.93528 + 5.08406i 0.160612 + 0.278187i
\(335\) −4.95366 3.58764i −0.270647 0.196014i
\(336\) 0 0
\(337\) 18.6696i 1.01700i 0.861063 + 0.508498i \(0.169799\pi\)
−0.861063 + 0.508498i \(0.830201\pi\)
\(338\) −3.17664 12.6059i −0.172786 0.685671i
\(339\) 0 0
\(340\) 10.7278 14.8125i 0.581797 0.803321i
\(341\) 0.607674 1.05252i 0.0329074 0.0569973i
\(342\) 0 0
\(343\) −11.4678 −0.619203
\(344\) 7.94476 4.58691i 0.428353 0.247310i
\(345\) 0 0
\(346\) 13.7028i 0.736665i
\(347\) −24.6009 + 14.2033i −1.32064 + 0.762474i −0.983831 0.179098i \(-0.942682\pi\)
−0.336813 + 0.941572i \(0.609349\pi\)
\(348\) 0 0
\(349\) 1.93797 + 1.11889i 0.103737 + 0.0598926i 0.550971 0.834524i \(-0.314258\pi\)
−0.447234 + 0.894417i \(0.647591\pi\)
\(350\) −4.23527 0.886885i −0.226385 0.0474060i
\(351\) 0 0
\(352\) 0.174856i 0.00931985i
\(353\) 0.813287 1.40866i 0.0432869 0.0749751i −0.843570 0.537019i \(-0.819550\pi\)
0.886857 + 0.462044i \(0.152884\pi\)
\(354\) 0 0
\(355\) −12.9270 28.9171i −0.686096 1.53476i
\(356\) 13.1393i 0.696382i
\(357\) 0 0
\(358\) 7.09191 + 12.2835i 0.374819 + 0.649206i
\(359\) 34.4613i 1.81880i −0.415923 0.909400i \(-0.636541\pi\)
0.415923 0.909400i \(-0.363459\pi\)
\(360\) 0 0
\(361\) 8.58515 14.8699i 0.451850 0.782627i
\(362\) −6.88641 + 11.9276i −0.361942 + 0.626901i
\(363\) 0 0
\(364\) 3.09052 + 0.430389i 0.161987 + 0.0225585i
\(365\) −2.96508 + 28.6263i −0.155199 + 1.49837i
\(366\) 0 0
\(367\) −12.6735 7.31703i −0.661550 0.381946i 0.131317 0.991340i \(-0.458079\pi\)
−0.792867 + 0.609394i \(0.791413\pi\)
\(368\) −2.52211 + 1.45614i −0.131474 + 0.0759065i
\(369\) 0 0
\(370\) −3.59108 + 1.60535i −0.186691 + 0.0834580i
\(371\) 1.86422 1.07631i 0.0967855 0.0558791i
\(372\) 0 0
\(373\) 19.1166 11.0370i 0.989819 0.571472i 0.0845988 0.996415i \(-0.473039\pi\)
0.905220 + 0.424943i \(0.139706\pi\)
\(374\) 0.715090 1.23857i 0.0369764 0.0640450i
\(375\) 0 0
\(376\) −11.9021 −0.613804
\(377\) 23.1757 + 3.22747i 1.19361 + 0.166223i
\(378\) 0 0
\(379\) 12.0573 + 6.96127i 0.619341 + 0.357577i 0.776612 0.629979i \(-0.216936\pi\)
−0.157272 + 0.987555i \(0.550270\pi\)
\(380\) 7.88817 10.8917i 0.404655 0.558730i
\(381\) 0 0
\(382\) 5.57642 0.285314
\(383\) −12.3044 21.3119i −0.628728 1.08899i −0.987807 0.155681i \(-0.950243\pi\)
0.359080 0.933307i \(-0.383091\pi\)
\(384\) 0 0
\(385\) −0.336572 0.0348618i −0.0171533 0.00177672i
\(386\) 0.110405 + 0.191227i 0.00561946 + 0.00973319i
\(387\) 0 0
\(388\) 4.32411 7.48957i 0.219523 0.380226i
