Properties

Label 1792.2.m.f.1345.8
Level $1792$
Weight $2$
Character 1792.1345
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 1345.8
Root \(0.339278 - 0.0446668i\) of defining polynomial
Character \(\chi\) \(=\) 1792.1345
Dual form 1792.2.m.f.449.8

$q$-expansion

\(f(q)\) \(=\) \(q+(1.48474 + 1.48474i) q^{3} +(-1.83598 + 1.83598i) q^{5} +1.00000i q^{7} +1.40890i q^{9} +O(q^{10})\) \(q+(1.48474 + 1.48474i) q^{3} +(-1.83598 + 1.83598i) q^{5} +1.00000i q^{7} +1.40890i q^{9} +(0.321444 - 0.321444i) q^{11} +(-4.61789 - 4.61789i) q^{13} -5.45192 q^{15} -1.84172 q^{17} +(-3.88948 - 3.88948i) q^{19} +(-1.48474 + 1.48474i) q^{21} +5.88497i q^{23} -1.74168i q^{25} +(2.36237 - 2.36237i) q^{27} +(-6.14570 - 6.14570i) q^{29} -5.69821 q^{31} +0.954522 q^{33} +(-1.83598 - 1.83598i) q^{35} +(-1.66877 + 1.66877i) q^{37} -13.7127i q^{39} +10.7333i q^{41} +(-0.533105 + 0.533105i) q^{43} +(-2.58672 - 2.58672i) q^{45} +0.465401 q^{47} -1.00000 q^{49} +(-2.73447 - 2.73447i) q^{51} +(0.623234 - 0.623234i) q^{53} +1.18033i q^{55} -11.5497i q^{57} +(7.32184 - 7.32184i) q^{59} +(7.57257 + 7.57257i) q^{61} -1.40890 q^{63} +16.9567 q^{65} +(-6.16327 - 6.16327i) q^{67} +(-8.73764 + 8.73764i) q^{69} -0.162532i q^{71} -3.49118i q^{73} +(2.58594 - 2.58594i) q^{75} +(0.321444 + 0.321444i) q^{77} -8.28703 q^{79} +11.2417 q^{81} +(-2.51275 - 2.51275i) q^{83} +(3.38136 - 3.38136i) q^{85} -18.2495i q^{87} -1.60040i q^{89} +(4.61789 - 4.61789i) q^{91} +(-8.46035 - 8.46035i) q^{93} +14.2821 q^{95} -8.88621 q^{97} +(0.452882 + 0.452882i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 4q^{3} + 4q^{5} + O(q^{10}) \) \( 16q - 4q^{3} + 4q^{5} + 8q^{11} - 12q^{13} - 8q^{17} - 4q^{19} + 4q^{21} + 56q^{27} + 8q^{31} + 16q^{33} + 4q^{35} + 8q^{37} + 24q^{43} + 36q^{45} + 40q^{47} - 16q^{49} - 24q^{51} + 32q^{53} + 4q^{59} + 20q^{61} - 24q^{63} + 72q^{65} - 32q^{67} - 56q^{69} + 28q^{75} + 8q^{77} - 40q^{81} - 36q^{83} + 12q^{91} - 8q^{93} + 80q^{95} - 72q^{97} + 8q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(1023\) \(1025\) \(1541\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{3}{4}\right)\)

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
\(3\) 1.48474 + 1.48474i 0.857214 + 0.857214i 0.991009 0.133795i \(-0.0427163\pi\)
−0.133795 + 0.991009i \(0.542716\pi\)
\(4\) 0 0
\(5\) −1.83598 + 1.83598i −0.821077 + 0.821077i −0.986263 0.165185i \(-0.947178\pi\)
0.165185 + 0.986263i \(0.447178\pi\)
\(6\) 0 0
\(7\) 1.00000i 0.377964i
\(8\) 0 0
\(9\) 1.40890i 0.469633i
\(10\) 0 0
\(11\) 0.321444 0.321444i 0.0969191 0.0969191i −0.656985 0.753904i \(-0.728168\pi\)
0.753904 + 0.656985i \(0.228168\pi\)
\(12\) 0 0
\(13\) −4.61789 4.61789i −1.28077 1.28077i −0.940230 0.340541i \(-0.889390\pi\)
−0.340541 0.940230i \(-0.610610\pi\)
\(14\) 0 0
\(15\) −5.45192 −1.40768
\(16\) 0 0
\(17\) −1.84172 −0.446682 −0.223341 0.974740i \(-0.571696\pi\)
−0.223341 + 0.974740i \(0.571696\pi\)
\(18\) 0 0
\(19\) −3.88948 3.88948i −0.892308 0.892308i 0.102432 0.994740i \(-0.467338\pi\)
−0.994740 + 0.102432i \(0.967338\pi\)
\(20\) 0 0
\(21\) −1.48474 + 1.48474i −0.323997 + 0.323997i
\(22\) 0 0
\(23\) 5.88497i 1.22710i 0.789656 + 0.613550i \(0.210259\pi\)
−0.789656 + 0.613550i \(0.789741\pi\)
\(24\) 0 0
\(25\) 1.74168i 0.348336i
\(26\) 0 0
\(27\) 2.36237 2.36237i 0.454639 0.454639i
\(28\) 0 0
\(29\) −6.14570 6.14570i −1.14123 1.14123i −0.988226 0.153002i \(-0.951106\pi\)
−0.153002 0.988226i \(-0.548894\pi\)
\(30\) 0 0
\(31\) −5.69821 −1.02343 −0.511714 0.859156i \(-0.670989\pi\)
−0.511714 + 0.859156i \(0.670989\pi\)
\(32\) 0 0
\(33\) 0.954522 0.166161
\(34\) 0 0
\(35\) −1.83598 1.83598i −0.310338 0.310338i
\(36\) 0 0
\(37\) −1.66877 + 1.66877i −0.274344 + 0.274344i −0.830846 0.556502i \(-0.812143\pi\)
0.556502 + 0.830846i \(0.312143\pi\)
\(38\) 0 0
\(39\) 13.7127i 2.19579i
\(40\) 0 0
\(41\) 10.7333i 1.67626i 0.545468 + 0.838132i \(0.316352\pi\)
−0.545468 + 0.838132i \(0.683648\pi\)
\(42\) 0 0
\(43\) −0.533105 + 0.533105i −0.0812978 + 0.0812978i −0.746586 0.665289i \(-0.768309\pi\)
