Properties

Label 1792.2.m.h.449.7
Level $1792$
Weight $2$
Character 1792.449
Analytic conductor $14.309$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1792 = 2^{8} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1792.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.3091920422\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} - 180 x^{7} + 358 x^{6} - 336 x^{5} + 390 x^{4} - 344 x^{3} + 164 x^{2} - 40 x + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{14} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 449.7
Root \(-0.709944 + 0.925217i\) of defining polynomial
Character \(\chi\) \(=\) 1792.449
Dual form 1792.2.m.h.1345.7

$q$-expansion

\(f(q)\) \(=\) \(q+(2.04137 - 2.04137i) q^{3} +(-0.701647 - 0.701647i) q^{5} +1.00000i q^{7} -5.33435i q^{9} +O(q^{10})\) \(q+(2.04137 - 2.04137i) q^{3} +(-0.701647 - 0.701647i) q^{5} +1.00000i q^{7} -5.33435i q^{9} +(-2.41989 - 2.41989i) q^{11} +(-1.96098 + 1.96098i) q^{13} -2.86464 q^{15} -6.93050 q^{17} +(1.38948 - 1.38948i) q^{19} +(2.04137 + 2.04137i) q^{21} +2.05612i q^{23} -4.01538i q^{25} +(-4.76526 - 4.76526i) q^{27} +(5.34414 - 5.34414i) q^{29} -5.23708 q^{31} -9.87975 q^{33} +(0.701647 - 0.701647i) q^{35} +(-6.58401 - 6.58401i) q^{37} +8.00617i q^{39} -0.949797i q^{41} +(-5.95343 - 5.95343i) q^{43} +(-3.74283 + 3.74283i) q^{45} -4.64785 q^{47} -1.00000 q^{49} +(-14.1477 + 14.1477i) q^{51} +(7.24791 + 7.24791i) q^{53} +3.39582i q^{55} -5.67289i q^{57} +(8.58048 + 8.58048i) q^{59} +(2.81502 - 2.81502i) q^{61} +5.33435 q^{63} +2.75184 q^{65} +(9.07198 - 9.07198i) q^{67} +(4.19729 + 4.19729i) q^{69} +3.60510i q^{71} -6.53179i q^{73} +(-8.19686 - 8.19686i) q^{75} +(2.41989 - 2.41989i) q^{77} -13.7819 q^{79} -3.45223 q^{81} +(-4.49372 + 4.49372i) q^{83} +(4.86277 + 4.86277i) q^{85} -21.8187i q^{87} -0.428825i q^{89} +(-1.96098 - 1.96098i) q^{91} +(-10.6908 + 10.6908i) q^{93} -1.94986 q^{95} +14.6339 q^{97} +(-12.9085 + 12.9085i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 4q^{3} + 4q^{5} + O(q^{10}) \) \( 16q + 4q^{3} + 4q^{5} - 8q^{11} - 12q^{13} - 8q^{17} + 4q^{19} + 4q^{21} - 56q^{27} - 8q^{31} + 16q^{33} - 4q^{35} + 8q^{37} - 24q^{43} + 36q^{45} - 40q^{47} - 16q^{49} + 24q^{51} + 32q^{53} - 4q^{59} + 20q^{61} + 24q^{63} + 72q^{65} + 32q^{67} - 56q^{69} - 28q^{75} + 8q^{77} - 40q^{81} + 36q^{83} - 12q^{91} - 8q^{93} - 80q^{95} - 72q^{97} - 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times\).

\(n\) \(1023\) \(1025\) \(1541\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{4}\right)\)

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 0
\(3\) 2.04137 2.04137i 1.17858 1.17858i 0.198478 0.980105i \(-0.436400\pi\)
0.980105 0.198478i \(-0.0635997\pi\)
\(4\) 0 0
\(5\) −0.701647 0.701647i −0.313786 0.313786i 0.532588 0.846375i \(-0.321219\pi\)
−0.846375 + 0.532588i \(0.821219\pi\)
\(6\) 0 0
\(7\) 1.00000i 0.377964i
\(8\) 0 0
\(9\) 5.33435i 1.77812i
\(10\) 0 0
\(11\) −2.41989 2.41989i −0.729624 0.729624i 0.240921 0.970545i \(-0.422551\pi\)
−0.970545 + 0.240921i \(0.922551\pi\)
\(12\) 0 0
\(13\) −1.96098 + 1.96098i −0.543879 + 0.543879i −0.924664 0.380784i \(-0.875654\pi\)
0.380784 + 0.924664i \(0.375654\pi\)
\(14\) 0 0
\(15\) −2.86464 −0.739646
\(16\) 0 0
\(17\) −6.93050 −1.68089 −0.840447 0.541894i \(-0.817707\pi\)
−0.840447 + 0.541894i \(0.817707\pi\)
\(18\) 0 0
\(19\) 1.38948 1.38948i 0.318770 0.318770i −0.529525 0.848294i \(-0.677630\pi\)
0.848294 + 0.529525i \(0.177630\pi\)
\(20\) 0 0
\(21\) 2.04137 + 2.04137i 0.445463 + 0.445463i
\(22\) 0 0
\(23\) 2.05612i 0.428730i 0.976754 + 0.214365i \(0.0687682\pi\)
−0.976754 + 0.214365i \(0.931232\pi\)
\(24\) 0 0
\(25\) 4.01538i 0.803076i
\(26\) 0 0
\(27\) −4.76526 4.76526i −0.917074 0.917074i
\(28\) 0 0
\(29\) 5.34414 5.34414i 0.992381 0.992381i −0.00758978 0.999971i \(-0.502416\pi\)
0.999971 + 0.00758978i \(0.00241593\pi\)
\(30\) 0 0
\(31\) −5.23708 −0.940607 −0.470304 0.882505i \(-0.655856\pi\)
−0.470304 + 0.882505i \(0.655856\pi\)
\(32\) 0 0
\(33\) −9.87975 −1.71984
\(34\) 0 0
\(35\) 0.701647 0.701647i 0.118600 0.118600i