\(389\) −5.60980 −0.284428 −0.142214 0.989836i \(-0.545422\pi\)
−0.142214 + 0.989836i \(0.545422\pi\)
\(390\) 0 0
\(391\) 23.8201 1.20463
\(392\) 3.12552 5.41356i 0.157863 0.273426i
\(393\) 0 0
\(394\) 0.861905 + 1.49286i 0.0434222 + 0.0752094i
\(395\) −2.18619 + 21.1065i −0.109999 + 1.06198i
\(396\) 0 0
\(397\) 1.18438 + 2.05141i 0.0594424 + 0.102957i 0.894215 0.447637i \(-0.147734\pi\)
−0.834773 + 0.550595i \(0.814401\pi\)
\(398\) 7.95853 0.398925
\(399\) 0 0
\(400\) 3.33442 3.72580i 0.166721 0.186290i
\(401\) −14.2942 8.25276i −0.713818 0.412123i 0.0986548 0.995122i \(-0.468546\pi\)
−0.812473 + 0.582998i \(0.801879\pi\)
\(402\) 0 0
\(403\) 23.2240 9.41704i 1.15687 0.469096i
\(404\) −10.5655 −0.525654
\(405\) 0 0
\(406\) −2.80823 + 4.86400i −0.139370 + 0.241396i
\(407\) −0.266387 + 0.153798i −0.0132043 + 0.00762351i
\(408\) 0 0
\(409\) 28.8448 16.6535i 1.42628 0.823464i 0.429457 0.903087i \(-0.358705\pi\)
0.996825 + 0.0796230i \(0.0253717\pi\)
\(410\) −7.46410 16.6968i −0.368626 0.824596i
\(411\) 0 0
\(412\) −7.73853 + 4.46784i −0.381250 + 0.220115i
\(413\) −5.27385 3.04486i −0.259509 0.149828i
\(414\) 0 0
\(415\) −0.0321476 + 0.310368i −0.00157806 + 0.0152354i
\(416\) −2.21623 + 2.84400i −0.108660 + 0.139438i
\(417\) 0 0
\(418\) 0.525807 0.910724i 0.0257181 0.0445450i
\(419\) −15.1303 + 26.2065i −0.739164 + 1.28027i 0.213708 + 0.976898i \(0.431446\pi\)
−0.952872 + 0.303372i \(0.901887\pi\)
\(420\) 0 0
\(421\) 40.2235i 1.96038i 0.198070 + 0.980188i \(0.436533\pi\)
−0.198070 + 0.980188i \(0.563467\pi\)
\(422\) 2.10991 + 3.65448i 0.102709 + 0.177897i
\(423\) 0 0
\(424\) 2.48735i 0.120796i
\(425\) −38.8561 + 12.7549i −1.88480 + 0.618702i
\(426\) 0 0
\(427\) 3.45041 5.97629i 0.166977 0.289213i
\(428\) 0.860777i 0.0416072i
\(429\) 0 0
\(430\) −20.4041 2.11344i −0.983974 0.101919i
\(431\) 28.1980 + 16.2801i 1.35825 + 0.784185i 0.989388 0.145300i \(-0.0464147\pi\)
0.368860 + 0.929485i \(0.379748\pi\)
\(432\) 0 0
\(433\) −26.6153 + 15.3663i −1.27905 + 0.738460i −0.976674 0.214729i \(-0.931113\pi\)
−0.302376 + 0.953189i \(0.597780\pi\)
\(434\) 6.01521i 0.288739i
\(435\) 0 0
\(436\) −4.72274 + 2.72668i −0.226178 + 0.130584i
\(437\) 17.5150 0.837854
\(438\) 0 0
\(439\) 3.26422 5.65380i 0.155793 0.269841i −0.777555 0.628815i \(-0.783540\pi\)
0.933347 + 0.358974i \(0.116873\pi\)
\(440\) 0.229340 0.316664i 0.0109334 0.0150963i
\(441\) 0 0
\(442\) 27.3292 11.0816i 1.29992 0.527100i
\(443\) 30.3111i 1.44012i −0.693911 0.720061i \(-0.744114\pi\)
0.693911 0.720061i \(-0.255886\pi\)
\(444\) 0 0