0.665289 + 0.746586i \(0.268309\pi\)
\(44\) 0 0
\(45\) −2.58672 2.58672i −0.385605 0.385605i
\(46\) 0 0
\(47\) 0.465401 0.0678856 0.0339428 0.999424i \(-0.489194\pi\)
0.0339428 + 0.999424i \(0.489194\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 0 0
\(51\) −2.73447 2.73447i −0.382902 0.382902i
\(52\) 0 0
\(53\) 0.623234 0.623234i 0.0856078 0.0856078i −0.663006 0.748614i \(-0.730720\pi\)
0.748614 + 0.663006i \(0.230720\pi\)
\(54\) 0 0
\(55\) 1.18033i 0.159156i
\(56\) 0 0
\(57\) 11.5497i 1.52980i
\(58\) 0 0
\(59\) 7.32184 7.32184i 0.953223 0.953223i −0.0457310 0.998954i \(-0.514562\pi\)
0.998954 + 0.0457310i \(0.0145617\pi\)
\(60\) 0 0
\(61\) 7.57257 + 7.57257i 0.969569 + 0.969569i 0.999550 0.0299816i \(-0.00954488\pi\)
−0.0299816 + 0.999550i \(0.509545\pi\)
\(62\) 0 0
\(63\) −1.40890 −0.177504
\(64\) 0 0
\(65\) 16.9567 2.10322
\(66\) 0 0
\(67\) −6.16327 6.16327i −0.752964 0.752964i 0.222068 0.975031i \(-0.428719\pi\)
−0.975031 + 0.222068i \(0.928719\pi\)
\(68\) 0 0
\(69\) −8.73764 + 8.73764i −1.05189 + 1.05189i
\(70\) 0 0
\(71\) 0.162532i 0.0192890i −0.999953 0.00964452i \(-0.996930\pi\)
0.999953 0.00964452i \(-0.00306999\pi\)
\(72\) 0 0
\(73\) 3.49118i 0.408612i −0.978907 0.204306i \(-0.934506\pi\)
0.978907 0.204306i \(-0.0654938\pi\)
\(74\) 0 0
\(75\) 2.58594 2.58594i 0.298599 0.298599i
\(76\) 0 0
\(77\) 0.321444 + 0.321444i 0.0366320 + 0.0366320i
\(78\) 0 0
\(79\) −8.28703 −0.932363 −0.466182 0.884689i \(-0.654371\pi\)
−0.466182 + 0.884689i \(0.654371\pi\)
\(80\) 0 0
\(81\) 11.2417 1.24908
\(82\) 0 0
\(83\) −2.51275 2.51275i −0.275810 0.275810i 0.555624 0.831434i \(-0.312479\pi\)
−0.831434 + 0.555624i \(0.812479\pi\)
\(84\) 0 0
\(85\) 3.38136 3.38136i 0.366760 0.366760i
\(86\) 0 0
\(87\) 18.2495i 1.95655i
\(88\) 0 0
\(89\) 1.60040i 0.169642i −0.996396 0.0848209i \(-0.972968\pi\)
0.996396 0.0848209i \(-0.0270318\pi\)
\(90\) 0 0
\(91\) 4.61789 4.61789i 0.484086 0.484086i
\(92\) 0 0
\(93\) −8.46035 8.46035i −0.877297 0.877297i
\(94\) 0 0
\(95\) 14.2821 1.46531
\(96\) 0 0
\(97\) −8.88621 −0.902258 −0.451129 0.892459i \(-0.648979\pi\)
−0.451129 + 0.892459i \(0.648979\pi\)
\(98\) 0 0
\(99\) 0.452882 + 0.452882i 0.0455164 + 0.0455164i
\(100\) 0 0
\(101\) −9.80533 + 9.80533i −0.975667 + 0.975667i −0.999711 0.0240439i \(-0.992346\pi\)
0.0240439 + 0.999711i \(0.492346\pi\)
\(102\) 0 0
\(103\) 14.3236i 1.41135i −0.708537 0.705674i \(-0.750644\pi\)
0.708537 0.705674i \(-0.249356\pi\)
\(104\) 0 0
\(105\) 5.45192i 0.532052i
\(106\) 0 0
\(107\) −10.6995 + 10.6995i −1.03436 + 1.03436i −0.0349695 + 0.999388i \(0.511133\pi\)
−0.999388 + 0.0349695i \(0.988867\pi\)
\(108\) 0 0
\(109\) 7.38679 + 7.38679i 0.707526 + 0.707526i 0.966014 0.258488i \(-0.0832244\pi\)
−0.258488 + 0.966014i \(0.583224\pi\)
\(110\) 0 0
\(111\) −4.95537 −0.470343
\(112\) 0 0
\(113\) 8.05995 0.758217 0.379108 0.925352i \(-0.376231\pi\)
0.379108 + 0.925352i \(0.376231\pi\)
\(114\) 0 0
\(115\) −10.8047 10.8047i −1.00754 1.00754i
\(116\) 0 0
\(117\) 6.50613 6.50613i 0.601492 0.601492i
\(118\) 0 0
\(119\) 1.84172i 0.168830i
\(120\) 0 0
\(121\) 10.7933i 0.981213i
\(122\) 0 0
\(123\) −15.9362 + 15.9362i −1.43692 + 1.43692i
\(124\) 0 0
\(125\) −5.98222 5.98222i −0.535066 0.535066i
\(126\) 0 0
\(127\) −0.367471 −0.0326078 −0.0163039 0.999867i \(-0.505190\pi\)
−0.0163039 + 0.999867i \(0.505190\pi\)
\(128\) 0 0
\(129\) −1.58304 −0.139379
\(130\) 0 0
\(131\) −9.30850 9.30850i −0.813288 0.813288i 0.171838 0.985125i \(-0.445030\pi\)
−0.985125 + 0.171838i \(0.945030\pi\)
\(132\) 0 0
\(133\) 3.88948 3.88948i 0.337261 0.337261i
\(134\) 0 0
\(135\) 8.67456i 0.746587i
\(136\) 0 0
\(137\) 6.85872i 0.585980i 0.956115 + 0.292990i \(0.0946503\pi\)
−0.956115 + 0.292990i \(0.905350\pi\)
\(138\) 0 0
\(139\) −16.1730 + 16.1730i −1.37177 + 1.37177i −0.513961 + 0.857814i \(0.671822\pi\)
−0.857814 + 0.513961i \(0.828178\pi\)
\(140\) 0 0
\(141\) 0.690998 + 0.690998i 0.0581925 + 0.0581925i
\(142\) 0 0
\(143\) −2.96879 −0.248262