\(36\) 0 0
\(37\) −6.58401 6.58401i −1.08240 1.08240i −0.996285 0.0861191i \(-0.972553\pi\)
−0.0861191 0.996285i \(-0.527447\pi\)
\(38\) 0 0
\(39\) 8.00617i 1.28201i
\(40\) 0 0
\(41\) 0.949797i 0.148333i −0.997246 0.0741667i \(-0.976370\pi\)
0.997246 0.0741667i \(-0.0236297\pi\)
\(42\) 0 0
\(43\) −5.95343 5.95343i −0.907889 0.907889i 0.0882122 0.996102i \(-0.471885\pi\)
−0.996102 + 0.0882122i \(0.971885\pi\)
\(44\) 0 0
\(45\) −3.74283 + 3.74283i −0.557948 + 0.557948i
\(46\) 0 0
\(47\) −4.64785 −0.677959 −0.338980 0.940794i \(-0.610082\pi\)
−0.338980 + 0.940794i \(0.610082\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 0 0
\(51\) −14.1477 + 14.1477i −1.98107 + 1.98107i
\(52\) 0 0
\(53\) 7.24791 + 7.24791i 0.995577 + 0.995577i 0.999990 0.00441361i \(-0.00140490\pi\)
−0.00441361 + 0.999990i \(0.501405\pi\)
\(54\) 0 0
\(55\) 3.39582i 0.457892i
\(56\) 0 0
\(57\) 5.67289i 0.751393i
\(58\) 0 0
\(59\) 8.58048 + 8.58048i 1.11708 + 1.11708i 0.992167 + 0.124916i \(0.0398661\pi\)
0.124916 + 0.992167i \(0.460134\pi\)
\(60\) 0 0
\(61\) 2.81502 2.81502i 0.360427 0.360427i −0.503543 0.863970i \(-0.667970\pi\)
0.863970 + 0.503543i \(0.167970\pi\)
\(62\) 0 0
\(63\) 5.33435 0.672065
\(64\) 0 0
\(65\) 2.75184 0.341324
\(66\) 0 0
\(67\) 9.07198 9.07198i 1.10832 1.10832i 0.114947 0.993372i \(-0.463330\pi\)
0.993372 0.114947i \(-0.0366699\pi\)
\(68\) 0 0
\(69\) 4.19729 + 4.19729i 0.505294 + 0.505294i
\(70\) 0 0
\(71\) 3.60510i 0.427847i 0.976850 + 0.213923i \(0.0686243\pi\)
−0.976850 + 0.213923i \(0.931376\pi\)
\(72\) 0 0
\(73\) 6.53179i 0.764488i −0.924061 0.382244i \(-0.875151\pi\)
0.924061 0.382244i \(-0.124849\pi\)
\(74\) 0 0
\(75\) −8.19686 8.19686i −0.946492 0.946492i
\(76\) 0 0
\(77\) 2.41989 2.41989i 0.275772 0.275772i
\(78\) 0 0
\(79\) −13.7819 −1.55059 −0.775293 0.631602i \(-0.782398\pi\)
−0.775293 + 0.631602i \(0.782398\pi\)
\(80\) 0 0
\(81\) −3.45223 −0.383581
\(82\) 0 0
\(83\) −4.49372 + 4.49372i −0.493250 + 0.493250i −0.909329 0.416079i \(-0.863404\pi\)
0.416079 + 0.909329i \(0.363404\pi\)
\(84\) 0 0
\(85\) 4.86277 + 4.86277i 0.527441 + 0.527441i
\(86\) 0 0
\(87\) 21.8187i 2.33921i
\(88\) 0 0
\(89\) 0.428825i 0.0454554i −0.999742 0.0227277i \(-0.992765\pi\)
0.999742 0.0227277i \(-0.00723508\pi\)
\(90\) 0 0
\(91\) −1.96098 1.96098i −0.205567 0.205567i
\(92\) 0 0
\(93\) −10.6908 + 10.6908i −1.10858 + 1.10858i
\(94\) 0 0
\(95\) −1.94986 −0.200051
\(96\) 0 0
\(97\) 14.6339 1.48584 0.742922 0.669378i \(-0.233439\pi\)
0.742922 + 0.669378i \(0.233439\pi\)
\(98\) 0 0
\(99\) −12.9085 + 12.9085i −1.29736 + 1.29736i
\(100\) 0 0
\(101\) 11.2007 + 11.2007i 1.11451 + 1.11451i 0.992533 + 0.121978i \(0.0389237\pi\)
0.121978 + 0.992533i \(0.461076\pi\)
\(102\) 0 0
\(103\) 18.4673i 1.81964i −0.415005 0.909819i \(-0.636220\pi\)
0.415005 0.909819i \(-0.363780\pi\)
\(104\) 0 0
\(105\) 2.86464i 0.279560i
\(106\) 0 0
\(107\) −0.146171 0.146171i −0.0141309 0.0141309i 0.700006 0.714137i \(-0.253181\pi\)
−0.714137 + 0.700006i \(0.753181\pi\)
\(108\) 0 0
\(109\) −0.309414 + 0.309414i −0.0296365 + 0.0296365i −0.721770 0.692133i \(-0.756671\pi\)
0.692133 + 0.721770i \(0.256671\pi\)
\(110\) 0 0
\(111\) −26.8807 −2.55141
\(112\) 0 0
\(113\) 16.7193 1.57282 0.786409 0.617706i \(-0.211938\pi\)
0.786409 + 0.617706i \(0.211938\pi\)
\(114\) 0 0
\(115\) 1.44267 1.44267i 0.134530 0.134530i
\(116\) 0 0
\(117\) 10.4606 + 10.4606i 0.967081 + 0.967081i
\(118\) 0 0
\(119\) 6.93050i 0.635318i
\(120\) 0 0
\(121\) 0.711717i 0.0647016i
\(122\) 0 0
\(123\) −1.93888 1.93888i −0.174823 0.174823i
\(124\) 0 0
\(125\) −6.32562 + 6.32562i −0.565781 + 0.565781i
\(126\) 0 0
\(127\) 4.91639 0.436259 0.218130 0.975920i \(-0.430004\pi\)
0.218130 + 0.975920i \(0.430004\pi\)
\(128\) 0 0
\(129\) −24.3063 −2.14005
\(130\) 0 0
\(131\) 1.10403 1.10403i 0.0964592 0.0964592i −0.657230 0.753690i \(-0.728272\pi\)
0.753690 + 0.657230i \(0.228272\pi\)
\(132\) 0 0
\(133\) 1.38948 + 1.38948i 0.120484 + 0.120484i
\(134\) 0 0
\(135\) 6.68706i 0.575531i
\(136\) 0 0
\(137\) 0.184924i 0.0157991i 0.999969 + 0.00789957i \(0.00251454\pi\)