\(445\) −17.2335 + 23.7953i −0.816945 + 1.12800i
\(446\) −3.47638 6.02126i −0.164611 0.285115i
\(447\) 0 0
\(448\) −0.432713 0.749482i −0.0204438 0.0354097i
\(449\) −13.8034 + 7.96938i −0.651421 + 0.376098i −0.789001 0.614392i \(-0.789401\pi\)
0.137579 + 0.990491i \(0.456068\pi\)
\(450\) 0 0
\(451\) −0.715090 1.23857i −0.0336723 0.0583221i
\(452\) 10.2036 + 5.89106i 0.479938 + 0.277092i
\(453\) 0 0
\(454\) −2.89645 −0.135937
\(455\) −5.03242 4.83294i −0.235924 0.226572i
\(456\) 0 0
\(457\) −9.90436 + 17.1548i −0.463306 + 0.802470i −0.999123 0.0418642i \(-0.986670\pi\)
0.535817 + 0.844334i \(0.320004\pi\)
\(458\) 6.83121 + 3.94400i 0.319202 + 0.184291i
\(459\) 0 0
\(460\) 6.47740 + 0.670922i 0.302010 + 0.0312819i
\(461\) 11.5898 6.69139i 0.539792 0.311649i −0.205202 0.978720i \(-0.565785\pi\)
0.744995 + 0.667070i \(0.232452\pi\)
\(462\) 0 0
\(463\) −42.3599 −1.96863 −0.984316 0.176412i \(-0.943551\pi\)
−0.984316 + 0.176412i \(0.943551\pi\)
\(464\) −3.24491 5.62035i −0.150641 0.260918i
\(465\) 0 0
\(466\) 1.23624 + 0.713746i 0.0572679 + 0.0330636i
\(467\) 33.4593i 1.54831i 0.632996 + 0.774155i \(0.281825\pi\)
−0.632996 + 0.774155i \(0.718175\pi\)
\(468\) 0 0
\(469\) 2.36722 0.109308
\(470\) 21.5547 + 15.6107i 0.994243 + 0.720070i
\(471\) 0 0
\(472\) 6.09393 3.51833i 0.280496 0.161944i
\(473\) −1.60410 −0.0737564
\(474\) 0 0
\(475\) −28.5709 + 9.37868i −1.31092 + 0.430323i
\(476\) 7.07849i 0.324442i
\(477\) 0 0
\(478\) 9.44692 + 5.45418i 0.432092 + 0.249469i
\(479\) 19.3387 + 11.1652i 0.883606 + 0.510150i 0.871846 0.489781i \(-0.162923\pi\)
0.0117600 + 0.999931i \(0.496257\pi\)
\(480\) 0 0
\(481\) −6.28207 0.874847i −0.286438 0.0398896i
\(482\) 29.3660i 1.33759i
\(483\) 0 0
\(484\) −5.48471 + 9.49980i −0.249305 + 0.431809i
\(485\) −17.6543 + 7.89212i −0.801638 + 0.358363i
\(486\) 0 0
\(487\) 14.3750 + 24.8982i 0.651392 + 1.12824i 0.982785 + 0.184751i \(0.0591479\pi\)
−0.331393 + 0.943493i \(0.607519\pi\)
\(488\) 3.98695 + 6.90559i 0.180481 + 0.312602i
\(489\) 0 0
\(490\) −12.7607 + 5.70452i −0.576470 + 0.257704i
\(491\) −8.02546 + 13.9005i −0.362184 + 0.627321i −0.988320 0.152393i \(-0.951302\pi\)
0.626136 + 0.779714i \(0.284636\pi\)
\(492\) 0 0
\(493\) 53.0815i 2.39067i
\(494\) 20.0952 8.14836i 0.904127 0.366612i
\(495\) 0 0
\(496\) −6.01937 3.47529i −0.270278 0.156045i
\(497\) 10.6168 + 6.12960i 0.476228 + 0.274950i
\(498\) 0 0
\(499\) 33.2509i 1.48851i 0.667894 + 0.744256i \(0.267196\pi\)
−0.667894 + 0.744256i \(0.732804\pi\)