\(144\) 0 0
\(145\) 22.5668 1.87407
\(146\) 0 0
\(147\) −1.48474 1.48474i −0.122459 0.122459i
\(148\) 0 0
\(149\) 15.2009 15.2009i 1.24530 1.24530i 0.287532 0.957771i \(-0.407165\pi\)
0.957771 0.287532i \(-0.0928347\pi\)
\(150\) 0 0
\(151\) 4.76306i 0.387612i −0.981040 0.193806i \(-0.937917\pi\)
0.981040 0.193806i \(-0.0620832\pi\)
\(152\) 0 0
\(153\) 2.59479i 0.209776i
\(154\) 0 0
\(155\) 10.4618 10.4618i 0.840314 0.840314i
\(156\) 0 0
\(157\) 11.7887 + 11.7887i 0.940844 + 0.940844i 0.998345 0.0575014i \(-0.0183134\pi\)
−0.0575014 + 0.998345i \(0.518313\pi\)
\(158\) 0 0
\(159\) 1.85068 0.146768
\(160\) 0 0
\(161\) −5.88497 −0.463800
\(162\) 0 0
\(163\) 9.68083 + 9.68083i 0.758261 + 0.758261i 0.976006 0.217745i \(-0.0698700\pi\)
−0.217745 + 0.976006i \(0.569870\pi\)
\(164\) 0 0
\(165\) −1.75249 + 1.75249i −0.136431 + 0.136431i
\(166\) 0 0
\(167\) 13.1916i 1.02079i −0.859939 0.510397i \(-0.829499\pi\)
0.859939 0.510397i \(-0.170501\pi\)
\(168\) 0 0
\(169\) 29.6497i 2.28075i
\(170\) 0 0
\(171\) 5.47988 5.47988i 0.419057 0.419057i
\(172\) 0 0
\(173\) −6.40858 6.40858i −0.487235 0.487235i 0.420198 0.907433i \(-0.361961\pi\)
−0.907433 + 0.420198i \(0.861961\pi\)
\(174\) 0 0
\(175\) 1.74168 0.131659
\(176\) 0 0
\(177\) 21.7420 1.63423
\(178\) 0 0
\(179\) 9.05982 + 9.05982i 0.677163 + 0.677163i 0.959357 0.282194i \(-0.0910623\pi\)
−0.282194 + 0.959357i \(0.591062\pi\)
\(180\) 0 0
\(181\) −13.7164 + 13.7164i −1.01953 + 1.01953i −0.0197290 + 0.999805i \(0.506280\pi\)
−0.999805 + 0.0197290i \(0.993720\pi\)
\(182\) 0 0
\(183\) 22.4866i 1.66226i
\(184\) 0 0
\(185\) 6.12766i 0.450515i
\(186\) 0 0
\(187\) −0.592009 + 0.592009i −0.0432920 + 0.0432920i
\(188\) 0 0
\(189\) 2.36237 + 2.36237i 0.171837 + 0.171837i
\(190\) 0 0
\(191\) 19.2622 1.39376 0.696882 0.717186i \(-0.254570\pi\)
0.696882 + 0.717186i \(0.254570\pi\)
\(192\) 0 0
\(193\) −2.38323 −0.171549 −0.0857744 0.996315i \(-0.527336\pi\)
−0.0857744 + 0.996315i \(0.527336\pi\)
\(194\) 0 0
\(195\) 25.1763 + 25.1763i 1.80291 + 1.80291i
\(196\) 0 0
\(197\) −6.16266 + 6.16266i −0.439072 + 0.439072i −0.891699 0.452628i \(-0.850487\pi\)
0.452628 + 0.891699i \(0.350487\pi\)
\(198\) 0 0
\(199\) 9.33136i 0.661483i 0.943721 + 0.330741i \(0.107299\pi\)
−0.943721 + 0.330741i \(0.892701\pi\)
\(200\) 0 0
\(201\) 18.3017i 1.29090i
\(202\) 0 0
\(203\) 6.14570 6.14570i 0.431344 0.431344i
\(204\) 0 0
\(205\) −19.7062 19.7062i −1.37634 1.37634i
\(206\) 0 0
\(207\) −8.29132 −0.576286
\(208\) 0 0
\(209\) −2.50050 −0.172963
\(210\) 0 0
\(211\) −19.3372 19.3372i −1.33123 1.33123i −0.904272 0.426957i \(-0.859586\pi\)
−0.426957 0.904272i \(-0.640414\pi\)
\(212\) 0 0
\(213\) 0.241318 0.241318i 0.0165348 0.0165348i
\(214\) 0 0
\(215\) 1.95755i 0.133504i
\(216\) 0 0
\(217\) 5.69821i 0.386819i
\(218\) 0 0
\(219\) 5.18350 5.18350i 0.350268 0.350268i
\(220\) 0 0
\(221\) 8.50483 + 8.50483i 0.572097 + 0.572097i
\(222\) 0 0
\(223\) −19.2604 −1.28977 −0.644886 0.764279i \(-0.723095\pi\)
−0.644886 + 0.764279i \(0.723095\pi\)
\(224\) 0 0
\(225\) 2.45385 0.163590
\(226\) 0 0
\(227\) −0.375264 0.375264i −0.0249071 0.0249071i 0.694544 0.719451i \(-0.255606\pi\)
−0.719451 + 0.694544i \(0.755606\pi\)
\(228\) 0 0
\(229\) 9.34559 9.34559i 0.617574 0.617574i −0.327334 0.944909i \(-0.606150\pi\)
0.944909 + 0.327334i \(0.106150\pi\)
\(230\) 0 0
\(231\) 0.954522i 0.0628029i
\(232\) 0 0
\(233\) 13.8761i 0.909055i 0.890733 + 0.454527i \(0.150192\pi\)
−0.890733 + 0.454527i \(0.849808\pi\)
\(234\) 0 0
\(235\) −0.854468 + 0.854468i −0.0557394 + 0.0557394i
\(236\) 0 0
\(237\) −12.3041 12.3041i −0.799235 0.799235i
\(238\) 0 0
\(239\) 15.2148 0.984165 0.492082 0.870549i \(-0.336236\pi\)
0.492082 + 0.870549i \(0.336236\pi\)
\(240\) 0 0
\(241\) −28.2964 −1.82273 −0.911364 0.411601i \(-0.864970\pi\)
−0.911364 + 0.411601i \(0.864970\pi\)
\(242\) 0 0
\(243\) 9.60387 + 9.60387i 0.616089 + 0.616089i
\(244\) 0 0
\(245\) 1.83598 1.83598i 0.117297 0.117297i
\(246\) 0 0
\(247\) 35.9223i 2.28568i
\(248\) 0 0
