Properties

Label 1170.2.bj.d.199.3
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 199.3
Root \(-1.44229 - 0.433312i\) of defining polynomial
Character \(\chi\) \(=\) 1170.199
Dual form 1170.2.bj.d.829.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.230377 + 2.22417i) q^{5} +(0.432713 + 0.749482i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.230377 + 2.22417i) q^{5} +(0.432713 + 0.749482i) q^{7} -1.00000 q^{8} +(2.04138 + 0.912572i) q^{10} +(-0.151430 - 0.0874279i) q^{11} +(1.35486 + 3.34131i) q^{13} +0.865427 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-7.08339 + 4.08960i) q^{17} +(5.20843 - 3.00709i) q^{19} +(1.81100 - 1.31160i) q^{20} +(-0.151430 + 0.0874279i) q^{22} +(-2.52211 - 1.45614i) q^{23} +(-4.89385 + 1.02479i) q^{25} +(3.57109 + 0.497314i) q^{26} +(0.432713 - 0.749482i) q^{28} +(-3.24491 + 5.62035i) q^{29} +6.95057i q^{31} +(0.500000 + 0.866025i) q^{32} +8.17919i q^{34} +(-1.56729 + 1.13509i) q^{35} +(-0.879573 + 1.52347i) q^{37} -6.01418i q^{38} +(-0.230377 - 2.22417i) q^{40} +(7.08339 + 4.08960i) q^{41} +(-7.94476 + 4.58691i) q^{43} +0.174856i q^{44} +(-2.52211 + 1.45614i) q^{46} +11.9021 q^{47} +(3.12552 - 5.41356i) q^{49} +(-1.55943 + 4.75060i) q^{50} +(2.21623 - 2.84400i) q^{52} -2.48735i q^{53} +(0.159569 - 0.356946i) q^{55} +(-0.432713 - 0.749482i) q^{56} +(3.24491 + 5.62035i) q^{58} +(6.09393 - 3.51833i) q^{59} +(3.98695 + 6.90559i) q^{61} +(6.01937 + 3.47529i) q^{62} +1.00000 q^{64} +(-7.11951 + 3.78319i) q^{65} +(1.36766 - 2.36886i) q^{67} +(7.08339 + 4.08960i) q^{68} +(0.199374 + 1.92486i) q^{70} +(-12.2677 + 7.08275i) q^{71} -12.8706 q^{73} +(0.879573 + 1.52347i) q^{74} +(-5.20843 - 3.00709i) q^{76} -0.151325i q^{77} +9.48961 q^{79} +(-2.04138 - 0.912572i) q^{80} +(7.08339 - 4.08960i) q^{82} -0.139544 q^{83} +(-10.7278 - 14.8125i) q^{85} +9.17382i q^{86} +(0.151430 + 0.0874279i) q^{88} +(11.3790 + 6.56966i) q^{89} +(-1.91799 + 2.46127i) q^{91} +2.91228i q^{92} +(5.95105 - 10.3075i) q^{94} +(7.88817 + 10.8917i) q^{95} +(-4.32411 - 7.48957i) q^{97} +(-3.12552 - 5.41356i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 6 q^{2} - 6 q^{4} + 2 q^{5} - 2 q^{7} - 12 q^{8} + O(q^{10}) \) \( 12 q + 6 q^{2} - 6 q^{4} + 2 q^{5} - 2 q^{7} - 12 q^{8} - 2 q^{10} - 6 q^{11} - 8 q^{13} - 4 q^{14} - 6 q^{16} - 18 q^{17} - 6 q^{19} - 4 q^{20} - 6 q^{22} - 6 q^{23} - 10 q^{25} + 2 q^{26} - 2 q^{28} - 14 q^{29} + 6 q^{32} - 26 q^{35} - 12 q^{37} - 2 q^{40} + 18 q^{41} - 36 q^{43} - 6 q^{46} - 16 q^{47} + 8 q^{49} + 10 q^{50} + 10 q^{52} - 28 q^{55} + 2 q^{56} + 14 q^{58} + 36 q^{59} + 10 q^{61} - 6 q^{62} + 12 q^{64} - 6 q^{65} + 4 q^{67} + 18 q^{68} - 4 q^{70} + 12 q^{71} + 28 q^{73} + 12 q^{74} + 6 q^{76} + 4 q^{79} + 2 q^{80} + 18 q^{82} - 72 q^{83} + 18 q^{85} + 6 q^{88} - 18 q^{89} + 2 q^{91} - 8 q^{94} + 42 q^{95} - 48 q^{97} - 8 q^{98} + O(q^{100}) \)