\(500\) −10.9254 + 2.37400i −0.488598 + 0.106169i
\(501\) 0 0
\(502\) 17.8942 0.798656
\(503\) −21.7736 + 12.5710i −0.970838 + 0.560514i −0.899492 0.436938i \(-0.856063\pi\)
−0.0713466 + 0.997452i \(0.522730\pi\)
\(504\) 0 0
\(505\) 19.1341 + 13.8577i 0.851458 + 0.616660i
\(506\) 0.509229 0.0226380
\(507\) 0 0
\(508\) 6.94238i 0.308018i
\(509\) −22.8809 13.2103i −1.01418 0.585536i −0.101766 0.994808i \(-0.532449\pi\)
−0.912412 + 0.409272i \(0.865783\pi\)
\(510\) 0 0
\(511\) −5.56927 9.64625i −0.246370 0.426725i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 10.5472 6.08945i 0.465219 0.268594i
\(515\) 19.8745 + 2.05858i 0.875774 + 0.0907117i
\(516\) 0 0
\(517\) 1.80233 + 1.04058i 0.0792664 + 0.0457645i
\(518\) 0.761206 1.31845i 0.0334455 0.0579293i
\(519\) 0 0
\(520\) 7.74377 2.24367i 0.339587 0.0983916i
\(521\) 22.4462 0.983384 0.491692 0.870769i \(-0.336379\pi\)
0.491692 + 0.870769i \(0.336379\pi\)
\(522\) 0 0
\(523\) −25.1815 14.5385i −1.10111 0.635726i −0.164598 0.986361i \(-0.552633\pi\)
−0.936512 + 0.350635i \(0.885966\pi\)
\(524\) 1.13567 + 1.96703i 0.0496118 + 0.0859301i
\(525\) 0 0
\(526\) 18.3309 10.5834i 0.799266 0.461456i
\(527\) 28.4250 + 49.2336i 1.23821 + 2.14465i
\(528\) 0 0
\(529\) −7.25931 12.5735i −0.315622 0.546674i
\(530\) 3.26239 4.50458i 0.141709 0.195666i
\(531\) 0 0
\(532\) 5.20483i 0.225658i
\(533\) 4.06762 29.2086i 0.176188 1.26517i
\(534\) 0 0
\(535\) 1.12899 1.55887i 0.0488106 0.0673956i
\(536\) −1.36766 + 2.36886i −0.0590739 + 0.102319i
\(537\) 0 0
\(538\) −12.0874 −0.521126
\(539\) −0.946592 + 0.546515i −0.0407726 + 0.0235401i
\(540\) 0 0
\(541\) 8.17282i 0.351377i −0.984446 0.175688i \(-0.943785\pi\)
0.984446 0.175688i \(-0.0562151\pi\)
\(542\) 12.7275 7.34824i 0.546694 0.315634i
\(543\) 0 0
\(544\) −7.08339 4.08960i −0.303698 0.175340i
\(545\) 12.1292 + 1.25633i 0.519557 + 0.0538152i
\(546\) 0 0
\(547\) 40.7393i 1.74188i −0.491385 0.870942i \(-0.663509\pi\)
0.491385 0.870942i \(-0.336491\pi\)
\(548\) 3.68809 6.38795i 0.157547 0.272880i
\(549\) 0 0
\(550\) −0.830670 + 0.272675i −0.0354199 + 0.0116269i
\(551\) 39.0309i 1.66277i
\(552\) 0 0
\(553\) −4.10628 7.11229i −0.174617 0.302445i
\(554\) 19.7128i 0.837515i
\(555\) 0 0
\(556\) 0.410380 0.710798i 0.0174040 0.0301446i
\(557\) −0.458421 + 0.794008i −0.0194239 + 0.0336432i −0.875574 0.483084i \(-0.839517\pi\)
0.856150 + 0.516727i \(0.172850\pi\)
\(558\) 0 0
\(559\) −26.0903 20.3313i −1.10350 0.859922i
\(560\) −0.199374 + 1.92486i −0.00842511 + 0.0813400i
\(561\) 0 0