\(249\) 7.46154i 0.472856i
\(250\) 0 0
\(251\) −8.92064 + 8.92064i −0.563066 + 0.563066i −0.930177 0.367111i \(-0.880347\pi\)
0.367111 + 0.930177i \(0.380347\pi\)
\(252\) 0 0
\(253\) 1.89169 + 1.89169i 0.118929 + 0.118929i
\(254\) 0 0
\(255\) 10.0409 0.628784
\(256\) 0 0
\(257\) −27.4810 −1.71422 −0.857110 0.515133i \(-0.827742\pi\)
−0.857110 + 0.515133i \(0.827742\pi\)
\(258\) 0 0
\(259\) −1.66877 1.66877i −0.103692 0.103692i
\(260\) 0 0
\(261\) 8.65867 8.65867i 0.535958 0.535958i
\(262\) 0 0
\(263\) 14.9308i 0.920674i −0.887744 0.460337i \(-0.847729\pi\)
0.887744 0.460337i \(-0.152271\pi\)
\(264\) 0 0
\(265\) 2.28850i 0.140581i
\(266\) 0 0
\(267\) 2.37617 2.37617i 0.145419 0.145419i
\(268\) 0 0
\(269\) 0.00456307 + 0.00456307i 0.000278216 + 0.000278216i 0.707246 0.706968i \(-0.249937\pi\)
−0.706968 + 0.707246i \(0.749937\pi\)
\(270\) 0 0
\(271\) 5.74567 0.349025 0.174512 0.984655i \(-0.444165\pi\)
0.174512 + 0.984655i \(0.444165\pi\)
\(272\) 0 0
\(273\) 13.7127 0.829931
\(274\) 0 0
\(275\) −0.559854 0.559854i −0.0337604 0.0337604i
\(276\) 0 0
\(277\) −11.2885 + 11.2885i −0.678259 + 0.678259i −0.959606 0.281347i \(-0.909219\pi\)
0.281347 + 0.959606i \(0.409219\pi\)
\(278\) 0 0
\(279\) 8.02819i 0.480635i
\(280\) 0 0
\(281\) 9.71094i 0.579306i −0.957132 0.289653i \(-0.906460\pi\)
0.957132 0.289653i \(-0.0935399\pi\)
\(282\) 0 0
\(283\) −12.6539 + 12.6539i −0.752197 + 0.752197i −0.974889 0.222692i \(-0.928516\pi\)
0.222692 + 0.974889i \(0.428516\pi\)
\(284\) 0 0
\(285\) 21.2051 + 21.2051i 1.25608 + 1.25608i
\(286\) 0 0
\(287\) −10.7333 −0.633568
\(288\) 0 0
\(289\) −13.6081 −0.800475
\(290\) 0 0
\(291\) −13.1937 13.1937i −0.773428 0.773428i
\(292\) 0 0
\(293\) −0.906335 + 0.906335i −0.0529486 + 0.0529486i −0.733085 0.680137i \(-0.761920\pi\)
0.680137 + 0.733085i \(0.261920\pi\)
\(294\) 0 0
\(295\) 26.8856i 1.56534i
\(296\) 0 0
\(297\) 1.51874i 0.0881263i
\(298\) 0 0
\(299\) 27.1761 27.1761i 1.57163 1.57163i
\(300\) 0 0
\(301\) −0.533105 0.533105i −0.0307277 0.0307277i
\(302\) 0 0
\(303\) −29.1167 −1.67271
\(304\) 0 0
\(305\) −27.8063 −1.59218
\(306\) 0 0
\(307\) 14.7928 + 14.7928i 0.844268 + 0.844268i 0.989411 0.145143i \(-0.0463642\pi\)
−0.145143 + 0.989411i \(0.546364\pi\)
\(308\) 0 0
\(309\) 21.2668 21.2668i 1.20983 1.20983i
\(310\) 0 0
\(311\) 11.6043i 0.658022i −0.944326 0.329011i \(-0.893285\pi\)
0.944326 0.329011i \(-0.106715\pi\)
\(312\) 0 0
\(313\) 18.5621i 1.04919i −0.851351 0.524596i \(-0.824216\pi\)
0.851351 0.524596i \(-0.175784\pi\)
\(314\) 0 0
\(315\) 2.58672 2.58672i 0.145745 0.145745i
\(316\) 0 0
\(317\) 15.8863 + 15.8863i 0.892261 + 0.892261i 0.994736 0.102474i \(-0.0326760\pi\)
−0.102474 + 0.994736i \(0.532676\pi\)
\(318\) 0 0
\(319\) −3.95100 −0.221214
\(320\) 0 0
\(321\) −31.7719 −1.77333
\(322\) 0 0
\(323\) 7.16332 + 7.16332i 0.398578 + 0.398578i
\(324\) 0 0
\(325\) −8.04288 + 8.04288i −0.446139 + 0.446139i
\(326\) 0 0
\(327\) 21.9349i 1.21300i
\(328\) 0 0
\(329\) 0.465401i 0.0256584i
\(330\) 0 0
\(331\) 5.49646 5.49646i 0.302113 0.302113i −0.539727 0.841840i \(-0.681473\pi\)
0.841840 + 0.539727i \(0.181473\pi\)
\(332\) 0 0
\(333\) −2.35112 2.35112i −0.128841 0.128841i
\(334\) 0 0
\(335\) 22.6314 1.23648
\(336\) 0 0
\(337\) −2.73515 −0.148993 −0.0744966 0.997221i \(-0.523735\pi\)
−0.0744966 + 0.997221i \(0.523735\pi\)
\(338\) 0 0
\(339\) 11.9669 + 11.9669i 0.649954 + 0.649954i
\(340\) 0 0
\(341\) −1.83166 + 1.83166i −0.0991897 + 0.0991897i
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 0 0
\(345\) 32.0843i 1.72736i
\(346\) 0 0
\(347\) 25.0209 25.0209i 1.34319 1.34319i 0.450326 0.892864i \(-0.351308\pi\)
0.892864 0.450326i \(-0.148692\pi\)
\(348\) 0 0
\(349\) 8.72637 + 8.72637i 0.467112 + 0.467112i 0.900978 0.433866i \(-0.142851\pi\)
−0.433866 + 0.900978i \(0.642851\pi\)
\(350\) 0 0
\(351\) −21.8183 −1.16458
\(352\) 0 0
\(353\) −22.2643 −1.18501 −0.592504 0.805567i \(-0.701861\pi\)
−0.592504 + 0.805567i \(0.701861\pi\)
\(354\) 0 0
\(355\) 0.298407 + 0.298407i 0.0158378 + 0.0158378i