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 0.936140 0.351629i \(-0.114372\pi\)
−0.772589 + 0.634906i \(0.781039\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 2.04138 + 0.912572i 0.645539 + 0.288581i
\(11\) −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 \(0.792723\pi\)
−0.922604 + 0.385748i \(0.873943\pi\)
\(18\) 0 0
\(19\) 5.20843 3.00709i 1.19490 0.689873i 0.235483 0.971879i \(-0.424333\pi\)
0.959413 + 0.282005i \(0.0909996\pi\)
\(20\) 1.81100 1.31160i 0.404951 0.293282i
\(21\) 0 0
\(22\) −0.151430 + 0.0874279i −0.0322849 + 0.0186397i
\(23\) −2.52211 1.45614i −0.525896 0.303626i 0.213448 0.976954i \(-0.431531\pi\)
−0.739344 + 0.673328i \(0.764864\pi\)
\(24\) 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
\(35\) −1.56729 + 1.13509i −0.264920 + 0.191865i
\(36\) 0 0
\(37\) −0.879573 + 1.52347i −0.144601 + 0.250456i −0.929224 0.369517i \(-0.879523\pi\)
0.784623 + 0.619973i \(0.212856\pi\)
\(38\) 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 −0.963100 0.269144i \(-0.913259\pi\)
−0.248465 + 0.968641i \(0.579926\pi\)
\(44\) 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 \(-0.165373\pi\)
0.868050 + 0.496478i \(0.165373\pi\)
\(48\) 0 0
\(49\) 3.12552 5.41356i 0.446503 0.773365i
\(50\) −1.55943 + 4.75060i −0.220537 + 0.671836i
\(51\) 0 0
\(52\) 2.21623 2.84400i 0.307336 0.394391i
\(53\) 2.48735i 0.341663i −0.985300 0.170832i \(-0.945355\pi\)
0.985300 0.170832i \(-0.0546454\pi\)
\(54\) 0 0
\(55\) 0.159569 0.356946i 0.0215162 0.0481306i
\(56\) −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
\(65\) −7.11951 + 3.78319i −0.883067 + 0.469248i
\(66\) 0 0
\(67\) 1.36766 2.36886i 0.167086 0.289402i −0.770308 0.637672i \(-0.779897\pi\)
0.937394 + 0.348270i \(0.113231\pi\)
\(68\) 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 \(-0.771487\pi\)
−0.753193 + 0.657800i \(0.771487\pi\)
\(74\) 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 \(0.320751\pi\)
\(80\) −2.04138 0.912572i −0.228233 0.102029i
\(81\) 0 0
\(82\) 7.08339 4.08960i 0.782229 0.451620i
\(83\) −0.139544 −0.0153169 −0.00765845 0.999971i \(-0.502438\pi\)
−0.00765845 + 0.999971i \(0.502438\pi\)
\(84\) 0 0
\(85\) −10.7278 14.8125i −1.16359 1.60664i
\(86\) 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
\(95\) 7.88817 + 10.8917i 0.809309 + 1.11746i
\(96\) 0 0
\(97\) −4.32411 7.48957i −0.439047 0.760451i 0.558570 0.829458i \(-0.311350\pi\)
−0.997616 + 0.0690066i \(0.978017\pi\)
\(98\) −3.12552 5.41356i −0.315725 0.546852i
\(99\) 0 0
\(100\) 3.33442 + 3.72580i 0.333442 + 0.372580i
\(101\) 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 \(0.145103\pi\)
−0.897885 + 0.440230i \(0.854897\pi\)
\(104\) −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 0.535600 0.844472i \(-0.320086\pi\)
−0.463534 + 0.886079i \(0.653419\pi\)
\(108\) 0 0
\(109\) 5.45336i 0.522337i −0.965293 0.261168i \(-0.915892\pi\)
0.965293 0.261168i \(-0.0841078\pi\)