\(562\) −8.60027 4.96537i −0.362780 0.209451i
\(563\) −10.9632 + 6.32961i −0.462044 + 0.266761i −0.712903 0.701262i \(-0.752620\pi\)
0.250859 + 0.968024i \(0.419287\pi\)
\(564\) 0 0
\(565\) −10.7520 24.0517i −0.452342 1.01186i
\(566\) 10.0790 5.81912i 0.423652 0.244596i
\(567\) 0 0
\(568\) −12.2677 + 7.08275i −0.514741 + 0.297186i
\(569\) −12.2559 + 21.2279i −0.513795 + 0.889918i 0.486077 + 0.873916i \(0.338427\pi\)
−0.999872 + 0.0160026i \(0.994906\pi\)
\(570\) 0 0
\(571\) −11.1443 −0.466376 −0.233188 0.972432i \(-0.574916\pi\)
−0.233188 + 0.972432i \(0.574916\pi\)
\(572\) 0.584248 0.236905i 0.0244286 0.00990549i
\(573\) 0 0
\(574\) 6.13015 + 3.53925i 0.255868 + 0.147725i
\(575\) −10.8506 9.71078i −0.452501 0.404967i
\(576\) 0 0
\(577\) −23.8325 −0.992161 −0.496081 0.868276i \(-0.665228\pi\)
−0.496081 + 0.868276i \(0.665228\pi\)
\(578\) 24.9496 + 43.2139i 1.03777 + 1.79746i
\(579\) 0 0
\(580\) −1.49510 + 14.4344i −0.0620808 + 0.599358i
\(581\) −0.0603824 0.104585i −0.00250508 0.00433893i
\(582\) 0 0
\(583\) 0.217463 0.376658i 0.00900642 0.0155996i
\(584\) 12.8706 0.532588
\(585\) 0 0
\(586\) −13.1527 −0.543334
\(587\) 18.6811 32.3566i 0.771051 1.33550i −0.165937 0.986136i \(-0.553065\pi\)
0.936988 0.349362i \(-0.113602\pi\)
\(588\) 0 0
\(589\) 20.9010 + 36.2016i 0.861210 + 1.49166i
\(590\) −15.6507 1.62109i −0.644331 0.0667391i
\(591\) 0 0
\(592\) 0.879573 + 1.52347i 0.0361502 + 0.0626140i
\(593\) 6.46136 0.265336 0.132668 0.991161i \(-0.457646\pi\)
0.132668 + 0.991161i \(0.457646\pi\)
\(594\) 0 0
\(595\) 9.28413 12.8191i 0.380612 0.525533i
\(596\) −8.90766 5.14284i −0.364872 0.210659i
\(597\) 0 0
\(598\) 8.28251 + 6.45428i 0.338697 + 0.263935i
\(599\) 38.5057 1.57330 0.786651 0.617398i \(-0.211813\pi\)
0.786651 + 0.617398i \(0.211813\pi\)
\(600\) 0 0
\(601\) −0.371169 + 0.642883i −0.0151403 + 0.0262237i −0.873496 0.486831i \(-0.838153\pi\)
0.858356 + 0.513055i \(0.171486\pi\)
\(602\) 6.87561 3.96963i 0.280229 0.161790i
\(603\) 0 0
\(604\) 10.1688 5.87096i 0.413763 0.238886i
\(605\) 22.3927 10.0104i 0.910393 0.406980i
\(606\) 0 0
\(607\) −25.5500 + 14.7513i −1.03704 + 0.598736i −0.918994 0.394272i \(-0.870997\pi\)
−0.118047 + 0.993008i \(0.537663\pi\)
\(608\) −5.20843 3.00709i −0.211230 0.121954i
\(609\) 0 0
\(610\) 1.83700 17.7353i 0.0743780 0.718081i
\(611\) 16.1257 + 39.7686i 0.652374 + 1.60887i
\(612\) 0 0
\(613\) 6.86720 11.8943i 0.277364 0.480408i −0.693365 0.720587i \(-0.743873\pi\)
0.970729 + 0.240178i \(0.0772059\pi\)
\(614\) −7.43044 + 12.8699i −0.299868 + 0.519387i