−0.999969 + 0.00789957i \(0.997485\pi\)
\(138\) 0 0
\(139\) 4.08707 + 4.08707i 0.346661 + 0.346661i 0.858864 0.512203i \(-0.171171\pi\)
−0.512203 + 0.858864i \(0.671171\pi\)
\(140\) 0 0
\(141\) −9.48797 + 9.48797i −0.799031 + 0.799031i
\(142\) 0 0
\(143\) 9.49073 0.793654
\(144\) 0 0
\(145\) −7.49940 −0.622791
\(146\) 0 0
\(147\) −2.04137 + 2.04137i −0.168369 + 0.168369i
\(148\) 0 0
\(149\) −5.37041 5.37041i −0.439961 0.439961i 0.452038 0.891999i \(-0.350697\pi\)
−0.891999 + 0.452038i \(0.850697\pi\)
\(150\) 0 0
\(151\) 11.4266i 0.929880i −0.885342 0.464940i \(-0.846076\pi\)
0.885342 0.464940i \(-0.153924\pi\)
\(152\) 0 0
\(153\) 36.9697i 2.98882i
\(154\) 0 0
\(155\) 3.67458 + 3.67458i 0.295150 + 0.295150i
\(156\) 0 0
\(157\) 9.41825 9.41825i 0.751658 0.751658i −0.223131 0.974789i \(-0.571628\pi\)
0.974789 + 0.223131i \(0.0716276\pi\)
\(158\) 0 0
\(159\) 29.5913 2.34674
\(160\) 0 0
\(161\) −2.05612 −0.162045
\(162\) 0 0
\(163\) −12.4770 + 12.4770i −0.977270 + 0.977270i −0.999747 0.0224770i \(-0.992845\pi\)
0.0224770 + 0.999747i \(0.492845\pi\)
\(164\) 0 0
\(165\) 6.93210 + 6.93210i 0.539664 + 0.539664i
\(166\) 0 0
\(167\) 16.0783i 1.24418i 0.782947 + 0.622088i \(0.213716\pi\)
−0.782947 + 0.622088i \(0.786284\pi\)
\(168\) 0 0
\(169\) 5.30908i 0.408391i
\(170\) 0 0
\(171\) −7.41200 7.41200i −0.566809 0.566809i
\(172\) 0 0
\(173\) 14.4256 14.4256i 1.09676 1.09676i 0.101973 0.994787i \(-0.467485\pi\)
0.994787 0.101973i \(-0.0325154\pi\)
\(174\) 0 0
\(175\) 4.01538 0.303534
\(176\) 0 0
\(177\) 35.0318 2.63315
\(178\) 0 0
\(179\) −3.32674 + 3.32674i −0.248652 + 0.248652i −0.820417 0.571765i \(-0.806259\pi\)
0.571765 + 0.820417i \(0.306259\pi\)
\(180\) 0 0
\(181\) 10.2899 + 10.2899i 0.764846 + 0.764846i 0.977194 0.212348i \(-0.0681112\pi\)
−0.212348 + 0.977194i \(0.568111\pi\)
\(182\) 0 0
\(183\) 11.4930i 0.849586i
\(184\) 0 0
\(185\) 9.23930i 0.679287i
\(186\) 0 0
\(187\) 16.7710 + 16.7710i 1.22642 + 1.22642i
\(188\) 0 0
\(189\) 4.76526 4.76526i 0.346622 0.346622i
\(190\) 0 0
\(191\) −26.6094 −1.92539 −0.962693 0.270595i \(-0.912780\pi\)
−0.962693 + 0.270595i \(0.912780\pi\)
\(192\) 0 0
\(193\) −25.2624 −1.81843 −0.909215 0.416327i \(-0.863317\pi\)
−0.909215 + 0.416327i \(0.863317\pi\)
\(194\) 0 0
\(195\) 5.61751 5.61751i 0.402278 0.402278i
\(196\) 0 0
\(197\) −6.96551 6.96551i −0.496272 0.496272i 0.414003 0.910275i \(-0.364130\pi\)
−0.910275 + 0.414003i \(0.864130\pi\)
\(198\) 0 0
\(199\) 15.2541i 1.08133i 0.841238 + 0.540666i \(0.181828\pi\)
−0.841238 + 0.540666i \(0.818172\pi\)
\(200\) 0 0
\(201\) 37.0385i 2.61249i
\(202\) 0 0
\(203\) 5.34414 + 5.34414i 0.375085 + 0.375085i
\(204\) 0 0
\(205\) −0.666423 + 0.666423i −0.0465450 + 0.0465450i
\(206\) 0 0
\(207\) 10.9680 0.762332
\(208\) 0 0
\(209\) −6.72480 −0.465164
\(210\) 0 0
\(211\) −2.46973 + 2.46973i −0.170023 + 0.170023i −0.786990 0.616966i \(-0.788361\pi\)
0.616966 + 0.786990i \(0.288361\pi\)
\(212\) 0 0
\(213\) 7.35933 + 7.35933i 0.504253 + 0.504253i
\(214\) 0 0
\(215\) 8.35442i 0.569767i
\(216\) 0 0
\(217\) 5.23708i 0.355516i
\(218\) 0 0
\(219\) −13.3338 13.3338i −0.901013 0.901013i
\(220\) 0 0
\(221\) 13.5906 13.5906i 0.914203 0.914203i
\(222\) 0 0
\(223\) −12.2245 −0.818610 −0.409305 0.912398i \(-0.634229\pi\)
−0.409305 + 0.912398i \(0.634229\pi\)
\(224\) 0 0
\(225\) −21.4194 −1.42796
\(226\) 0 0
\(227\) 10.6687 10.6687i 0.708107 0.708107i −0.258030 0.966137i \(-0.583073\pi\)
0.966137 + 0.258030i \(0.0830733\pi\)
\(228\) 0 0
\(229\) −6.75289 6.75289i −0.446244 0.446244i 0.447860 0.894104i \(-0.352186\pi\)
−0.894104 + 0.447860i \(0.852186\pi\)
\(230\) 0 0
\(231\) 9.87975i 0.650040i
\(232\) 0 0
\(233\) 7.42241i 0.486258i −0.969994 0.243129i \(-0.921826\pi\)
0.969994 0.243129i \(-0.0781739\pi\)
\(234\) 0 0
\(235\) 3.26115 + 3.26115i 0.212734 + 0.212734i
\(236\) 0 0
\(237\) −28.1339 + 28.1339i −1.82749 + 1.82749i
\(238\) 0 0
\(239\) −3.44262 −0.222685 −0.111342 0.993782i \(-0.535515\pi\)
−0.111342 + 0.993782i \(0.535515\pi\)
\(240\) 0 0