\(110\) −0.229340 0.316664i −0.0218667 0.0301927i
\(111\) 0 0
\(112\) −0.865427 −0.0817752
\(113\) 10.2036 5.89106i 0.959876 0.554184i 0.0637409 0.997966i \(-0.479697\pi\)
0.896135 + 0.443782i \(0.146364\pi\)
\(114\) 0 0
\(115\) 2.65766 5.94505i 0.247829 0.554379i
\(116\) 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 0.742442 0.669911i \(-0.233668\pi\)
−0.208939 + 0.977929i \(0.567001\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) −0.283413 + 8.05727i −0.0248569 + 0.706670i
\(131\) −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 0.664363 0.747410i \(-0.268703\pi\)
−0.979458 + 0.201650i \(0.935370\pi\)
\(138\) 0 0
\(139\) 0.410380 + 0.710798i 0.0348079 + 0.0602891i 0.882905 0.469552i \(-0.155585\pi\)
−0.848097 + 0.529842i \(0.822251\pi\)
\(140\) 1.76666 + 0.789764i 0.149310 + 0.0667473i
\(141\) 0 0
\(142\) 14.1655i 1.18874i
\(143\) 0.0869582 0.624426i 0.00727181 0.0522171i
\(144\) 0 0
\(145\) −13.2482 5.92243i −1.10020 0.491831i
\(146\) −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 \(-0.913053\pi\)
0.962926 0.269767i \(-0.0869467\pi\)
\(158\) 4.74480 8.21824i 0.377476 0.653808i
\(159\) 0 0
\(160\) −1.81100 + 1.31160i −0.143172 + 0.103691i
\(161\) 2.52036i 0.198633i
\(162\) 0 0
\(163\) −0.713746 1.23624i −0.0559049 0.0968301i 0.836719 0.547633i \(-0.184471\pi\)
−0.892623 + 0.450803i \(0.851138\pi\)
\(164\) 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 −0.956959 0.290223i \(-0.906271\pi\)
0.729820 + 0.683639i \(0.239604\pi\)
\(168\) 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 −0.877922 0.478804i \(-0.841070\pi\)
−0.0243045 + 0.999705i \(0.507737\pi\)
\(174\) 0 0
\(175\) −2.88570 3.22441i −0.218138 0.243743i
\(176\) 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
\(185\) −3.59108 1.60535i −0.264021 0.118027i
\(186\) 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 −0.869972 0.493102i \(-0.835863\pi\)
0.862024 + 0.506867i \(0.169196\pi\)
\(194\) −8.64822 −0.620906
\(195\) 0 0
\(196\) −6.25104 −0.446503
\(197\) −0.861905 + 1.49286i −0.0614082 + 0.106362i −0.895095 0.445875i \(-0.852892\pi\)
0.833687 + 0.552237i \(0.186226\pi\)
\(198\) 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
\(205\) −7.46410 + 16.6968i −0.521315 + 1.16615i
\(206\) 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
\(215\) −12.0323 16.6138i −0.820599 1.13305i
\(216\) 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 −0.725834 0.687870i \(-0.758546\pi\)
0.958630 + 0.284656i \(0.0918794\pi\)
\(224\) −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 0.813954 0.580929i \(-0.197311\pi\)
−0.910076 + 0.414441i \(0.863977\pi\)
\(228\) 0 0
\(229\) 7.88800i 0.521254i −0.965440 0.260627i \(-0.916071\pi\)
0.965440 0.260627i \(-0.0839293\pi\)
\(230\) −3.81974 5.27413i −0.251866 0.347766i
\(231\) 0 0
\(232\) 3.24491 5.62035i 0.213039 0.368994i
\(233\) 1.42749i 0.0935181i 0.998906 + 0.0467590i \(0.0148893\pi\)