\(615\) 0 0
\(616\) 0.151325i 0.00609706i
\(617\) 21.4394 + 37.1342i 0.863119 + 1.49497i 0.868902 + 0.494983i \(0.164826\pi\)
−0.00578297 + 0.999983i \(0.501841\pi\)
\(618\) 0 0
\(619\) 30.0054i 1.20602i 0.797734 + 0.603010i \(0.206032\pi\)
−0.797734 + 0.603010i \(0.793968\pi\)
\(620\) 6.34290 + 14.1887i 0.254737 + 0.569833i
\(621\) 0 0
\(622\) 4.58833 7.94722i 0.183975 0.318655i
\(623\) 11.3711i 0.455574i
\(624\) 0 0
\(625\) 22.8996 + 10.0304i 0.915984 + 0.401215i
\(626\) −6.44240 3.71952i −0.257490 0.148662i
\(627\) 0 0
\(628\) 5.85463 3.38017i 0.233625 0.134884i
\(629\) 14.3884i 0.573703i
\(630\) 0 0
\(631\) 7.73137 4.46371i 0.307781 0.177697i −0.338152 0.941091i \(-0.609802\pi\)
0.645933 + 0.763394i \(0.276468\pi\)
\(632\) 9.48961 0.377476
\(633\) 0 0
\(634\) 12.8755 22.3011i 0.511352 0.885688i
\(635\) 9.10560 12.5726i 0.361345 0.498930i
\(636\) 0 0
\(637\) −22.3230 3.10873i −0.884470 0.123172i
\(638\) 1.13478i 0.0449265i
\(639\) 0 0
\(640\) −1.81100 1.31160i −0.0715860 0.0518454i
\(641\) 11.9079 + 20.6250i 0.470332 + 0.814639i 0.999424 0.0339254i \(-0.0108008\pi\)
−0.529092 + 0.848564i \(0.677468\pi\)
\(642\) 0 0
\(643\) 4.79374 + 8.30300i 0.189047 + 0.327439i 0.944933 0.327265i \(-0.106127\pi\)
−0.755886 + 0.654703i \(0.772794\pi\)
\(644\) −2.18270 + 1.26018i −0.0860104 + 0.0496581i
\(645\) 0 0
\(646\) 24.5955 + 42.6007i 0.967699 + 1.67610i
\(647\) −39.2219 22.6448i −1.54197 0.890259i −0.998714 0.0506940i \(-0.983857\pi\)
−0.543259 0.839565i \(-0.682810\pi\)
\(648\) 0 0
\(649\) −1.23040 −0.0482975
\(650\) −16.9667 6.09341i −0.665490 0.239003i
\(651\) 0 0
\(652\) 0.713746 1.23624i 0.0279524 0.0484150i
\(653\) 8.00988 + 4.62451i 0.313451 + 0.180971i 0.648470 0.761241i \(-0.275409\pi\)
−0.335019 + 0.942211i \(0.608743\pi\)
\(654\) 0 0
\(655\) 0.523262 5.05182i 0.0204455 0.197391i
\(656\) −7.08339 + 4.08960i −0.276560 + 0.159672i
\(657\) 0 0
\(658\) −10.3004 −0.401551
\(659\) 11.0666 + 19.1679i 0.431093 + 0.746676i 0.996968 0.0778159i \(-0.0247946\pi\)
−0.565874 + 0.824491i \(0.691461\pi\)
\(660\) 0 0
\(661\) 8.75083 + 5.05229i 0.340368 + 0.196511i 0.660435 0.750884i \(-0.270372\pi\)
−0.320067 + 0.947395i \(0.603705\pi\)
\(662\) 6.50437i 0.252800i
\(663\) 0 0
\(664\) 0.139544 0.00541534
\(665\) 6.82664 9.42594i 0.264726 0.365522i
\(666\) 0 0
\(667\) −16.3680 + 9.45008i −0.633772 + 0.365909i
\(668\) −5.87057 −0.227139
\(669\) 0 0
\(670\) 5.58382 2.49618i 0.215722 0.0964358i
\(671\) 1.39428i 0.0538256i
\(672\) 0 0
