Properties

Label 2352.2.q.bc.961.2
Level $2352$
Weight $2$
Character 2352.961
Analytic conductor $18.781$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2352.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.7808145554\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1176)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 961.2
Root \(0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 2352.961
Dual form 2352.2.q.bc.1537.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{3} +(1.70711 - 2.95680i) q^{5} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{3} +(1.70711 - 2.95680i) q^{5} +(-0.500000 + 0.866025i) q^{9} +(2.41421 + 4.18154i) q^{11} -1.41421 q^{13} -3.41421 q^{15} +(-3.12132 - 5.40629i) q^{17} +(-0.585786 + 1.01461i) q^{19} +(-0.414214 + 0.717439i) q^{23} +(-3.32843 - 5.76500i) q^{25} +1.00000 q^{27} -8.48528 q^{29} +(-5.41421 - 9.37769i) q^{31} +(2.41421 - 4.18154i) q^{33} +(4.82843 - 8.36308i) q^{37} +(0.707107 + 1.22474i) q^{39} +3.41421 q^{41} +8.00000 q^{43} +(1.70711 + 2.95680i) q^{45} +(-0.585786 + 1.01461i) q^{47} +(-3.12132 + 5.40629i) q^{51} +(-4.65685 - 8.06591i) q^{53} +16.4853 q^{55} +1.17157 q^{57} +(-5.41421 - 9.37769i) q^{59} +(-2.94975 + 5.10911i) q^{61} +(-2.41421 + 4.18154i) q^{65} +(-4.00000 - 6.92820i) q^{67} +0.828427 q^{69} -4.82843 q^{71} +(1.53553 + 2.65962i) q^{73} +(-3.32843 + 5.76500i) q^{75} +(-6.82843 + 11.8272i) q^{79} +(-0.500000 - 0.866025i) q^{81} -7.31371 q^{83} -21.3137 q^{85} +(4.24264 + 7.34847i) q^{87} +(7.36396 - 12.7548i) q^{89} +(-5.41421 + 9.37769i) q^{93} +(2.00000 + 3.46410i) q^{95} +16.2426 q^{97} -4.82843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{3} + 4q^{5} - 2q^{9} + O(q^{10}) \) \( 4q - 2q^{3} + 4q^{5} - 2q^{9} + 4q^{11} - 8q^{15} - 4q^{17} - 8q^{19} + 4q^{23} - 2q^{25} + 4q^{27} - 16q^{31} + 4q^{33} + 8q^{37} + 8q^{41} + 32q^{43} + 4q^{45} - 8q^{47} - 4q^{51} + 4q^{53} + 32q^{55} + 16q^{57} - 16q^{59} + 8q^{61} - 4q^{65} - 16q^{67} - 8q^{69} - 8q^{71} - 8q^{73} - 2q^{75} - 16q^{79} - 2q^{81} + 16q^{83} - 40q^{85} + 4q^{89} - 16q^{93} + 8q^{95} + 48q^{97} - 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1471\) \(1765\) \(2257\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) 0 0
\(5\) 1.70711 2.95680i 0.763441 1.32232i −0.177625 0.984098i \(-0.556842\pi\)
0.941067 0.338221i \(-0.109825\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) 2.41421 + 4.18154i 0.727913 + 1.26078i 0.957764 + 0.287556i \(0.0928428\pi\)
−0.229851 + 0.973226i \(0.573824\pi\)
\(12\) 0 0
\(13\) −1.41421 −0.392232 −0.196116 0.980581i \(-0.562833\pi\)
−0.196116 + 0.980581i \(0.562833\pi\)
\(14\) 0 0
\(15\) −3.41421 −0.881546
\(16\) 0 0
\(17\) −3.12132 5.40629i −0.757031 1.31122i −0.944358 0.328919i \(-0.893316\pi\)
0.187327 0.982298i \(-0.440018\pi\)
\(18\) 0 0
\(19\) −0.585786 + 1.01461i −0.134389 + 0.232768i −0.925364 0.379080i \(-0.876240\pi\)
0.790975 + 0.611848i \(0.209574\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −0.414214 + 0.717439i −0.0863695 + 0.149596i −0.905974 0.423333i \(-0.860860\pi\)
0.819604 + 0.572930i \(0.194193\pi\)
\(24\) 0 0