−0.998906 + 0.0467590i \(0.985111\pi\)
\(234\) 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
\(245\) 12.7607 + 5.70452i 0.815252 + 0.364448i
\(246\) 0 0
\(247\) 17.1043 + 13.3288i 1.08832 + 0.848091i
\(248\) 6.95057i 0.441362i
\(249\) 0 0
\(250\) −10.9254 2.37400i −0.690982 0.150145i
\(251\) −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 0.791483 0.611191i \(-0.209309\pi\)
−0.133565 + 0.991040i \(0.542642\pi\)
\(258\) 0 0
\(259\) −1.52241 −0.0945981
\(260\) 6.83610 + 4.27408i 0.423957 + 0.265067i
\(261\) 0 0
\(262\) −1.13567 + 1.96703i −0.0701616 + 0.121524i
\(263\) 18.3309 + 10.5834i 1.13033 + 0.652598i 0.944019 0.329892i \(-0.107012\pi\)
0.186314 + 0.982490i \(0.440346\pi\)
\(264\) 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
\(275\) 0.830670 + 0.272675i 0.0500913 + 0.0164429i
\(276\) 0 0
\(277\) −17.0717 + 9.85638i −1.02574 + 0.592212i −0.915762 0.401722i \(-0.868412\pi\)
−0.109980 + 0.993934i \(0.535079\pi\)
\(278\) 0.820759 0.0492259
\(279\) 0 0
\(280\) 1.56729 1.13509i 0.0936633 0.0678347i
\(281\) 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 0.768701 0.639608i \(-0.220903\pi\)
−0.169566 + 0.985519i \(0.554237\pi\)
\(284\) 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
\(290\) −11.7530 + 8.51202i −0.690163 + 0.499843i
\(291\) 0 0
\(292\) 6.43528 + 11.1462i 0.376596 + 0.652284i
\(293\) −6.57636 11.3906i −0.384195 0.665445i 0.607462 0.794349i \(-0.292188\pi\)
−0.991657 + 0.128903i \(0.958854\pi\)
\(294\) 0 0
\(295\) 9.22927 + 12.7434i 0.537349 + 0.741949i
\(296\) 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
\(305\) −14.4407 + 10.4585i −0.826872 + 0.598854i
\(306\) 0 0
\(307\) −14.8609 −0.848155 −0.424077 0.905626i \(-0.639402\pi\)
−0.424077 + 0.905626i \(0.639402\pi\)
\(308\) −0.131051 + 0.0756625i −0.00746734 + 0.00431127i
\(309\) 0 0
\(310\) −6.34290 + 14.1887i −0.360252 + 0.805865i
\(311\) −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 \(-0.932576\pi\)
0.977650 0.210240i \(-0.0674245\pi\)
\(314\) −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 \(-0.242688\pi\)
0.723161 + 0.690679i \(0.242688\pi\)
\(318\) 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
\(325\) −10.0546 14.9634i −0.557731 0.830022i
\(326\) −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
\(335\) 5.58382 + 2.49618i 0.305076 + 0.136381i
\(336\) 0 0
\(337\) 18.6696i 1.01700i −0.861063 0.508498i \(-0.830201\pi\)
0.861063 0.508498i \(-0.169799\pi\)
\(338\) 3.17664 + 12.6059i 0.172786 + 0.685671i
\(339\) 0 0
\(340\) −7.46410 + 16.6968i −0.404798 + 0.905511i
\(341\) 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 0.336813 0.941572i \(-0.390651\pi\)
0.983831 + 0.179098i \(0.0573178\pi\)
\(348\) 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 −0.886857 0.462044i \(-0.847116\pi\)
0.843570 + 0.537019i \(0.180450\pi\)
\(354\) 0 0
\(355\) −18.5794 25.6537i −0.986093 1.36156i