\(673\) −11.6594 6.73157i −0.449437 0.259483i 0.258155 0.966103i \(-0.416885\pi\)
−0.707593 + 0.706621i \(0.750219\pi\)
\(674\) −16.1683 9.33479i −0.622781 0.359562i
\(675\) 0 0
\(676\) 12.5054 + 3.55190i 0.480975 + 0.136612i
\(677\) 7.86444i 0.302255i −0.988514 0.151127i \(-0.951710\pi\)
0.988514 0.151127i \(-0.0482904\pi\)
\(678\) 0 0
\(679\) 3.74220 6.48168i 0.143612 0.248744i
\(680\) 7.46410 + 16.6968i 0.286235 + 0.640293i
\(681\) 0 0
\(682\) 0.607674 + 1.05252i 0.0232690 + 0.0403032i
\(683\) 9.21246 + 15.9565i 0.352505 + 0.610557i 0.986688 0.162627i \(-0.0519966\pi\)
−0.634183 + 0.773183i \(0.718663\pi\)
\(684\) 0 0
\(685\) −15.0575 + 6.73129i −0.575319 + 0.257189i
\(686\) 5.73390 9.93141i 0.218921 0.379183i
\(687\) 0 0
\(688\) 9.17382i 0.349749i
\(689\) 8.31100 3.37000i 0.316624 0.128387i
\(690\) 0 0
\(691\) −20.5618 11.8714i −0.782208 0.451608i 0.0550042 0.998486i \(-0.482483\pi\)
−0.837212 + 0.546878i \(0.815816\pi\)
\(692\) −11.8669 6.85138i −0.451113 0.260450i
\(693\) 0 0
\(694\) 28.4066i 1.07830i
\(695\) −1.67548 + 0.749002i −0.0635545 + 0.0284113i
\(696\) 0 0
\(697\) 66.8992 2.53399
\(698\) −1.93797 + 1.11889i −0.0733532 + 0.0423505i
\(699\) 0 0
\(700\) 2.88570 3.22441i 0.109069 0.121871i
\(701\) 6.52189 0.246328 0.123164 0.992386i \(-0.460696\pi\)
0.123164 + 0.992386i \(0.460696\pi\)
\(702\) 0 0
\(703\) 10.5798i 0.399025i
\(704\) −0.151430 0.0874279i −0.00570722 0.00329506i
\(705\) 0 0
\(706\) 0.813287 + 1.40866i 0.0306085 + 0.0530154i
\(707\) −9.14369 −0.343884
\(708\) 0 0
\(709\) 27.5565 15.9098i 1.03491 0.597504i 0.116521 0.993188i \(-0.462826\pi\)
0.918387 + 0.395684i \(0.129493\pi\)
\(710\) 31.5065 + 3.26340i 1.18242 + 0.122473i
\(711\) 0 0
\(712\) 11.3790 + 6.56966i 0.426445 + 0.246208i
\(713\) −10.1210 + 17.5301i −0.379035 + 0.656507i
\(714\) 0 0
\(715\) −1.36880 0.337263i −0.0511900 0.0126129i
\(716\) −14.1838 −0.530074
\(717\) 0 0
\(718\) 29.8444 + 17.2307i 1.11378 + 0.643043i
\(719\) −11.6970 20.2597i −0.436223 0.755560i 0.561172 0.827699i \(-0.310351\pi\)
−0.997395 + 0.0721392i \(0.977017\pi\)
\(720\) 0 0
\(721\) −6.69713 + 3.86659i −0.249414 + 0.143999i
\(722\) 8.58515 + 14.8699i 0.319506 + 0.553401i
\(723\) 0 0
\(724\) −6.88641 11.9276i −0.255931 0.443286i
\(725\) 21.6398 24.1798i 0.803682 0.898015i
\(726\) 0 0
\(727\) 36.0471i 1.33691i 0.743750 + 0.668457i \(0.233045\pi\)
−0.743750 + 0.668457i \(0.766955\pi\)
\(728\) −1.91799 + 2.46127i −0.0710853 + 0.0912208i
\(729\) 0 0
\(730\) −23.3086 16.8810i −0.862689 0.624794i
\(731\) 37.5172 64.9817i 1.38762 2.40344i