\(25\) −3.32843 5.76500i −0.665685 1.15300i
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −8.48528 −1.57568 −0.787839 0.615882i \(-0.788800\pi\)
−0.787839 + 0.615882i \(0.788800\pi\)
\(30\) 0 0
\(31\) −5.41421 9.37769i −0.972421 1.68428i −0.688194 0.725526i \(-0.741596\pi\)
−0.284227 0.958757i \(-0.591737\pi\)
\(32\) 0 0
\(33\) 2.41421 4.18154i 0.420261 0.727913i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 4.82843 8.36308i 0.793789 1.37488i −0.129817 0.991538i \(-0.541439\pi\)
0.923606 0.383344i \(-0.125228\pi\)
\(38\) 0 0
\(39\) 0.707107 + 1.22474i 0.113228 + 0.196116i
\(40\) 0 0
\(41\) 3.41421 0.533211 0.266605 0.963806i \(-0.414098\pi\)
0.266605 + 0.963806i \(0.414098\pi\)
\(42\) 0 0
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) 0 0
\(45\) 1.70711 + 2.95680i 0.254480 + 0.440773i
\(46\) 0 0
\(47\) −0.585786 + 1.01461i −0.0854457 + 0.147996i −0.905581 0.424173i \(-0.860565\pi\)
0.820135 + 0.572170i \(0.193898\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −3.12132 + 5.40629i −0.437072 + 0.757031i
\(52\) 0 0
\(53\) −4.65685 8.06591i −0.639668 1.10794i −0.985506 0.169643i \(-0.945738\pi\)
0.345837 0.938294i \(-0.387595\pi\)
\(54\) 0 0
\(55\) 16.4853 2.22287
\(56\) 0 0
\(57\) 1.17157 0.155179
\(58\) 0 0
\(59\) −5.41421 9.37769i −0.704871 1.22087i −0.966738 0.255768i \(-0.917672\pi\)
0.261868 0.965104i \(-0.415662\pi\)
\(60\) 0 0
\(61\) −2.94975 + 5.10911i −0.377676 + 0.654155i −0.990724 0.135891i \(-0.956610\pi\)
0.613047 + 0.790046i \(0.289944\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −2.41421 + 4.18154i −0.299446 + 0.518656i
\(66\) 0 0
\(67\) −4.00000 6.92820i −0.488678 0.846415i 0.511237 0.859440i \(-0.329187\pi\)
−0.999915 + 0.0130248i \(0.995854\pi\)
\(68\) 0 0
\(69\) 0.828427 0.0997309
\(70\) 0 0
\(71\) −4.82843 −0.573029 −0.286514 0.958076i \(-0.592497\pi\)
−0.286514 + 0.958076i \(0.592497\pi\)
\(72\) 0 0
\(73\) 1.53553 + 2.65962i 0.179721 + 0.311285i 0.941785 0.336216i \(-0.109147\pi\)
−0.762064 + 0.647501i \(0.775814\pi\)
\(74\) 0 0
\(75\) −3.32843 + 5.76500i −0.384334 + 0.665685i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −6.82843 + 11.8272i −0.768258 + 1.33066i 0.170249 + 0.985401i \(0.445543\pi\)
−0.938507 + 0.345261i \(0.887790\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) −7.31371 −0.802784 −0.401392 0.915906i \(-0.631473\pi\)
−0.401392 + 0.915906i \(0.631473\pi\)
\(84\) 0 0
\(85\) −21.3137 −2.31180
\(86\) 0 0
\(87\) 4.24264 + 7.34847i 0.454859 + 0.787839i
\(88\) 0 0
\(89\) 7.36396 12.7548i 0.780578 1.35200i −0.151027 0.988530i \(-0.548258\pi\)
0.931605 0.363472i \(-0.118409\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −5.41421 + 9.37769i −0.561428 + 0.972421i
\(94\) 0 0
\(95\) 2.00000 + 3.46410i 0.205196 + 0.355409i
\(96\) 0 0
\(97\) 16.2426 1.64919 0.824595 0.565723i \(-0.191403\pi\)
0.824595 + 0.565723i \(0.191403\pi\)
\(98\) 0 0
\(99\) −4.82843 −0.485275
\(100\) 0 0
\(101\) 0.292893 + 0.507306i 0.0291440 + 0.0504788i 0.880230 0.474548i \(-0.157389\pi\)
−0.851086 + 0.525027i \(0.824055\pi\)
\(102\) 0 0
\(103\) −2.58579 + 4.47871i −0.254785 + 0.441301i −0.964837 0.262848i \(-0.915338\pi\)