\(241\) 23.0386 1.48404 0.742022 0.670376i \(-0.233867\pi\)
0.742022 + 0.670376i \(0.233867\pi\)
\(242\) 0 0
\(243\) 7.24852 7.24852i 0.464993 0.464993i
\(244\) 0 0
\(245\) 0.701647 + 0.701647i 0.0448266 + 0.0448266i
\(246\) 0 0
\(247\) 5.44952i 0.346744i
\(248\) 0 0
\(249\) 18.3466i 1.16267i
\(250\) 0 0
\(251\) 12.0833 + 12.0833i 0.762690 + 0.762690i 0.976808 0.214118i \(-0.0686876\pi\)
−0.214118 + 0.976808i \(0.568688\pi\)
\(252\) 0 0
\(253\) 4.97557 4.97557i 0.312812 0.312812i
\(254\) 0 0
\(255\) 19.8534 1.24327
\(256\) 0 0
\(257\) 2.15842 0.134638 0.0673191 0.997731i \(-0.478555\pi\)
0.0673191 + 0.997731i \(0.478555\pi\)
\(258\) 0 0
\(259\) 6.58401 6.58401i 0.409110 0.409110i
\(260\) 0 0
\(261\) −28.5075 28.5075i −1.76457 1.76457i
\(262\) 0 0
\(263\) 0.124319i 0.00766581i −0.999993 0.00383290i \(-0.998780\pi\)
0.999993 0.00383290i \(-0.00122005\pi\)
\(264\) 0 0
\(265\) 10.1710i 0.624797i
\(266\) 0 0
\(267\) −0.875390 0.875390i −0.0535730 0.0535730i
\(268\) 0 0
\(269\) 7.93651 7.93651i 0.483897 0.483897i −0.422476 0.906374i \(-0.638839\pi\)
0.906374 + 0.422476i \(0.138839\pi\)
\(270\) 0 0
\(271\) −0.326600 −0.0198395 −0.00991976 0.999951i \(-0.503158\pi\)
−0.00991976 + 0.999951i \(0.503158\pi\)
\(272\) 0 0
\(273\) −8.00617 −0.484556
\(274\) 0 0
\(275\) −9.71677 + 9.71677i −0.585944 + 0.585944i
\(276\) 0 0
\(277\) −14.9992 14.9992i −0.901214 0.901214i 0.0943269 0.995541i \(-0.469930\pi\)
−0.995541 + 0.0943269i \(0.969930\pi\)
\(278\) 0 0
\(279\) 27.9364i 1.67251i
\(280\) 0 0
\(281\) 27.8495i 1.66136i −0.556750 0.830680i \(-0.687952\pi\)
0.556750 0.830680i \(-0.312048\pi\)
\(282\) 0 0
\(283\) −16.4548 16.4548i −0.978134 0.978134i 0.0216317 0.999766i \(-0.493114\pi\)
−0.999766 + 0.0216317i \(0.993114\pi\)
\(284\) 0 0
\(285\) −3.98037 + 3.98037i −0.235777 + 0.235777i
\(286\) 0 0
\(287\) 0.949797 0.0560648
\(288\) 0 0
\(289\) 31.0318 1.82540
\(290\) 0 0
\(291\) 29.8731 29.8731i 1.75119 1.75119i
\(292\) 0 0
\(293\) −20.0525 20.0525i −1.17148 1.17148i −0.981857 0.189624i \(-0.939273\pi\)
−0.189624 0.981857i \(-0.560727\pi\)
\(294\) 0 0
\(295\) 12.0409i 0.701051i
\(296\) 0 0
\(297\) 23.0628i 1.33824i
\(298\) 0 0
\(299\) −4.03201 4.03201i −0.233177 0.233177i
\(300\) 0 0
\(301\) 5.95343 5.95343i 0.343150 0.343150i
\(302\) 0 0
\(303\) 45.7294 2.62709
\(304\) 0 0
\(305\) −3.95031 −0.226194
\(306\) 0 0
\(307\) 18.8054 18.8054i 1.07328 1.07328i 0.0761901 0.997093i \(-0.475724\pi\)
0.997093 0.0761901i \(-0.0242756\pi\)
\(308\) 0 0
\(309\) −37.6985 37.6985i −2.14460 2.14460i
\(310\) 0 0
\(311\) 5.25843i 0.298178i 0.988824 + 0.149089i \(0.0476341\pi\)
−0.988824 + 0.149089i \(0.952366\pi\)
\(312\) 0 0
\(313\) 7.82442i 0.442262i 0.975244 + 0.221131i \(0.0709749\pi\)
−0.975244 + 0.221131i \(0.929025\pi\)
\(314\) 0 0
\(315\) −3.74283 3.74283i −0.210885 0.210885i
\(316\) 0 0
\(317\) 18.0890 18.0890i 1.01598 1.01598i 0.0161108 0.999870i \(-0.494872\pi\)
0.999870 0.0161108i \(-0.00512846\pi\)
\(318\) 0 0
\(319\) −25.8644 −1.44813
\(320\) 0 0
\(321\) −0.596777 −0.0333089
\(322\) 0 0
\(323\) −9.62983 + 9.62983i −0.535818 + 0.535818i
\(324\) 0 0
\(325\) 7.87410 + 7.87410i 0.436777 + 0.436777i
\(326\) 0 0
\(327\) 1.26325i 0.0698581i
\(328\) 0 0
\(329\) 4.64785i 0.256244i
\(330\) 0 0
\(331\) −0.702951 0.702951i −0.0386377 0.0386377i 0.687524 0.726162i \(-0.258698\pi\)
−0.726162 + 0.687524i \(0.758698\pi\)
\(332\) 0 0
\(333\) −35.1214 + 35.1214i −1.92464 + 1.92464i
\(334\) 0 0
\(335\) −12.7307 −0.695551
\(336\) 0 0
\(337\) 13.4691 0.733710 0.366855 0.930278i \(-0.380434\pi\)
0.366855 + 0.930278i \(0.380434\pi\)
\(338\) 0 0
\(339\) 34.1302 34.1302i 1.85370 1.85370i
\(340\) 0 0
\(341\) 12.6731 + 12.6731i 0.686289 + 0.686289i
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 0 0
\(345\) 5.89003i 0.317109i
\(346\) 0 0
\(347\) 2.54293 + 2.54293i 0.136512 + 0.136512i 0.772061 0.635549i \(-0.219226\pi\)
−0.635549 + 0.772061i \(0.719226\pi\)
\(348\) 0 0
\(349\) −1.81167 + 1.81167i −0.0969765 + 0.0969765i −0.753931 0.656954i \(-0.771845\pi\)
0.656954 + 0.753931i \(0.271845\pi\)
\(350\) 0 0