\(356\) 0 0
\(357\) 2.73447 2.73447i 0.144723 0.144723i
\(358\) 0 0
\(359\) 18.3142i 0.966588i 0.875458 + 0.483294i \(0.160560\pi\)
−0.875458 + 0.483294i \(0.839440\pi\)
\(360\) 0 0
\(361\) 11.2561i 0.592427i
\(362\) 0 0
\(363\) −16.0253 + 16.0253i −0.841110 + 0.841110i
\(364\) 0 0
\(365\) 6.40976 + 6.40976i 0.335502 + 0.335502i
\(366\) 0 0
\(367\) 19.3398 1.00953 0.504764 0.863257i \(-0.331580\pi\)
0.504764 + 0.863257i \(0.331580\pi\)
\(368\) 0 0
\(369\) −15.1222 −0.787228
\(370\) 0 0
\(371\) 0.623234 + 0.623234i 0.0323567 + 0.0323567i
\(372\) 0 0
\(373\) 5.63668 5.63668i 0.291856 0.291856i −0.545957 0.837813i \(-0.683834\pi\)
0.837813 + 0.545957i \(0.183834\pi\)
\(374\) 0 0
\(375\) 17.7641i 0.917333i
\(376\) 0 0
\(377\) 56.7603i 2.92330i
\(378\) 0 0
\(379\) 3.24191 3.24191i 0.166526 0.166526i −0.618925 0.785450i \(-0.712431\pi\)
0.785450 + 0.618925i \(0.212431\pi\)
\(380\) 0 0
\(381\) −0.545598 0.545598i −0.0279518 0.0279518i
\(382\) 0 0
\(383\) −5.39804 −0.275827 −0.137913 0.990444i \(-0.544040\pi\)
−0.137913 + 0.990444i \(0.544040\pi\)
\(384\) 0 0
\(385\) −1.18033 −0.0601554
\(386\) 0 0
\(387\) −0.751091 0.751091i −0.0381801 0.0381801i
\(388\) 0 0
\(389\) −15.6572 + 15.6572i −0.793854 + 0.793854i −0.982118 0.188264i \(-0.939714\pi\)
0.188264 + 0.982118i \(0.439714\pi\)
\(390\) 0 0
\(391\) 10.8384i 0.548123i
\(392\) 0 0
\(393\) 27.6414i 1.39432i
\(394\) 0 0
\(395\) 15.2149 15.2149i 0.765542 0.765542i
\(396\) 0 0
\(397\) −2.24563 2.24563i −0.112705 0.112705i 0.648505 0.761210i \(-0.275394\pi\)
−0.761210 + 0.648505i \(0.775394\pi\)
\(398\) 0 0
\(399\) 11.5497 0.578209
\(400\) 0 0
\(401\) 19.3307 0.965331 0.482665 0.875805i \(-0.339669\pi\)
0.482665 + 0.875805i \(0.339669\pi\)
\(402\) 0 0
\(403\) 26.3137 + 26.3137i 1.31078 + 1.31078i
\(404\) 0 0
\(405\) −20.6396 + 20.6396i −1.02559 + 1.02559i
\(406\) 0 0
\(407\) 1.07283i 0.0531783i
\(408\) 0 0
\(409\) 0.497591i 0.0246043i −0.999924 0.0123021i \(-0.996084\pi\)
0.999924 0.0123021i \(-0.00391599\pi\)
\(410\) 0 0
\(411\) −10.1834 + 10.1834i −0.502311 + 0.502311i
\(412\) 0 0
\(413\) 7.32184 + 7.32184i 0.360284 + 0.360284i
\(414\) 0 0
\(415\) 9.22673 0.452922
\(416\) 0 0
\(417\) −48.0253 −2.35181
\(418\) 0 0
\(419\) −3.51076 3.51076i −0.171512 0.171512i 0.616131 0.787643i \(-0.288699\pi\)
−0.787643 + 0.616131i \(0.788699\pi\)
\(420\) 0 0
\(421\) −1.35086 + 1.35086i −0.0658368 + 0.0658368i −0.739259 0.673422i \(-0.764824\pi\)
0.673422 + 0.739259i \(0.264824\pi\)
\(422\) 0 0
\(423\) 0.655702i 0.0318813i
\(424\) 0 0
\(425\) 3.20768i 0.155595i
\(426\) 0 0
\(427\) −7.57257 + 7.57257i −0.366463 + 0.366463i
\(428\) 0 0
\(429\) −4.40787 4.40787i −0.212814 0.212814i
\(430\) 0 0
\(431\) 19.6166 0.944896 0.472448 0.881358i \(-0.343370\pi\)
0.472448 + 0.881358i \(0.343370\pi\)
\(432\) 0 0
\(433\) −2.76217 −0.132741 −0.0663706 0.997795i \(-0.521142\pi\)
−0.0663706 + 0.997795i \(0.521142\pi\)
\(434\) 0 0
\(435\) 33.5058 + 33.5058i 1.60648 + 1.60648i
\(436\) 0 0
\(437\) 22.8895 22.8895i 1.09495 1.09495i
\(438\) 0 0
\(439\) 3.05296i 0.145710i 0.997343 + 0.0728550i \(0.0232110\pi\)
−0.997343 + 0.0728550i \(0.976789\pi\)
\(440\) 0 0
\(441\) 1.40890i 0.0670904i
\(442\) 0 0
\(443\) 1.37047 1.37047i 0.0651129 0.0651129i −0.673800 0.738913i \(-0.735339\pi\)
0.738913 + 0.673800i \(0.235339\pi\)
\(444\) 0 0
\(445\) 2.93831 + 2.93831i 0.139289 + 0.139289i
\(446\) 0 0
\(447\) 45.1386 2.13498
\(448\) 0 0
\(449\) 38.6173 1.82246 0.911232 0.411894i \(-0.135133\pi\)
0.911232 + 0.411894i \(0.135133\pi\)
\(450\) 0 0
\(451\) 3.45017 + 3.45017i 0.162462 + 0.162462i
\(452\) 0 0
\(453\) 7.07190 7.07190i 0.332267 0.332267i
\(454\) 0 0
\(455\) 16.9567i 0.794944i
\(456\) 0 0
\(457\) 36.0959i 1.68849i −0.535955 0.844247i \(-0.680048\pi\)
0.535955 0.844247i \(-0.319952\pi\)
\(458\) 0 0
\(459\) −4.35082 + 4.35082i −0.203079 + 0.203079i
\(460\) 0 0
\(461\) 4.29295 + 4.29295i 0.199943 + 0.199943i 0.799975 0.600033i \(-0.204846\pi\)
−0.600033 + 0.799975i \(0.704846\pi\)