\(356\) 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 0.792867 0.609394i \(-0.208587\pi\)
−0.131317 + 0.991340i \(0.541921\pi\)
\(368\) 2.52211 1.45614i 0.131474 0.0759065i
\(369\) 0 0
\(370\) −3.18581 + 2.30729i −0.165622 + 0.119950i
\(371\) 1.86422 1.07631i 0.0967855 0.0558791i
\(372\) 0 0
\(373\) −19.1166 + 11.0370i −0.989819 + 0.571472i −0.905220 0.424943i \(-0.860294\pi\)
−0.0845988 + 0.996415i \(0.526961\pi\)
\(374\) 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 \(0.550270\pi\)
\(380\) 5.48837 12.2772i 0.281547 0.629806i
\(381\) 0 0
\(382\) −5.57642 −0.285314
\(383\) 12.3044 + 21.3119i 0.628728 + 1.08899i 0.987807 + 0.155681i \(0.0497573\pi\)
−0.359080 + 0.933307i \(0.616909\pi\)
\(384\) 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 0.834773 0.550595i \(-0.185599\pi\)
−0.894215 + 0.447637i \(0.852266\pi\)
\(398\) −7.95853 −0.398925
\(399\) 0 0
\(400\) 1.55943 4.75060i 0.0779714 0.237530i
\(401\) −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 \(0.0253717\pi\)
\(410\) 10.7278 + 14.8125i 0.529808 + 0.731537i
\(411\) 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
\(425\) 30.4741 27.2729i 1.47821 1.32293i
\(426\) 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 0.302376 0.953189i \(-0.402220\pi\)
0.976674 + 0.214729i \(0.0688869\pi\)
\(434\) 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 \(0.116873\pi\)
\(440\) −0.159569 + 0.356946i −0.00760713 + 0.0170167i
\(441\) 0 0
\(442\) −27.3292 + 11.0816i −1.29992 + 0.527100i
\(443\) 30.3111i 1.44012i 0.693911 + 0.720061i \(0.255886\pi\)
−0.693911 + 0.720061i \(0.744114\pi\)
\(444\) 0 0
\(445\) −11.9906 + 26.8223i −0.568407 + 1.27150i
\(446\) −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
\(455\) −5.91614 3.69890i −0.277353 0.173407i
\(456\) 0 0
\(457\) 9.90436 17.1548i 0.463306 0.802470i −0.535817 0.844334i \(-0.679996\pi\)
0.999123 + 0.0418642i \(0.0133297\pi\)
\(458\) −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 \(-0.0564493\pi\)
0.984316 + 0.176412i \(0.0564493\pi\)
\(464\) −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 \(-0.718175\pi\)
0.632996 0.774155i \(-0.281825\pi\)
\(468\) 0 0
\(469\) 2.36722 0.109308
\(470\) 24.2966 + 10.8615i 1.12072 + 0.501005i
\(471\) 0 0
\(472\) −6.09393 + 3.51833i −0.280496 + 0.161944i
\(473\) 1.60410 0.0737564
\(474\) 0 0
\(475\) −22.4076 + 20.0538i −1.02813 + 0.920132i
\(476\) 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
\(485\) 15.6619 11.3430i 0.711170 0.515058i
\(486\) 0 0
\(487\) −14.3750 24.8982i −0.651392 1.12824i −0.982785 0.184751i \(-0.940852\pi\)
0.331393 0.943493i \(-0.392481\pi\)
\(488\) −3.98695 6.90559i −0.180481 0.312602i
\(489\) 0 0
\(490\) 11.3206 8.19884i 0.511413 0.370386i
\(491\) −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 \(0.732804\pi\)
\(500\) −7.51864 + 8.27466i −0.336244 + 0.370054i
\(501\) 0 0
\(502\) −17.8942 −0.798656