\(351\) 18.6892 0.997556
\(352\) 0 0
\(353\) −4.72060 −0.251252 −0.125626 0.992078i \(-0.540094\pi\)
−0.125626 + 0.992078i \(0.540094\pi\)
\(354\) 0 0
\(355\) 2.52951 2.52951i 0.134252 0.134252i
\(356\) 0 0
\(357\) −14.1477 14.1477i −0.748775 0.748775i
\(358\) 0 0
\(359\) 16.9233i 0.893177i 0.894739 + 0.446589i \(0.147361\pi\)
−0.894739 + 0.446589i \(0.852639\pi\)
\(360\) 0 0
\(361\) 15.1387i 0.796772i
\(362\) 0 0
\(363\) 1.45287 + 1.45287i 0.0762562 + 0.0762562i
\(364\) 0 0
\(365\) −4.58301 + 4.58301i −0.239886 + 0.239886i
\(366\) 0 0
\(367\) 19.8872 1.03810 0.519051 0.854743i \(-0.326286\pi\)
0.519051 + 0.854743i \(0.326286\pi\)
\(368\) 0 0
\(369\) −5.06655 −0.263754
\(370\) 0 0
\(371\) −7.24791 + 7.24791i −0.376293 + 0.376293i
\(372\) 0 0
\(373\) −6.84947 6.84947i −0.354652 0.354652i 0.507185 0.861837i \(-0.330686\pi\)
−0.861837 + 0.507185i \(0.830686\pi\)
\(374\) 0 0
\(375\) 25.8258i 1.33364i
\(376\) 0 0
\(377\) 20.9595i 1.07947i
\(378\) 0 0
\(379\) 11.9445 + 11.9445i 0.613548 + 0.613548i 0.943869 0.330320i \(-0.107157\pi\)
−0.330320 + 0.943869i \(0.607157\pi\)
\(380\) 0 0
\(381\) 10.0362 10.0362i 0.514168 0.514168i
\(382\) 0 0
\(383\) 24.7947 1.26695 0.633476 0.773763i \(-0.281628\pi\)
0.633476 + 0.773763i \(0.281628\pi\)
\(384\) 0 0
\(385\) −3.39582 −0.173067
\(386\) 0 0
\(387\) −31.7577 + 31.7577i −1.61433 + 1.61433i
\(388\) 0 0
\(389\) −2.18643 2.18643i −0.110857 0.110857i 0.649503 0.760359i \(-0.274977\pi\)
−0.760359 + 0.649503i \(0.774977\pi\)
\(390\) 0 0
\(391\) 14.2499i 0.720649i
\(392\) 0 0
\(393\) 4.50744i 0.227370i
\(394\) 0 0
\(395\) 9.67004 + 9.67004i 0.486553 + 0.486553i
\(396\) 0 0
\(397\) 0.272216 0.272216i 0.0136621 0.0136621i −0.700243 0.713905i \(-0.746925\pi\)
0.713905 + 0.700243i \(0.246925\pi\)
\(398\) 0 0
\(399\) 5.67289 0.284000
\(400\) 0 0
\(401\) −14.6370 −0.730937 −0.365468 0.930824i \(-0.619091\pi\)
−0.365468 + 0.930824i \(0.619091\pi\)
\(402\) 0 0
\(403\) 10.2698 10.2698i 0.511577 0.511577i
\(404\) 0 0
\(405\) 2.42225 + 2.42225i 0.120362 + 0.120362i
\(406\) 0 0
\(407\) 31.8651i 1.57950i
\(408\) 0 0
\(409\) 5.20342i 0.257292i −0.991691 0.128646i \(-0.958937\pi\)
0.991691 0.128646i \(-0.0410632\pi\)
\(410\) 0 0
\(411\) 0.377498 + 0.377498i 0.0186206 + 0.0186206i
\(412\) 0 0
\(413\) −8.58048 + 8.58048i −0.422218 + 0.422218i
\(414\) 0 0
\(415\) 6.30601 0.309550
\(416\) 0 0
\(417\) 16.6864 0.817138
\(418\) 0 0
\(419\) 9.91249 9.91249i 0.484257 0.484257i −0.422231 0.906488i \(-0.638753\pi\)
0.906488 + 0.422231i \(0.138753\pi\)
\(420\) 0 0
\(421\) 5.87543 + 5.87543i 0.286351 + 0.286351i 0.835635 0.549285i \(-0.185100\pi\)
−0.549285 + 0.835635i \(0.685100\pi\)
\(422\) 0 0
\(423\) 24.7933i 1.20549i
\(424\) 0 0
\(425\) 27.8286i 1.34989i
\(426\) 0 0
\(427\) 2.81502 + 2.81502i 0.136229 + 0.136229i
\(428\) 0 0
\(429\) 19.3740 19.3740i 0.935388 0.935388i
\(430\) 0 0
\(431\) −18.4777 −0.890039 −0.445019 0.895521i \(-0.646803\pi\)
−0.445019 + 0.895521i \(0.646803\pi\)
\(432\) 0 0
\(433\) 8.69984 0.418088 0.209044 0.977906i \(-0.432965\pi\)
0.209044 + 0.977906i \(0.432965\pi\)
\(434\) 0 0
\(435\) −15.3090 + 15.3090i −0.734011 + 0.734011i
\(436\) 0 0
\(437\) 2.85694 + 2.85694i 0.136666 + 0.136666i
\(438\) 0 0
\(439\) 2.08886i 0.0996959i −0.998757 0.0498479i \(-0.984126\pi\)
0.998757 0.0498479i \(-0.0158737\pi\)
\(440\) 0 0
\(441\) 5.33435i 0.254017i
\(442\) 0 0
\(443\) 1.57395 + 1.57395i 0.0747808 + 0.0747808i 0.743508 0.668727i \(-0.233161\pi\)
−0.668727 + 0.743508i \(0.733161\pi\)
\(444\) 0 0
\(445\) −0.300884 + 0.300884i −0.0142633 + 0.0142633i
\(446\) 0 0
\(447\) −21.9260 −1.03706
\(448\) 0 0
\(449\) −22.6235 −1.06767 −0.533835 0.845589i \(-0.679250\pi\)
−0.533835 + 0.845589i \(0.679250\pi\)
\(450\) 0 0
\(451\) −2.29840 + 2.29840i −0.108228 + 0.108228i
\(452\) 0 0
\(453\) −23.3258 23.3258i −1.09594 1.09594i
\(454\) 0 0
\(455\) 2.75184i 0.129008i
\(456\) 0 0
\(457\) 22.9357i 1.07289i −0.843937 0.536443i \(-0.819768\pi\)
0.843937 0.536443i \(-0.180232\pi\)
\(458\) 0 0
\(459\) 33.0256 + 33.0256i 1.54150 + 1.54150i
\(460\) 0 0