\(462\) 0 0
\(463\) −3.38348 −0.157243 −0.0786217 0.996905i \(-0.525052\pi\)
−0.0786217 + 0.996905i \(0.525052\pi\)
\(464\) 0 0
\(465\) 31.0661 1.44066
\(466\) 0 0
\(467\) −21.7747 21.7747i −1.00761 1.00761i −0.999971 0.00764098i \(-0.997568\pi\)
−0.00764098 0.999971i \(-0.502432\pi\)
\(468\) 0 0
\(469\) 6.16327 6.16327i 0.284594 0.284594i
\(470\) 0 0
\(471\) 35.0064i 1.61301i
\(472\) 0 0
\(473\) 0.342727i 0.0157586i
\(474\) 0 0
\(475\) −6.77424 + 6.77424i −0.310823 + 0.310823i
\(476\) 0 0
\(477\) 0.878073 + 0.878073i 0.0402042 + 0.0402042i
\(478\) 0 0
\(479\) 6.74054 0.307983 0.153992 0.988072i \(-0.450787\pi\)
0.153992 + 0.988072i \(0.450787\pi\)
\(480\) 0 0
\(481\) 15.4123 0.702743
\(482\) 0 0
\(483\) −8.73764 8.73764i −0.397576 0.397576i
\(484\) 0 0
\(485\) 16.3149 16.3149i 0.740823 0.740823i
\(486\) 0 0
\(487\) 30.4472i 1.37970i 0.723954 + 0.689848i \(0.242323\pi\)
−0.723954 + 0.689848i \(0.757677\pi\)
\(488\) 0 0
\(489\) 28.7470i 1.29998i
\(490\) 0 0
\(491\) −11.1585 + 11.1585i −0.503578 + 0.503578i −0.912548 0.408970i \(-0.865888\pi\)
0.408970 + 0.912548i \(0.365888\pi\)
\(492\) 0 0
\(493\) 11.3186 + 11.3186i 0.509766 + 0.509766i
\(494\) 0 0
\(495\) −1.66297 −0.0747449
\(496\) 0 0
\(497\) 0.162532 0.00729057
\(498\) 0 0
\(499\) −17.4556 17.4556i −0.781420 0.781420i 0.198651 0.980070i \(-0.436344\pi\)
−0.980070 + 0.198651i \(0.936344\pi\)
\(500\) 0 0
\(501\) 19.5860 19.5860i 0.875039 0.875039i
\(502\) 0 0
\(503\) 26.7354i 1.19207i −0.802958 0.596035i \(-0.796742\pi\)
0.802958 0.596035i \(-0.203258\pi\)
\(504\) 0 0
\(505\) 36.0049i 1.60220i
\(506\) 0 0
\(507\) −44.0221 + 44.0221i −1.95509 + 1.95509i
\(508\) 0 0
\(509\) −13.7609 13.7609i −0.609942 0.609942i 0.332989 0.942931i \(-0.391943\pi\)
−0.942931 + 0.332989i \(0.891943\pi\)
\(510\) 0 0
\(511\) 3.49118 0.154441
\(512\) 0 0
\(513\) −18.3768 −0.811355
\(514\) 0 0
\(515\) 26.2979 + 26.2979i 1.15883 + 1.15883i
\(516\) 0 0
\(517\) 0.149600 0.149600i 0.00657942 0.00657942i
\(518\) 0 0
\(519\) 19.0301i 0.835330i
\(520\) 0 0
\(521\) 36.5859i 1.60286i 0.598091 + 0.801428i \(0.295926\pi\)
−0.598091 + 0.801428i \(0.704074\pi\)
\(522\) 0 0
\(523\) 4.02294 4.02294i 0.175911 0.175911i −0.613660 0.789571i \(-0.710303\pi\)
0.789571 + 0.613660i \(0.210303\pi\)
\(524\) 0 0
\(525\) 2.58594 + 2.58594i 0.112860 + 0.112860i
\(526\) 0 0
\(527\) 10.4945 0.457147
\(528\) 0 0
\(529\) −11.6328 −0.505776
\(530\) 0 0
\(531\) 10.3157 + 10.3157i 0.447664 + 0.447664i
\(532\) 0 0
\(533\) 49.5652 49.5652i 2.14691 2.14691i
\(534\) 0 0
\(535\) 39.2882i 1.69858i
\(536\) 0 0
\(537\) 26.9029i 1.16095i
\(538\) 0 0
\(539\) −0.321444 + 0.321444i −0.0138456 + 0.0138456i
\(540\) 0 0
\(541\) 17.9463 + 17.9463i 0.771572 + 0.771572i 0.978381 0.206809i \(-0.0663078\pi\)
−0.206809 + 0.978381i \(0.566308\pi\)
\(542\) 0 0
\(543\) −40.7306 −1.74792
\(544\) 0 0
\(545\) −27.1241 −1.16187
\(546\) 0 0
\(547\) −18.9329 18.9329i −0.809512 0.809512i 0.175048 0.984560i \(-0.443992\pi\)
−0.984560 + 0.175048i \(0.943992\pi\)
\(548\) 0 0
\(549\) −10.6690 + 10.6690i −0.455341 + 0.455341i
\(550\) 0 0
\(551\) 47.8072i 2.03665i
\(552\) 0 0
\(553\) 8.28703i 0.352400i
\(554\) 0 0
\(555\) 9.09798 9.09798i 0.386188 0.386188i
\(556\) 0 0
\(557\) −30.3516 30.3516i −1.28604 1.28604i −0.937173 0.348864i \(-0.886568\pi\)
−0.348864 0.937173i \(-0.613432\pi\)
\(558\) 0 0
\(559\) 4.92364 0.208248
\(560\) 0 0
\(561\) −1.75796 −0.0742210
\(562\) 0 0
\(563\) 18.2195 + 18.2195i 0.767858 + 0.767858i 0.977729 0.209871i \(-0.0673043\pi\)
−0.209871 + 0.977729i \(0.567304\pi\)
\(564\) 0 0
\(565\) −14.7980 + 14.7980i −0.622555 + 0.622555i
\(566\) 0 0
\(567\) 11.2417i 0.472107i
\(568\) 0 0
\(569\) 40.3261i 1.69056i 0.534325 + 0.845279i \(0.320566\pi\)
−0.534325 + 0.845279i \(0.679434\pi\)
\(570\) 0 0
\(571\) −18.1528 + 18.1528i −0.759672 + 0.759672i −0.976262 0.216591i \(-0.930506\pi\)
0.216591 + 0.976262i \(0.430506\pi\)
\(572\) 0 0
\(573\) 28.5993 + 28.5993i 1.19475 + 1.19475i
\(574\) 0 0
\(575\) 10.2497 0.427444
\(576\) 0 0