0.710052 + 0.704149i \(0.248671\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1.24264 + 2.15232i −0.120131 + 0.208072i −0.919819 0.392343i \(-0.871665\pi\)
0.799688 + 0.600415i \(0.204998\pi\)
\(108\) 0 0
\(109\) −5.65685 9.79796i −0.541828 0.938474i −0.998799 0.0489926i \(-0.984399\pi\)
0.456971 0.889482i \(-0.348934\pi\)
\(110\) 0 0
\(111\) −9.65685 −0.916588
\(112\) 0 0
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 0 0
\(115\) 1.41421 + 2.44949i 0.131876 + 0.228416i
\(116\) 0 0
\(117\) 0.707107 1.22474i 0.0653720 0.113228i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −6.15685 + 10.6640i −0.559714 + 0.969453i
\(122\) 0 0
\(123\) −1.70711 2.95680i −0.153925 0.266605i
\(124\) 0 0
\(125\) −5.65685 −0.505964
\(126\) 0 0
\(127\) −7.31371 −0.648987 −0.324493 0.945888i \(-0.605194\pi\)
−0.324493 + 0.945888i \(0.605194\pi\)
\(128\) 0 0
\(129\) −4.00000 6.92820i −0.352180 0.609994i
\(130\) 0 0
\(131\) −7.65685 + 13.2621i −0.668982 + 1.15871i 0.309207 + 0.950995i \(0.399937\pi\)
−0.978189 + 0.207717i \(0.933397\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 1.70711 2.95680i 0.146924 0.254480i
\(136\) 0 0
\(137\) 6.24264 + 10.8126i 0.533345 + 0.923780i 0.999242 + 0.0389412i \(0.0123985\pi\)
−0.465897 + 0.884839i \(0.654268\pi\)
\(138\) 0 0
\(139\) 9.65685 0.819084 0.409542 0.912291i \(-0.365689\pi\)
0.409542 + 0.912291i \(0.365689\pi\)
\(140\) 0 0
\(141\) 1.17157 0.0986642
\(142\) 0 0
\(143\) −3.41421 5.91359i −0.285511 0.494519i
\(144\) 0 0
\(145\) −14.4853 + 25.0892i −1.20294 + 2.08355i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 5.00000 8.66025i 0.409616 0.709476i −0.585231 0.810867i \(-0.698996\pi\)
0.994847 + 0.101391i \(0.0323294\pi\)
\(150\) 0 0
\(151\) −0.828427 1.43488i −0.0674164 0.116769i 0.830347 0.557247i \(-0.188142\pi\)
−0.897763 + 0.440478i \(0.854809\pi\)
\(152\) 0 0
\(153\) 6.24264 0.504688
\(154\) 0 0
\(155\) −36.9706 −2.96955
\(156\) 0 0
\(157\) 2.94975 + 5.10911i 0.235415 + 0.407752i 0.959393 0.282072i \(-0.0910216\pi\)
−0.723978 + 0.689823i \(0.757688\pi\)
\(158\) 0 0
\(159\) −4.65685 + 8.06591i −0.369313 + 0.639668i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −1.17157 + 2.02922i −0.0917647 + 0.158941i −0.908254 0.418420i \(-0.862584\pi\)
0.816489 + 0.577361i \(0.195917\pi\)
\(164\) 0 0
\(165\) −8.24264 14.2767i −0.641689 1.11144i
\(166\) 0 0
\(167\) 6.82843 0.528400 0.264200 0.964468i \(-0.414892\pi\)
0.264200 + 0.964468i \(0.414892\pi\)
\(168\) 0 0
\(169\) −11.0000 −0.846154
\(170\) 0 0
\(171\) −0.585786 1.01461i −0.0447962 0.0775893i
\(172\) 0 0
\(173\) −0.292893 + 0.507306i −0.0222683 + 0.0385698i −0.876945 0.480591i \(-0.840422\pi\)
0.854677 + 0.519161i \(0.173755\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −5.41421 + 9.37769i −0.406957 + 0.704871i
\(178\) 0 0
\(179\) −10.8995 18.8785i −0.814667 1.41104i −0.909567 0.415557i \(-0.863587\pi\)
0.0949006 0.995487i \(-0.469747\pi\)
\(180\) 0 0
\(181\) −9.89949 −0.735824 −0.367912 0.929861i \(-0.619927\pi\)
−0.367912 + 0.929861i \(0.619927\pi\)
\(182\) 0 0
\(183\) 5.89949 0.436103
\(184\) 0 0
\(185\) −16.4853 28.5533i −1.21202 2.09928i