\(461\) 9.77472 9.77472i 0.455254 0.455254i −0.441840 0.897094i \(-0.645674\pi\)
0.897094 + 0.441840i \(0.145674\pi\)
\(462\) 0 0
\(463\) 22.4440 1.04306 0.521531 0.853233i \(-0.325361\pi\)
0.521531 + 0.853233i \(0.325361\pi\)
\(464\) 0 0
\(465\) 15.0023 0.695717
\(466\) 0 0
\(467\) 1.55804 1.55804i 0.0720976 0.0720976i −0.670138 0.742236i \(-0.733765\pi\)
0.742236 + 0.670138i \(0.233765\pi\)
\(468\) 0 0
\(469\) 9.07198 + 9.07198i 0.418905 + 0.418905i
\(470\) 0 0
\(471\) 38.4522i 1.77178i
\(472\) 0 0
\(473\) 28.8133i 1.32484i
\(474\) 0 0
\(475\) −5.57931 5.57931i −0.255996 0.255996i
\(476\) 0 0
\(477\) 38.6629 38.6629i 1.77025 1.77025i
\(478\) 0 0
\(479\) −36.0952 −1.64923 −0.824615 0.565694i \(-0.808608\pi\)
−0.824615 + 0.565694i \(0.808608\pi\)
\(480\) 0 0
\(481\) 25.8223 1.17739
\(482\) 0 0
\(483\) −4.19729 + 4.19729i −0.190983 + 0.190983i
\(484\) 0 0
\(485\) −10.2678 10.2678i −0.466237 0.466237i
\(486\) 0 0
\(487\) 40.4748i 1.83409i −0.398785 0.917044i \(-0.630568\pi\)
0.398785 0.917044i \(-0.369432\pi\)
\(488\) 0 0
\(489\) 50.9400i 2.30359i
\(490\) 0 0
\(491\) 27.1284 + 27.1284i 1.22429 + 1.22429i 0.966094 + 0.258192i \(0.0831266\pi\)
0.258192 + 0.966094i \(0.416873\pi\)
\(492\) 0 0
\(493\) −37.0375 + 37.0375i −1.66809 + 1.66809i
\(494\) 0 0
\(495\) 18.1145 0.814185
\(496\) 0 0
\(497\) −3.60510 −0.161711
\(498\) 0 0
\(499\) 1.38687 1.38687i 0.0620847 0.0620847i −0.675383 0.737467i \(-0.736022\pi\)
0.737467 + 0.675383i \(0.236022\pi\)
\(500\) 0 0
\(501\) 32.8217 + 32.8217i 1.46637 + 1.46637i
\(502\) 0 0
\(503\) 16.6445i 0.742140i 0.928605 + 0.371070i \(0.121009\pi\)
−0.928605 + 0.371070i \(0.878991\pi\)
\(504\) 0 0
\(505\) 15.7179i 0.699436i
\(506\) 0 0
\(507\) 10.8378 + 10.8378i 0.481322 + 0.481322i
\(508\) 0 0
\(509\) 17.4276 17.4276i 0.772463 0.772463i −0.206074 0.978536i \(-0.566069\pi\)
0.978536 + 0.206074i \(0.0660686\pi\)
\(510\) 0 0
\(511\) 6.53179 0.288949
\(512\) 0 0
\(513\) −13.2425 −0.584671
\(514\) 0 0
\(515\) −12.9575 + 12.9575i −0.570978 + 0.570978i
\(516\) 0 0
\(517\) 11.2473 + 11.2473i 0.494655 + 0.494655i
\(518\) 0 0
\(519\) 58.8960i 2.58525i
\(520\) 0 0
\(521\) 2.69192i 0.117935i −0.998260 0.0589676i \(-0.981219\pi\)
0.998260 0.0589676i \(-0.0187809\pi\)
\(522\) 0 0
\(523\) −10.9962 10.9962i −0.480830 0.480830i 0.424566 0.905397i \(-0.360427\pi\)
−0.905397 + 0.424566i \(0.860427\pi\)
\(524\) 0 0
\(525\) 8.19686 8.19686i 0.357740 0.357740i
\(526\) 0 0
\(527\) 36.2956 1.58106
\(528\) 0 0
\(529\) 18.7724 0.816191
\(530\) 0 0
\(531\) 45.7713 45.7713i 1.98630 1.98630i
\(532\) 0 0
\(533\) 1.86254 + 1.86254i 0.0806755 + 0.0806755i
\(534\) 0 0
\(535\) 0.205121i 0.00886816i
\(536\) 0 0
\(537\) 13.5822i 0.586115i
\(538\) 0 0
\(539\) 2.41989 + 2.41989i 0.104232 + 0.104232i
\(540\) 0 0
\(541\) −6.46720 + 6.46720i −0.278047 + 0.278047i −0.832329 0.554282i \(-0.812993\pi\)
0.554282 + 0.832329i \(0.312993\pi\)
\(542\) 0 0
\(543\) 42.0111 1.80287
\(544\) 0 0
\(545\) 0.434199 0.0185990
\(546\) 0 0
\(547\) 20.5089 20.5089i 0.876896 0.876896i −0.116316 0.993212i \(-0.537109\pi\)
0.993212 + 0.116316i \(0.0371085\pi\)
\(548\) 0 0
\(549\) −15.0163 15.0163i −0.640881 0.640881i
\(550\) 0 0
\(551\) 14.8512i 0.632682i
\(552\) 0 0
\(553\) 13.7819i 0.586066i
\(554\) 0 0
\(555\) 18.8608 + 18.8608i 0.800596 + 0.800596i
\(556\) 0 0
\(557\) 11.0551 11.0551i 0.468421 0.468421i −0.432981 0.901403i \(-0.642538\pi\)
0.901403 + 0.432981i \(0.142538\pi\)
\(558\) 0 0
\(559\) 23.3492 0.987565
\(560\) 0 0
\(561\) 68.4716 2.89087
\(562\) 0 0
\(563\) −15.3790 + 15.3790i −0.648147 + 0.648147i −0.952545 0.304398i \(-0.901545\pi\)
0.304398 + 0.952545i \(0.401545\pi\)
\(564\) 0 0
\(565\) −11.7310 11.7310i −0.493529 0.493529i
\(566\) 0 0
\(567\) 3.45223i 0.144980i
\(568\) 0 0
\(569\) 9.21322i 0.386238i 0.981175 + 0.193119i \(0.0618604\pi\)
−0.981175 + 0.193119i \(0.938140\pi\)
\(570\) 0 0
\(571\) −10.3471 10.3471i −0.433014 0.433014i 0.456638 0.889653i \(-0.349053\pi\)
−0.889653 + 0.456638i \(0.849053\pi\)
\(572\) 0 0
\(573\) −54.3195 + 54.3195i −2.26923 + 2.26923i
\(574\) 0 0