\(577\) 28.8535 1.20119 0.600594 0.799554i \(-0.294931\pi\)
0.600594 + 0.799554i \(0.294931\pi\)
\(578\) 0 0
\(579\) −3.53848 3.53848i −0.147054 0.147054i
\(580\) 0 0
\(581\) 2.51275 2.51275i 0.104246 0.104246i
\(582\) 0 0
\(583\) 0.400670i 0.0165941i
\(584\) 0 0
\(585\) 23.8903i 0.987743i
\(586\) 0 0
\(587\) −22.0073 + 22.0073i −0.908338 + 0.908338i −0.996138 0.0877997i \(-0.972016\pi\)
0.0877997 + 0.996138i \(0.472016\pi\)
\(588\) 0 0
\(589\) 22.1631 + 22.1631i 0.913213 + 0.913213i
\(590\) 0 0
\(591\) −18.2999 −0.752757
\(592\) 0 0
\(593\) 24.6606 1.01269 0.506344 0.862331i \(-0.330996\pi\)
0.506344 + 0.862331i \(0.330996\pi\)
\(594\) 0 0
\(595\) 3.38136 + 3.38136i 0.138622 + 0.138622i
\(596\) 0 0
\(597\) −13.8546 + 13.8546i −0.567033 + 0.567033i
\(598\) 0 0
\(599\) 10.8236i 0.442239i 0.975247 + 0.221120i \(0.0709711\pi\)
−0.975247 + 0.221120i \(0.929029\pi\)
\(600\) 0 0
\(601\) 16.6417i 0.678828i −0.940637 0.339414i \(-0.889771\pi\)
0.940637 0.339414i \(-0.110229\pi\)
\(602\) 0 0
\(603\) 8.68342 8.68342i 0.353616 0.353616i
\(604\) 0 0
\(605\) −19.8164 19.8164i −0.805652 0.805652i
\(606\) 0 0
\(607\) −22.3716 −0.908037 −0.454019 0.890992i \(-0.650010\pi\)
−0.454019 + 0.890992i \(0.650010\pi\)
\(608\) 0 0
\(609\) 18.2495 0.739508
\(610\) 0 0
\(611\) −2.14917 2.14917i −0.0869460 0.0869460i
\(612\) 0 0
\(613\) −32.7313 + 32.7313i −1.32201 + 1.32201i −0.409857 + 0.912150i \(0.634421\pi\)
−0.912150 + 0.409857i \(0.865579\pi\)
\(614\) 0 0
\(615\) 58.5172i 2.35964i
\(616\) 0 0
\(617\) 3.37531i 0.135885i 0.997689 + 0.0679424i \(0.0216434\pi\)
−0.997689 + 0.0679424i \(0.978357\pi\)
\(618\) 0 0
\(619\) −3.57465 + 3.57465i −0.143677 + 0.143677i −0.775287 0.631609i \(-0.782395\pi\)
0.631609 + 0.775287i \(0.282395\pi\)
\(620\) 0 0
\(621\) 13.9025 + 13.9025i 0.557887 + 0.557887i
\(622\) 0 0
\(623\) 1.60040 0.0641186
\(624\) 0 0
\(625\) 30.6750 1.22700
\(626\) 0 0
\(627\) −3.71259 3.71259i −0.148267 0.148267i
\(628\) 0 0
\(629\) 3.07340 3.07340i 0.122544 0.122544i
\(630\) 0 0
\(631\) 31.2089i 1.24241i 0.783649 + 0.621204i \(0.213356\pi\)
−0.783649 + 0.621204i \(0.786644\pi\)
\(632\) 0 0
\(633\) 57.4214i 2.28230i
\(634\) 0 0
\(635\) 0.674671 0.674671i 0.0267735 0.0267735i
\(636\) 0 0
\(637\) 4.61789 + 4.61789i 0.182967 + 0.182967i
\(638\) 0 0
\(639\) 0.228991 0.00905876
\(640\) 0 0
\(641\) 25.7829 1.01836 0.509182 0.860659i \(-0.329948\pi\)
0.509182 + 0.860659i \(0.329948\pi\)
\(642\) 0 0
\(643\) 1.82352 + 1.82352i 0.0719127 + 0.0719127i 0.742148 0.670236i \(-0.233807\pi\)
−0.670236 + 0.742148i \(0.733807\pi\)
\(644\) 0 0
\(645\) 2.90645 2.90645i 0.114441 0.114441i
\(646\) 0 0
\(647\) 10.0909i 0.396713i 0.980130 + 0.198356i \(0.0635603\pi\)
−0.980130 + 0.198356i \(0.936440\pi\)
\(648\) 0 0
\(649\) 4.70713i 0.184771i
\(650\) 0 0
\(651\) 8.46035 8.46035i 0.331587 0.331587i
\(652\) 0 0
\(653\) 13.8599 + 13.8599i 0.542380 + 0.542380i 0.924226 0.381846i \(-0.124712\pi\)
−0.381846 + 0.924226i \(0.624712\pi\)
\(654\) 0 0
\(655\) 34.1805 1.33554
\(656\) 0 0
\(657\) 4.91872 0.191898
\(658\) 0 0
\(659\) −13.9075 13.9075i −0.541758 0.541758i 0.382286 0.924044i \(-0.375137\pi\)
−0.924044 + 0.382286i \(0.875137\pi\)
\(660\) 0 0
\(661\) 1.13544 1.13544i 0.0441633 0.0441633i −0.684680 0.728844i \(-0.740058\pi\)
0.728844 + 0.684680i \(0.240058\pi\)
\(662\) 0 0
\(663\) 25.2549i 0.980820i
\(664\) 0 0
\(665\) 14.2821i 0.553834i
\(666\) 0 0
\(667\) 36.1673 36.1673i 1.40040 1.40040i
\(668\) 0 0
\(669\) −28.5967 28.5967i −1.10561 1.10561i
\(670\) 0 0
\(671\) 4.86832 0.187939
\(672\) 0 0
\(673\) 9.91726 0.382282 0.191141 0.981563i \(-0.438781\pi\)
0.191141 + 0.981563i \(0.438781\pi\)
\(674\) 0 0
\(675\) −4.11450 4.11450i −0.158367 0.158367i
\(676\) 0 0
\(677\) 16.4673 16.4673i 0.632890 0.632890i −0.315902 0.948792i \(-0.602307\pi\)
0.948792 + 0.315902i \(0.102307\pi\)
\(678\) 0 0
\(679\) 8.88621i 0.341021i
\(680\) 0 0
\(681\) 1.11434i 0.0427015i
\(682\) 0 0
\(683\) −5.51571 + 5.51571i −0.211053 + 0.211053i −0.804715 0.593662i \(-0.797682\pi\)