\(503\) 21.7736 12.5710i 0.970838 0.560514i 0.0713466 0.997452i \(-0.477270\pi\)
0.899492 + 0.436938i \(0.143937\pi\)
\(504\) 0 0
\(505\) 21.5682 + 9.64180i 0.959772 + 0.429055i
\(506\) 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
\(520\) 7.11951 3.78319i 0.312211 0.165904i
\(521\) 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 0.936512 0.350635i \(-0.114034\pi\)
0.164598 + 0.986361i \(0.447367\pi\)
\(524\) 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
\(530\) 2.26988 5.07761i 0.0985974 0.220557i
\(531\) 0 0
\(532\) 5.20483i 0.225658i
\(533\) −4.06762 + 29.2086i −0.176188 + 1.26517i
\(534\) 0 0
\(535\) −0.785521 + 1.75717i −0.0339610 + 0.0759690i
\(536\) −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 \(0.336491\pi\)
−0.491385 + 0.870942i \(0.663509\pi\)
\(548\) −3.68809 + 6.38795i −0.157547 + 0.272880i
\(549\) 0 0
\(550\) 0.651479 0.583044i 0.0277791 0.0248611i
\(551\) 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 −0.856150 0.516727i \(-0.827150\pi\)
0.875574 + 0.483084i \(0.160483\pi\)
\(558\) 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 −0.250859 0.968024i \(-0.580713\pi\)
0.712903 + 0.701262i \(0.247380\pi\)
\(564\) 0 0
\(565\) 15.4534 + 21.3374i 0.650129 + 0.897671i
\(566\) 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
\(575\) 13.8351 + 4.54149i 0.576962 + 0.189393i
\(576\) 0 0
\(577\) 23.8325 0.992161 0.496081 0.868276i \(-0.334772\pi\)
0.496081 + 0.868276i \(0.334772\pi\)
\(578\) −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 \(0.446935\pi\)
−0.936988 + 0.349362i \(0.886398\pi\)
\(588\) 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 \(-0.542354\pi\)
−0.132668 + 0.991161i \(0.542354\pi\)
\(594\) 0 0
\(595\) 6.45963 14.4499i 0.264819 0.592386i
\(596\) −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
\(605\) 19.8656 14.3875i 0.807652 0.584933i
\(606\) 0 0
\(607\) 25.5500 14.7513i 1.03704 0.598736i 0.118047 0.993008i \(-0.462337\pi\)
0.918994 + 0.394272i \(0.129003\pi\)
\(608\) 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 −0.970729 0.240178i \(-0.922794\pi\)
0.693365 + 0.720587i \(0.256127\pi\)
\(614\) −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 \(-0.835174\pi\)
0.00578297 0.999983i \(-0.498159\pi\)
\(618\) 0 0
\(619\) 30.0054i 1.20602i 0.797734 + 0.603010i \(0.206032\pi\)
−0.797734 + 0.603010i \(0.793968\pi\)
\(620\) 9.11635 + 12.5875i 0.366121 + 0.505525i
\(621\) 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
\(635\) −6.33542 + 14.1720i −0.251414 + 0.562399i
\(636\) 0 0
\(637\) 22.3230 + 3.10873i 0.884470 + 0.123172i
\(638\) 1.13478i 0.0449265i
\(639\) 0 0
\(640\) 2.04138 + 0.912572i 0.0806924 + 0.0360726i
\(641\) 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 0.755886 0.654703i \(-0.227206\pi\)
−0.944933 + 0.327265i \(0.893873\pi\)
\(644\) −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 \(0.0161433\pi\)