\(575\) 8.25609 0.344303
\(576\) 0 0
\(577\) 2.75852 0.114839 0.0574193 0.998350i \(-0.481713\pi\)
0.0574193 + 0.998350i \(0.481713\pi\)
\(578\) 0 0
\(579\) −51.5699 + 51.5699i −2.14317 + 2.14317i
\(580\) 0 0
\(581\) −4.49372 4.49372i −0.186431 0.186431i
\(582\) 0 0
\(583\) 35.0783i 1.45279i
\(584\) 0 0
\(585\) 14.6793i 0.606913i
\(586\) 0 0
\(587\) 4.18689 + 4.18689i 0.172812 + 0.172812i 0.788213 0.615402i \(-0.211006\pi\)
−0.615402 + 0.788213i \(0.711006\pi\)
\(588\) 0 0
\(589\) −7.27684 + 7.27684i −0.299837 + 0.299837i
\(590\) 0 0
\(591\) −28.4383 −1.16980
\(592\) 0 0
\(593\) −3.11656 −0.127982 −0.0639908 0.997950i \(-0.520383\pi\)
−0.0639908 + 0.997950i \(0.520383\pi\)
\(594\) 0 0
\(595\) −4.86277 + 4.86277i −0.199354 + 0.199354i
\(596\) 0 0
\(597\) 31.1391 + 31.1391i 1.27444 + 1.27444i
\(598\) 0 0
\(599\) 5.12382i 0.209354i 0.994506 + 0.104677i \(0.0333808\pi\)
−0.994506 + 0.104677i \(0.966619\pi\)
\(600\) 0 0
\(601\) 28.1920i 1.14997i 0.818162 + 0.574987i \(0.194993\pi\)
−0.818162 + 0.574987i \(0.805007\pi\)
\(602\) 0 0
\(603\) −48.3931 48.3931i −1.97072 1.97072i
\(604\) 0 0
\(605\) 0.499374 0.499374i 0.0203025 0.0203025i
\(606\) 0 0
\(607\) −40.0403 −1.62518 −0.812592 0.582832i \(-0.801944\pi\)
−0.812592 + 0.582832i \(0.801944\pi\)
\(608\) 0 0
\(609\) 21.8187 0.884137
\(610\) 0 0
\(611\) 9.11437 9.11437i 0.368728 0.368728i
\(612\) 0 0
\(613\) 12.6820 + 12.6820i 0.512222 + 0.512222i 0.915207 0.402985i \(-0.132027\pi\)
−0.402985 + 0.915207i \(0.632027\pi\)
\(614\) 0 0
\(615\) 2.72083i 0.109714i
\(616\) 0 0
\(617\) 35.2965i 1.42098i 0.703706 + 0.710491i \(0.251527\pi\)
−0.703706 + 0.710491i \(0.748473\pi\)
\(618\) 0 0
\(619\) 6.40966 + 6.40966i 0.257626 + 0.257626i 0.824088 0.566462i \(-0.191688\pi\)
−0.566462 + 0.824088i \(0.691688\pi\)
\(620\) 0 0
\(621\) 9.79793 9.79793i 0.393177 0.393177i
\(622\) 0 0
\(623\) 0.428825 0.0171805
\(624\) 0 0
\(625\) −11.2002 −0.448008
\(626\) 0 0
\(627\) −13.7278 + 13.7278i −0.548234 + 0.548234i
\(628\) 0 0
\(629\) 45.6305 + 45.6305i 1.81941 + 1.81941i
\(630\) 0 0
\(631\) 8.85344i 0.352450i 0.984350 + 0.176225i \(0.0563886\pi\)
−0.984350 + 0.176225i \(0.943611\pi\)
\(632\) 0 0
\(633\) 10.0832i 0.400773i
\(634\) 0 0
\(635\) −3.44957 3.44957i −0.136892 0.136892i
\(636\) 0 0
\(637\) 1.96098 1.96098i 0.0776970 0.0776970i
\(638\) 0 0
\(639\) 19.2309 0.760761
\(640\) 0 0
\(641\) −0.523959 −0.0206951 −0.0103476 0.999946i \(-0.503294\pi\)
−0.0103476 + 0.999946i \(0.503294\pi\)
\(642\) 0 0
\(643\) 7.52914 7.52914i 0.296920 0.296920i −0.542886 0.839806i \(-0.682668\pi\)
0.839806 + 0.542886i \(0.182668\pi\)
\(644\) 0 0
\(645\) 17.0544 + 17.0544i 0.671517 + 0.671517i
\(646\) 0 0
\(647\) 17.9059i 0.703955i −0.936009 0.351977i \(-0.885509\pi\)
0.936009 0.351977i \(-0.114491\pi\)
\(648\) 0 0
\(649\) 41.5276i 1.63010i
\(650\) 0 0
\(651\) −10.6908 10.6908i −0.419005 0.419005i
\(652\) 0 0
\(653\) −7.60327 + 7.60327i −0.297539 + 0.297539i −0.840049 0.542510i \(-0.817474\pi\)
0.542510 + 0.840049i \(0.317474\pi\)
\(654\) 0 0
\(655\) −1.54927 −0.0605351
\(656\) 0 0
\(657\) −34.8428 −1.35935
\(658\) 0 0
\(659\) −12.7271 + 12.7271i −0.495776 + 0.495776i −0.910120 0.414344i \(-0.864011\pi\)
0.414344 + 0.910120i \(0.364011\pi\)
\(660\) 0 0
\(661\) −22.3267 22.3267i −0.868410 0.868410i 0.123887 0.992296i \(-0.460464\pi\)
−0.992296 + 0.123887i \(0.960464\pi\)
\(662\) 0 0
\(663\) 55.4868i 2.15493i
\(664\) 0 0
\(665\) 1.94986i 0.0756122i
\(666\) 0 0
\(667\) 10.9882 + 10.9882i 0.425464 + 0.425464i
\(668\) 0 0
\(669\) −24.9546 + 24.9546i −0.964800 + 0.964800i
\(670\) 0 0
\(671\) −13.6241 −0.525952
\(672\) 0 0
\(673\) −29.7030 −1.14497 −0.572483 0.819917i \(-0.694020\pi\)
−0.572483 + 0.819917i \(0.694020\pi\)
\(674\) 0 0
\(675\) −19.1343 + 19.1343i −0.736481 + 0.736481i
\(676\) 0 0
\(677\) −1.03778 1.03778i −0.0398853 0.0398853i 0.686883 0.726768i \(-0.258979\pi\)
−0.726768 + 0.686883i \(0.758979\pi\)
\(678\) 0 0
\(679\) 14.6339i 0.561596i
\(680\) 0 0
\(681\) 43.5575i 1.66913i
\(682\) 0 0
\(683\) −5.91035 5.91035i −0.226153 0.226153i 0.584930 0.811084i \(-0.301122\pi\)
