Properties

Label 1792.2.m.e.449.2
Level $1792$
Weight $2$
Character 1792.449
Analytic conductor $14.309$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 449.2
Root \(-0.709944 + 0.925217i\) of defining polynomial
Character \(\chi\) \(=\) 1792.449
Dual form 1792.2.m.e.1345.2

$q$-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 \(0.563600\pi\)
−0.980105 + 0.198478i \(0.936400\pi\)
\(4\) 0 0
\(5\) 0.701647 + 0.701647i 0.313786 + 0.313786i 0.846375 0.532588i \(-0.178781\pi\)
−0.532588 + 0.846375i \(0.678781\pi\)
\(6\) 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 0.970545 0.240921i \(-0.0774495\pi\)
−0.240921 + 0.970545i \(0.577449\pi\)
\(12\) 0 0
\(13\) 1.96098 1.96098i 0.543879 0.543879i −0.380784 0.924664i \(-0.624346\pi\)
0.924664 + 0.380784i \(0.124346\pi\)
\(14\) 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 −0.848294 0.529525i \(-0.822370\pi\)
0.529525 + 0.848294i \(0.322370\pi\)
\(20\) 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 −0.999971 0.00758978i \(-0.997584\pi\)
0.00758978 + 0.999971i \(0.497584\pi\)
\(30\) 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 \(0.0274466\pi\)
0.0861191 + 0.996285i \(0.472553\pi\)
\(38\) 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 0.996102 0.0882122i \(-0.0281154\pi\)
−0.0882122 + 0.996102i \(0.528115\pi\)
\(44\) 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 0.00441361 0.999990i \(-0.498595\pi\)
−0.999990 + 0.00441361i \(0.998595\pi\)
\(54\) 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 \(-0.960134\pi\)
−0.124916 0.992167i \(-0.539866\pi\)
\(60\) 0 0
\(61\) −2.81502 + 2.81502i −0.360427 + 0.360427i −0.863970 0.503543i \(-0.832030\pi\)
0.503543 + 0.863970i \(0.332030\pi\)
\(62\) 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 \(0.536670\pi\)
−0.993372 + 0.114947i \(0.963330\pi\)
\(68\) 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 −0.416079 0.909329i \(-0.636596\pi\)
0.909329 + 0.416079i \(0.136596\pi\)
\(84\) 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 \(-0.961076\pi\)
−0.121978 0.992533i \(-0.538924\pi\)
\(102\) 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 0.714137 0.700006i \(-0.246819\pi\)
−0.700006 + 0.714137i \(0.746819\pi\)
\(108\) 0 0
\(109\) 0.309414 0.309414i 0.0296365 0.0296365i −0.692133 0.721770i \(-0.743329\pi\)
0.721770 + 0.692133i \(0.243329\pi\)
\(110\) 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 −0.753690 0.657230i \(-0.771728\pi\)
0.657230 + 0.753690i \(0.271728\pi\)
\(132\) 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 0.512203 0.858864i \(-0.328829\pi\)
−0.858864 + 0.512203i \(0.828829\pi\)
\(140\) 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 0.891999 0.452038i \(-0.149303\pi\)
−0.452038 + 0.891999i \(0.649303\pi\)
\(150\) 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 −0.974789 0.223131i \(-0.928372\pi\)
0.223131 + 0.974789i \(0.428372\pi\)
\(158\) 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 −0.0224770 0.999747i \(-0.507155\pi\)
0.999747 + 0.0224770i \(0.00715525\pi\)
\(164\) 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 \(0.532515\pi\)
−0.994787 + 0.101973i \(0.967485\pi\)
\(174\) 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 −0.571765 0.820417i \(-0.693741\pi\)
0.820417 + 0.571765i \(0.193741\pi\)
\(180\) 0 0
\(181\) −10.2899 10.2899i −0.764846 0.764846i 0.212348 0.977194i \(-0.431889\pi\)
−0.977194 + 0.212348i \(0.931889\pi\)
\(182\) 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 0.910275 0.414003i \(-0.135870\pi\)
−0.414003 + 0.910275i \(0.635870\pi\)
\(198\) 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 −0.616966 0.786990i \(-0.711639\pi\)
0.786990 + 0.616966i \(0.211639\pi\)
\(212\) 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 −0.966137 0.258030i \(-0.916927\pi\)
0.258030 + 0.966137i \(0.416927\pi\)
\(228\) 0 0
\(229\) 6.75289 + 6.75289i 0.446244 + 0.446244i 0.894104 0.447860i \(-0.147814\pi\)
−0.447860 + 0.894104i \(0.647814\pi\)
\(230\) 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 0.214118 0.976808i \(-0.431312\pi\)
−0.976808 + 0.214118i \(0.931312\pi\)
\(252\) 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 −0.906374 0.422476i \(-0.861161\pi\)
0.422476 + 0.906374i \(0.361161\pi\)
\(270\) 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 0.995541 0.0943269i \(-0.0300699\pi\)
−0.0943269 + 0.995541i \(0.530070\pi\)
\(278\) 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 0.999766 0.0216317i \(-0.00688613\pi\)
−0.0216317 + 0.999766i \(0.506886\pi\)
\(284\) 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 \(0.0607270\pi\)
0.189624 + 0.981857i \(0.439273\pi\)
\(294\) 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 \(0.524276\pi\)
−0.997093 + 0.0761901i \(0.975724\pi\)
\(308\) 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 \(0.505128\pi\)
−0.999870 + 0.0161108i \(0.994872\pi\)
\(318\) 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 0.726162 0.687524i \(-0.241302\pi\)
−0.687524 + 0.726162i \(0.741302\pi\)
\(332\) 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 0.635549 0.772061i \(-0.280774\pi\)