\(186\) 0 0
\(187\) 15.0711 26.1039i 1.10211 1.90890i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 10.4142 18.0379i 0.753546 1.30518i −0.192548 0.981288i \(-0.561675\pi\)
0.946094 0.323892i \(-0.104992\pi\)
\(192\) 0 0
\(193\) 10.3137 + 17.8639i 0.742397 + 1.28587i 0.951401 + 0.307955i \(0.0996445\pi\)
−0.209004 + 0.977915i \(0.567022\pi\)
\(194\) 0 0
\(195\) 4.82843 0.345771
\(196\) 0 0
\(197\) 2.00000 0.142494 0.0712470 0.997459i \(-0.477302\pi\)
0.0712470 + 0.997459i \(0.477302\pi\)
\(198\) 0 0
\(199\) 2.82843 + 4.89898i 0.200502 + 0.347279i 0.948690 0.316207i \(-0.102409\pi\)
−0.748188 + 0.663486i \(0.769076\pi\)
\(200\) 0 0
\(201\) −4.00000 + 6.92820i −0.282138 + 0.488678i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 5.82843 10.0951i 0.407075 0.705075i
\(206\) 0 0
\(207\) −0.414214 0.717439i −0.0287898 0.0498655i
\(208\) 0 0
\(209\) −5.65685 −0.391293
\(210\) 0 0
\(211\) 25.6569 1.76629 0.883145 0.469099i \(-0.155421\pi\)
0.883145 + 0.469099i \(0.155421\pi\)
\(212\) 0 0
\(213\) 2.41421 + 4.18154i 0.165419 + 0.286514i
\(214\) 0 0
\(215\) 13.6569 23.6544i 0.931390 1.61321i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 1.53553 2.65962i 0.103762 0.179721i
\(220\) 0 0
\(221\) 4.41421 + 7.64564i 0.296932 + 0.514302i
\(222\) 0 0
\(223\) −2.34315 −0.156909 −0.0784543 0.996918i \(-0.524998\pi\)
−0.0784543 + 0.996918i \(0.524998\pi\)
\(224\) 0 0
\(225\) 6.65685 0.443790
\(226\) 0 0
\(227\) −9.89949 17.1464i −0.657053 1.13805i −0.981375 0.192102i \(-0.938470\pi\)
0.324322 0.945947i \(-0.394864\pi\)
\(228\) 0 0
\(229\) 0.464466 0.804479i 0.0306928 0.0531615i −0.850271 0.526345i \(-0.823562\pi\)
0.880964 + 0.473184i \(0.156895\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 5.75736 9.97204i 0.377177 0.653290i −0.613473 0.789716i \(-0.710228\pi\)
0.990650 + 0.136426i \(0.0435615\pi\)
\(234\) 0 0
\(235\) 2.00000 + 3.46410i 0.130466 + 0.225973i
\(236\) 0 0
\(237\) 13.6569 0.887108
\(238\) 0 0
\(239\) 8.82843 0.571063 0.285532 0.958369i \(-0.407830\pi\)
0.285532 + 0.958369i \(0.407830\pi\)
\(240\) 0 0
\(241\) −1.05025 1.81909i −0.0676527 0.117178i 0.830215 0.557443i \(-0.188218\pi\)
−0.897868 + 0.440265i \(0.854884\pi\)
\(242\) 0 0
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0.828427 1.43488i 0.0527116 0.0912991i
\(248\) 0 0
\(249\) 3.65685 + 6.33386i 0.231744 + 0.401392i
\(250\) 0 0
\(251\) −8.48528 −0.535586 −0.267793 0.963476i \(-0.586294\pi\)
−0.267793 + 0.963476i \(0.586294\pi\)
\(252\) 0 0
\(253\) −4.00000 −0.251478
\(254\) 0 0
\(255\) 10.6569 + 18.4582i 0.667358 + 1.15590i
\(256\) 0 0
\(257\) −10.8787 + 18.8424i −0.678593 + 1.17536i 0.296811 + 0.954936i \(0.404077\pi\)
−0.975405 + 0.220422i \(0.929257\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 4.24264 7.34847i 0.262613 0.454859i
\(262\) 0 0
\(263\) 9.58579 + 16.6031i 0.591085 + 1.02379i 0.994087 + 0.108590i \(0.0346335\pi\)
−0.403002 + 0.915199i \(0.632033\pi\)
\(264\) 0 0
\(265\) −31.7990 −1.95340
\(266\) 0 0
\(267\) −14.7279 −0.901334
\(268\) 0 0
\(269\) −9.02082 15.6245i −0.550009 0.952643i −0.998273 0.0587422i \(-0.981291\pi\)