0.543259 + 0.839565i \(0.317190\pi\)
\(648\) 0 0
\(649\) −1.23040 −0.0482975
\(650\) −17.9860 + 1.22585i −0.705470 + 0.0480819i
\(651\) 0 0
\(652\) −0.713746 + 1.23624i −0.0279524 + 0.0484150i
\(653\) −8.00988 4.62451i −0.313451 0.180971i 0.335019 0.942211i \(-0.391257\pi\)
−0.648470 + 0.761241i \(0.724591\pi\)
\(654\) 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
\(665\) −4.74978 + 10.6250i −0.184189 + 0.412020i
\(666\) 0 0
\(667\) 16.3680 9.45008i 0.633772 0.365909i
\(668\) 5.87057 0.227139
\(669\) 0 0
\(670\) 4.95366 3.58764i 0.191377 0.138603i
\(671\) 1.39428i 0.0538256i
\(672\) 0 0
\(673\) 11.6594 + 6.73157i 0.449437 + 0.259483i 0.707593 0.706621i \(-0.249781\pi\)
−0.258155 + 0.966103i \(0.583115\pi\)
\(674\) −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 \(0.0482904\pi\)
−0.988514 + 0.151127i \(0.951710\pi\)
\(678\) 0 0
\(679\) 3.74220 6.48168i 0.143612 0.248744i
\(680\) 10.7278 + 14.8125i 0.411392 + 0.568033i
\(681\) 0 0
\(682\) −0.607674 1.05252i −0.0232690 0.0403032i
\(683\) −9.21246 15.9565i −0.352505 0.610557i 0.634183 0.773183i \(-0.281337\pi\)
−0.986688 + 0.162627i \(0.948003\pi\)
\(684\) 0 0
\(685\) 13.3582 9.67456i 0.510392 0.369646i
\(686\) 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
\(695\) −1.48639 + 1.07650i −0.0563821 + 0.0408342i
\(696\) 0 0
\(697\) −66.8992 −2.53399
\(698\) 1.93797 1.11889i 0.0733532 0.0423505i
\(699\) 0 0
\(700\) −1.34957 + 4.11130i −0.0510090 + 0.155392i
\(701\) 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
\(715\) 1.40886 + 0.0495564i 0.0526884 + 0.00185330i
\(716\) −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
\(725\) 10.1204 30.8305i 0.375862 1.14502i
\(726\) 0 0
\(727\) 36.0471i 1.33691i −0.743750 0.668457i \(-0.766955\pi\)
0.743750 0.668457i \(-0.233045\pi\)
\(728\) 1.91799 2.46127i 0.0710853 0.0912208i
\(729\) 0 0
\(730\) −26.2737 11.7453i −0.972432 0.434714i
\(731\) 37.5172 64.9817i 1.38762 2.40344i
\(732\) 0 0
\(733\) −17.0888 −0.631189 −0.315594 0.948894i \(-0.602204\pi\)
−0.315594 + 0.948894i \(0.602204\pi\)
\(734\) 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 −0.870133 0.492817i \(-0.835967\pi\)
0.861859 + 0.507148i \(0.169300\pi\)
\(744\) 0 0
\(745\) 13.4907 + 18.6274i 0.494260 + 0.682453i
\(746\) 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 0.626814 0.779169i \(-0.284358\pi\)
−0.361373 + 0.932421i \(0.617692\pi\)
\(758\) 12.0573 6.96127i 0.437940 0.252845i
\(759\) 0 0
\(760\) −7.88817 10.8917i −0.286134 0.395082i
\(761\) −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 \(0.644460\pi\)
\(770\) 0.138095 0.308911i 0.00497660 0.0111324i
\(771\) 0 0
\(772\) 0.220810 0.00794712
\(773\) 16.6218 + 28.7898i 0.597845 + 1.03550i 0.993139 + 0.116944i \(0.0373097\pi\)
−0.395293 + 0.918555i \(0.629357\pi\)
\(774\) 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 \(0.0263459\pi\)
−0.426691 + 0.904398i \(0.640321\pi\)