0.593662 + 0.804715i \(0.297682\pi\)
\(684\) 0 0
\(685\) −12.5925 12.5925i −0.481135 0.481135i
\(686\) 0 0
\(687\) 27.7515 1.05879
\(688\) 0 0
\(689\) −5.75605 −0.219288
\(690\) 0 0
\(691\) 31.1271 + 31.1271i 1.18413 + 1.18413i 0.978664 + 0.205468i \(0.0658717\pi\)
0.205468 + 0.978664i \(0.434128\pi\)
\(692\) 0 0
\(693\) −0.452882 + 0.452882i −0.0172036 + 0.0172036i
\(694\) 0 0
\(695\) 59.3867i 2.25267i
\(696\) 0 0
\(697\) 19.7677i 0.748756i
\(698\) 0 0
\(699\) −20.6024 + 20.6024i −0.779255 + 0.779255i
\(700\) 0 0
\(701\) −21.7631 21.7631i −0.821981 0.821981i 0.164411 0.986392i \(-0.447428\pi\)
−0.986392 + 0.164411i \(0.947428\pi\)
\(702\) 0 0
\(703\) 12.9813 0.489598
\(704\) 0 0
\(705\) −2.53732 −0.0955612
\(706\) 0 0
\(707\) −9.80533 9.80533i −0.368767 0.368767i
\(708\) 0 0
\(709\) 12.9756 12.9756i 0.487309 0.487309i −0.420147 0.907456i \(-0.638021\pi\)
0.907456 + 0.420147i \(0.138021\pi\)
\(710\) 0 0
\(711\) 11.6756i 0.437868i
\(712\) 0 0
\(713\) 33.5338i 1.25585i
\(714\) 0 0
\(715\) 5.45065 5.45065i 0.203843 0.203843i
\(716\) 0 0
\(717\) 22.5900 + 22.5900i 0.843640 + 0.843640i
\(718\) 0 0
\(719\) 36.4527 1.35946 0.679728 0.733464i \(-0.262098\pi\)
0.679728 + 0.733464i \(0.262098\pi\)
\(720\) 0 0
\(721\) 14.3236 0.533439
\(722\) 0 0
\(723\) −42.0127 42.0127i −1.56247 1.56247i
\(724\) 0 0
\(725\) −10.7039 + 10.7039i −0.397531 + 0.397531i
\(726\) 0 0
\(727\) 37.9281i 1.40668i −0.710855 0.703338i \(-0.751692\pi\)
0.710855 0.703338i \(-0.248308\pi\)
\(728\) 0 0
\(729\) 5.20661i 0.192838i
\(730\) 0 0
\(731\) 0.981829 0.981829i 0.0363143 0.0363143i
\(732\) 0 0
\(733\) −12.8899 12.8899i −0.476099 0.476099i 0.427782 0.903882i \(-0.359295\pi\)
−0.903882 + 0.427782i \(0.859295\pi\)
\(734\) 0 0
\(735\) 5.45192 0.201097
\(736\) 0 0
\(737\) −3.96230 −0.145953
\(738\) 0 0
\(739\) −7.97047 7.97047i −0.293199 0.293199i 0.545144 0.838342i \(-0.316475\pi\)
−0.838342 + 0.545144i \(0.816475\pi\)
\(740\) 0 0
\(741\) −53.3353 + 53.3353i −1.95932 + 1.95932i
\(742\) 0 0
\(743\) 41.0385i 1.50556i −0.658273 0.752779i \(-0.728713\pi\)
0.658273 0.752779i \(-0.271287\pi\)
\(744\) 0 0
\(745\) 55.8171i 2.04498i
\(746\) 0 0
\(747\) 3.54020 3.54020i 0.129529 0.129529i
\(748\) 0 0
\(749\) −10.6995 10.6995i −0.390951 0.390951i
\(750\) 0 0
\(751\) −16.8700 −0.615594 −0.307797 0.951452i \(-0.599592\pi\)
−0.307797 + 0.951452i \(0.599592\pi\)
\(752\) 0 0
\(753\) −26.4896 −0.965336
\(754\) 0 0
\(755\) 8.74490 + 8.74490i 0.318260 + 0.318260i
\(756\) 0 0
\(757\) −21.7021 + 21.7021i −0.788778 + 0.788778i −0.981294 0.192516i \(-0.938335\pi\)
0.192516 + 0.981294i \(0.438335\pi\)
\(758\) 0 0
\(759\) 5.61733i 0.203896i
\(760\) 0 0
\(761\) 8.35285i 0.302791i 0.988473 + 0.151395i \(0.0483766\pi\)
−0.988473 + 0.151395i \(0.951623\pi\)
\(762\) 0 0
\(763\) −7.38679 + 7.38679i −0.267420 + 0.267420i
\(764\) 0 0
\(765\) 4.76400 + 4.76400i 0.172243 + 0.172243i
\(766\) 0 0
\(767\) −67.6229 −2.44172
\(768\) 0 0
\(769\) −21.8388 −0.787527 −0.393764 0.919212i \(-0.628827\pi\)
−0.393764 + 0.919212i \(0.628827\pi\)
\(770\) 0 0
\(771\) −40.8022 40.8022i −1.46945 1.46945i
\(772\) 0 0
\(773\) 6.55450 6.55450i 0.235749 0.235749i −0.579338 0.815087i \(-0.696689\pi\)
0.815087 + 0.579338i \(0.196689\pi\)
\(774\) 0 0
\(775\) 9.92446i 0.356497i
\(776\) 0 0
\(777\) 4.95537i 0.177773i
\(778\) 0 0
\(779\) 41.7470 41.7470i 1.49574 1.49574i
\(780\) 0 0
\(781\) −0.0522451 0.0522451i −0.00186948 0.00186948i
\(782\) 0 0
\(783\) −29.0369 −1.03769
\(784\) 0 0
\(785\) −43.2879 −1.54501
\(786\) 0 0
\(787\) −17.8764 17.8764i −0.637224 0.637224i 0.312646 0.949870i \(-0.398785\pi\)
−0.949870 + 0.312646i \(0.898785\pi\)
\(788\) 0 0
\(789\) 22.1684 22.1684i 0.789215 0.789215i
\(790\) 0 0
\(791\) 8.05995i 0.286579i
\(792\) 0 0
\(793\) 69.9386i 2.48359i
\(794\) 0 0
\(795\) −3.39782 + 3.39782i −0.120508 + 0.120508i
\(796\) 0 0
\(797\) 15.9981 + 15.9981i 0.566683 + 0.566683i 0.931198 0.364515i \(-0.118765\pi\)
−0.364515 + 0.931198i \(0.618765\pi\)
\(798\) 0 0