\(732\) 0 0
\(733\) 17.0888 0.631189 0.315594 0.948894i \(-0.397796\pi\)
0.315594 + 0.948894i \(0.397796\pi\)
\(734\) 12.6735 7.31703i 0.467787 0.270077i
\(735\) 0 0
\(736\) 2.91228i 0.107348i
\(737\) 0.414209 0.239143i 0.0152576 0.00880896i
\(738\) 0 0
\(739\) 33.4931 + 19.3373i 1.23206 + 0.711333i 0.967460 0.253024i \(-0.0814253\pi\)
0.264604 + 0.964357i \(0.414759\pi\)
\(740\) 0.405267 3.91264i 0.0148979 0.143831i
\(741\) 0 0
\(742\) 2.15262i 0.0790250i
\(743\) 0.225532 0.390632i 0.00827395 0.0143309i −0.861859 0.507148i \(-0.830700\pi\)
0.870133 + 0.492817i \(0.164033\pi\)
\(744\) 0 0
\(745\) 9.38643 + 20.9969i 0.343892 + 0.769268i
\(746\) 22.0739i 0.808184i
\(747\) 0 0
\(748\) 0.715090 + 1.23857i 0.0261463 + 0.0452867i
\(749\) 0.744940i 0.0272195i
\(750\) 0 0
\(751\) −11.1206 + 19.2614i −0.405795 + 0.702858i −0.994414 0.105553i \(-0.966339\pi\)
0.588618 + 0.808411i \(0.299672\pi\)
\(752\) 5.95105 10.3075i 0.217012 0.375876i
\(753\) 0 0
\(754\) −14.3829 + 18.4570i −0.523796 + 0.672165i
\(755\) −26.1160 2.70507i −0.950459 0.0984475i
\(756\) 0 0
\(757\) −7.30326 4.21654i −0.265442 0.153253i 0.361373 0.932421i \(-0.382308\pi\)
−0.626814 + 0.779169i \(0.715642\pi\)
\(758\) −12.0573 + 6.96127i −0.437940 + 0.252845i
\(759\) 0 0
\(760\) 5.48837 + 12.2772i 0.199084 + 0.445340i
\(761\) −18.3585 + 10.5993i −0.665496 + 0.384224i −0.794368 0.607437i \(-0.792198\pi\)
0.128872 + 0.991661i \(0.458864\pi\)
\(762\) 0 0
\(763\) −4.08719 + 2.35974i −0.147966 + 0.0854283i
\(764\) −2.78821 + 4.82932i −0.100874 + 0.174719i
\(765\) 0 0
\(766\) 24.6089 0.889155
\(767\) −20.0123 15.5949i −0.722601 0.563099i
\(768\) 0 0
\(769\) 3.34820 + 1.93308i 0.120739 + 0.0697088i 0.559153 0.829064i \(-0.311126\pi\)
−0.438414 + 0.898773i \(0.644460\pi\)
\(770\) 0.198477 0.274049i 0.00715262 0.00987605i
\(771\) 0 0
\(772\) −0.220810 −0.00794712
\(773\) −16.6218 28.7898i −0.597845 1.03550i −0.993139 0.116944i \(-0.962690\pi\)
0.395293 0.918555i \(-0.370643\pi\)
\(774\) 0 0
\(775\) 7.12291 34.0151i 0.255862 1.22186i
\(776\) 4.32411 + 7.48957i 0.155226 + 0.268860i
\(777\) 0 0
\(778\) 2.80490 4.85823i 0.100561 0.174176i
\(779\) 49.1911 1.76245
\(780\) 0 0
\(781\) 2.47692 0.0886312
\(782\) −11.9100 + 20.6288i −0.425902 + 0.737684i
\(783\) 0 0
\(784\) 3.12552 + 5.41356i 0.111626 + 0.193341i
\(785\) −15.0361 1.55743i −0.536663 0.0555870i
\(786\) 0 0
\(787\) −15.9873 27.6908i −0.569886 0.987071i −0.996577 0.0826737i \(-0.973654\pi\)
0.426691 0.904398i \(-0.359679\pi\)
\(788\)