−0.772061 + 0.635549i \(0.780774\pi\)
\(348\) 0 0
\(349\) 1.81167 1.81167i 0.0969765 0.0969765i −0.656954 0.753931i \(-0.728155\pi\)
0.753931 + 0.656954i \(0.228155\pi\)
\(350\) 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 0.861837 0.507185i \(-0.169314\pi\)
−0.507185 + 0.861837i \(0.669314\pi\)
\(374\) 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 0.330320 0.943869i \(-0.392843\pi\)
−0.943869 + 0.330320i \(0.892843\pi\)
\(380\) 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 0.760359 0.649503i \(-0.225023\pi\)
−0.649503 + 0.760359i \(0.725023\pi\)
\(390\) 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 −0.713905 0.700243i \(-0.753075\pi\)
0.700243 + 0.713905i \(0.253075\pi\)
\(398\) 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 −0.906488 0.422231i \(-0.861247\pi\)
0.422231 + 0.906488i \(0.361247\pi\)
\(420\) 0 0
\(421\) −5.87543 5.87543i −0.286351 0.286351i 0.549285 0.835635i \(-0.314900\pi\)
−0.835635 + 0.549285i \(0.814900\pi\)
\(422\) 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 0.668727 0.743508i \(-0.266839\pi\)
−0.743508 + 0.668727i \(0.766839\pi\)
\(444\) 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 −0.897094 0.441840i \(-0.854326\pi\)
0.441840 + 0.897094i \(0.354326\pi\)
\(462\) 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 −0.742236 0.670138i \(-0.766235\pi\)
0.670138 + 0.742236i \(0.266235\pi\)
\(468\) 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 \(-0.916873\pi\)
−0.258192 0.966094i \(-0.583127\pi\)
\(492\) 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 −0.737467 0.675383i \(-0.763978\pi\)
0.675383 + 0.737467i \(0.263978\pi\)
\(500\) 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 −0.978536 0.206074i \(-0.933931\pi\)
0.206074 + 0.978536i \(0.433931\pi\)
\(510\) 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 0.905397 0.424566i \(-0.139573\pi\)
−0.424566 + 0.905397i \(0.639573\pi\)
\(524\) 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 −0.554282 0.832329i \(-0.687007\pi\)
0.832329 + 0.554282i \(0.187007\pi\)
\(542\) 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 −0.993212 0.116316i \(-0.962891\pi\)
0.116316 + 0.993212i \(0.462891\pi\)
\(548\) 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 −0.901403 0.432981i \(-0.857462\pi\)
0.432981 + 0.901403i \(0.357462\pi\)
\(558\) 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 −0.304398 0.952545i \(-0.598455\pi\)
0.952545 + 0.304398i \(0.0984552\pi\)
\(564\) 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 0.889653 0.456638i \(-0.150947\pi\)
−0.456638 + 0.889653i \(0.650947\pi\)
\(572\) 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 0.615402 0.788213i \(-0.288994\pi\)
−0.788213 + 0.615402i \(0.788994\pi\)
\(588\) 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 0.402985 0.915207i \(-0.367973\pi\)
−0.915207 + 0.402985i \(0.867973\pi\)
\(614\) 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 0.566462 0.824088i \(-0.308312\pi\)
−0.824088 + 0.566462i \(0.808312\pi\)
\(620\) 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 −0.839806 0.542886i \(-0.817332\pi\)
0.542886 + 0.839806i \(0.317332\pi\)
\(644\) 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 −0.542510 0.840049i \(-0.682526\pi\)
0.840049 + 0.542510i \(0.182526\pi\)
\(654\) 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 −0.414344 0.910120i \(-0.635989\pi\)
0.910120 + 0.414344i \(0.135989\pi\)
\(660\) 0 0
\(661\) 22.3267 + 22.3267i 0.868410 + 0.868410i 0.992296 0.123887i \(-0.0395360\pi\)
−0.123887 + 0.992296i \(0.539536\pi\)
\(662\) 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 0.726768 0.686883i \(-0.241021\pi\)
−0.686883 + 0.726768i \(0.741021\pi\)
\(678\) 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 0.811084 0.584930i \(-0.198878\pi\)
−0.584930 + 0.811084i \(0.698878\pi\)
\(684\) 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 −0.576710 0.816949i \(-0.695664\pi\)
0.816949 + 0.576710i \(0.195664\pi\)
\(692\) 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 \(0.643127\pi\)
−0.900601 + 0.434647i \(0.856873\pi\)
\(702\) 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 0.0374956 0.999297i \(-0.488062\pi\)
−0.999297 + 0.0374956i \(0.988062\pi\)
\(710\) 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 −0.190250 0.981736i \(-0.560930\pi\)
0.981736 + 0.190250i \(0.0609300\pi\)
\(734\) 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 −0.662231 0.749300i \(-0.730390\pi\)
0.749300 + 0.662231i \(0.230390\pi\)
\(740\) 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 0.996449 0.0842043i \(-0.0268348\pi\)
−0.0842043 + 0.996449i \(0.526835\pi\)
\(758\) 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 0.871928 0.489635i \(-0.162870\pi\)
−0.489635 + 0.871928i \(0.662870\pi\)
\(774\) 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 −0.330908 0.943663i \(-0.607355\pi\)
0.943663 + 0.330908i \(0.107355\pi\)
\(788\) 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 −0.963014 0.269453i \(-0.913157\pi\)
0.269453 + 0.963014i \(0.413157\pi\)
\(798\) 0 0