−0.811084 + 0.584930i \(0.801122\pi\)
\(684\) 0 0
\(685\) 0.129752 0.129752i 0.00495755 0.00495755i
\(686\) 0 0
\(687\) −27.5702 −1.05187
\(688\) 0 0
\(689\) −28.4261 −1.08295
\(690\) 0 0
\(691\) −6.31513 + 6.31513i −0.240239 + 0.240239i −0.816949 0.576710i \(-0.804336\pi\)
0.576710 + 0.816949i \(0.304336\pi\)
\(692\) 0 0
\(693\) −12.9085 12.9085i −0.490354 0.490354i
\(694\) 0 0
\(695\) 5.73537i 0.217555i
\(696\) 0 0
\(697\) 6.58257i 0.249333i
\(698\) 0 0
\(699\) −15.1519 15.1519i −0.573096 0.573096i
\(700\) 0 0
\(701\) 35.3526 35.3526i 1.33525 1.33525i 0.434647 0.900601i \(-0.356873\pi\)
0.900601 0.434647i \(-0.143127\pi\)
\(702\) 0 0
\(703\) −18.2968 −0.690075
\(704\) 0 0
\(705\) 13.3144 0.501450
\(706\) 0 0
\(707\) −11.2007 + 11.2007i −0.421245 + 0.421245i
\(708\) 0 0
\(709\) 25.6099 + 25.6099i 0.961801 + 0.961801i 0.999297 0.0374956i \(-0.0119380\pi\)
−0.0374956 + 0.999297i \(0.511938\pi\)
\(710\) 0 0
\(711\) 73.5175i 2.75712i
\(712\) 0 0
\(713\) 10.7680i 0.403267i
\(714\) 0 0
\(715\) −6.65914 6.65914i −0.249038 0.249038i
\(716\) 0 0
\(717\) −7.02764 + 7.02764i −0.262452 + 0.262452i
\(718\) 0 0
\(719\) 12.8390 0.478816 0.239408 0.970919i \(-0.423047\pi\)
0.239408 + 0.970919i \(0.423047\pi\)
\(720\) 0 0
\(721\) 18.4673 0.687759
\(722\) 0 0
\(723\) 47.0301 47.0301i 1.74907 1.74907i
\(724\) 0 0
\(725\) −21.4588 21.4588i −0.796958 0.796958i
\(726\) 0 0
\(727\) 50.1537i 1.86010i 0.367436 + 0.930049i \(0.380236\pi\)
−0.367436 + 0.930049i \(0.619764\pi\)
\(728\) 0 0
\(729\) 39.9504i 1.47965i
\(730\) 0 0
\(731\) 41.2602 + 41.2602i 1.52607 + 1.52607i
\(732\) 0 0
\(733\) −21.4286 + 21.4286i −0.791485 + 0.791485i −0.981736 0.190250i \(-0.939070\pi\)
0.190250 + 0.981736i \(0.439070\pi\)
\(734\) 0 0
\(735\) 2.86464 0.105664
\(736\) 0 0
\(737\) −43.9064 −1.61731
\(738\) 0 0
\(739\) −2.36694 + 2.36694i −0.0870693 + 0.0870693i −0.749300 0.662231i \(-0.769610\pi\)
0.662231 + 0.749300i \(0.269610\pi\)
\(740\) 0 0
\(741\) 11.1245 + 11.1245i 0.408667 + 0.408667i
\(742\) 0 0
\(743\) 4.56306i 0.167403i 0.996491 + 0.0837013i \(0.0266742\pi\)
−0.996491 + 0.0837013i \(0.973326\pi\)
\(744\) 0 0
\(745\) 7.53627i 0.276108i
\(746\) 0 0
\(747\) 23.9711 + 23.9711i 0.877055 + 0.877055i
\(748\) 0 0
\(749\) 0.146171 0.146171i 0.00534097 0.00534097i
\(750\) 0 0
\(751\) −6.04590 −0.220618 −0.110309 0.993897i \(-0.535184\pi\)
−0.110309 + 0.993897i \(0.535184\pi\)
\(752\) 0 0
\(753\) 49.3328 1.79779
\(754\) 0 0
\(755\) −8.01741 + 8.01741i −0.291784 + 0.291784i
\(756\) 0 0
\(757\) −25.0992 25.0992i −0.912244 0.912244i 0.0842043 0.996449i \(-0.473165\pi\)
−0.996449 + 0.0842043i \(0.973165\pi\)
\(758\) 0 0
\(759\) 20.3139i 0.737349i
\(760\) 0 0
\(761\) 16.2508i 0.589089i 0.955638 + 0.294545i \(0.0951680\pi\)
−0.955638 + 0.294545i \(0.904832\pi\)
\(762\) 0 0
\(763\) −0.309414 0.309414i −0.0112015 0.0112015i
\(764\) 0 0
\(765\) 25.9397 25.9397i 0.937852 0.937852i
\(766\) 0 0
\(767\) −33.6524 −1.21512
\(768\) 0 0
\(769\) −18.6812 −0.673660 −0.336830 0.941565i \(-0.609355\pi\)
−0.336830 + 0.941565i \(0.609355\pi\)
\(770\) 0 0
\(771\) 4.40612 4.40612i 0.158682 0.158682i
\(772\) 0 0
\(773\) −10.6288 10.6288i −0.382293 0.382293i 0.489635 0.871928i \(-0.337130\pi\)
−0.871928 + 0.489635i \(0.837130\pi\)
\(774\) 0 0
\(775\) 21.0289i 0.755380i
\(776\) 0 0
\(777\) 26.8807i 0.964341i
\(778\) 0 0
\(779\) −1.31973 1.31973i −0.0472842 0.0472842i
\(780\) 0 0
\(781\) 8.72394 8.72394i 0.312167 0.312167i
\(782\) 0 0
\(783\) −50.9324 −1.82018
\(784\) 0 0
\(785\) −13.2166 −0.471720
\(786\) 0 0
\(787\) −17.1899 + 17.1899i −0.612755 + 0.612755i −0.943663 0.330908i \(-0.892645\pi\)
0.330908 + 0.943663i \(0.392645\pi\)
\(788\) 0 0
\(789\) −0.253780 0.253780i −0.00903479 0.00903479i
\(790\) 0 0
\(791\) 16.7193i 0.594470i
\(792\) 0 0
\(793\) 11.0404i 0.392058i
\(794\) 0 0
\(795\) −20.7626 20.7626i −0.736375 0.736375i
\(796\) 0 0
\(797\) 19.5801 19.5801i 0.693561 0.693561i −0.269453 0.963014i \(-0.586843\pi\)
0.963014 + 0.269453i \(0.0868427\pi\)
\(798\) 0 0
\(799\) 32.2120