0.448264 0.893901i \(-0.352042\pi\)
\(270\) 0 0
\(271\) 9.41421 16.3059i 0.571873 0.990513i −0.424501 0.905427i \(-0.639550\pi\)
0.996374 0.0850852i \(-0.0271162\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 16.0711 27.8359i 0.969122 1.67857i
\(276\) 0 0
\(277\) 3.00000 + 5.19615i 0.180253 + 0.312207i 0.941966 0.335707i \(-0.108975\pi\)
−0.761714 + 0.647913i \(0.775642\pi\)
\(278\) 0 0
\(279\) 10.8284 0.648281
\(280\) 0 0
\(281\) 4.48528 0.267569 0.133785 0.991010i \(-0.457287\pi\)
0.133785 + 0.991010i \(0.457287\pi\)
\(282\) 0 0
\(283\) 4.58579 + 7.94282i 0.272597 + 0.472151i 0.969526 0.244989i \(-0.0787842\pi\)
−0.696929 + 0.717140i \(0.745451\pi\)
\(284\) 0 0
\(285\) 2.00000 3.46410i 0.118470 0.205196i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −10.9853 + 19.0271i −0.646193 + 1.11924i
\(290\) 0 0
\(291\) −8.12132 14.0665i −0.476080 0.824595i
\(292\) 0 0
\(293\) 13.0711 0.763620 0.381810 0.924241i \(-0.375301\pi\)
0.381810 + 0.924241i \(0.375301\pi\)
\(294\) 0 0
\(295\) −36.9706 −2.15251
\(296\) 0 0
\(297\) 2.41421 + 4.18154i 0.140087 + 0.242638i
\(298\) 0 0
\(299\) 0.585786 1.01461i 0.0338769 0.0586765i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0.292893 0.507306i 0.0168263 0.0291440i
\(304\) 0 0
\(305\) 10.0711 + 17.4436i 0.576668 + 0.998818i
\(306\) 0 0
\(307\) −28.4853 −1.62574 −0.812870 0.582445i \(-0.802096\pi\)
−0.812870 + 0.582445i \(0.802096\pi\)
\(308\) 0 0
\(309\) 5.17157 0.294201
\(310\) 0 0
\(311\) −1.07107 1.85514i −0.0607347 0.105196i 0.834059 0.551675i \(-0.186011\pi\)
−0.894794 + 0.446479i \(0.852678\pi\)
\(312\) 0 0
\(313\) −7.29289 + 12.6317i −0.412219 + 0.713984i −0.995132 0.0985506i \(-0.968579\pi\)
0.582913 + 0.812534i \(0.301913\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0.656854 1.13770i 0.0368926 0.0638999i −0.846990 0.531610i \(-0.821587\pi\)
0.883882 + 0.467710i \(0.154921\pi\)
\(318\) 0 0
\(319\) −20.4853 35.4815i −1.14696 1.98659i
\(320\) 0 0
\(321\) 2.48528 0.138715
\(322\) 0 0
\(323\) 7.31371 0.406946
\(324\) 0 0
\(325\) 4.70711 + 8.15295i 0.261103 + 0.452244i
\(326\) 0 0
\(327\) −5.65685 + 9.79796i −0.312825 + 0.541828i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −15.6569 + 27.1185i −0.860579 + 1.49057i 0.0107928 + 0.999942i \(0.496564\pi\)
−0.871371 + 0.490624i \(0.836769\pi\)
\(332\) 0 0
\(333\) 4.82843 + 8.36308i 0.264596 + 0.458294i
\(334\) 0 0
\(335\) −27.3137 −1.49231
\(336\) 0 0
\(337\) 16.9706 0.924445 0.462223 0.886764i \(-0.347052\pi\)
0.462223 + 0.886764i \(0.347052\pi\)
\(338\) 0 0
\(339\) −3.00000 5.19615i −0.162938 0.282216i
\(340\) 0 0
\(341\) 26.1421 45.2795i 1.41568 2.45202i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 1.41421 2.44949i 0.0761387 0.131876i
\(346\) 0 0
\(347\) 12.0711 + 20.9077i 0.648009 + 1.12238i 0.983598 + 0.180376i \(0.0577314\pi\)
−0.335589 + 0.942009i \(0.608935\pi\)
\(348\) 0 0
\(349\) 6.38478 0.341769 0.170885 0.985291i \(-0.445337\pi\)
0.170885 + 0.985291i \(0.445337\pi\)
\(350\) 0 0
\(351\) −1.41421 −0.0754851
\(352\) 0 0
\(353\) 1.94975 + 3.37706i 0.103775 + 0.179743i 0.913237 0.407429i \(-0.133575\pi\)
−0.809462 + 0.587172i \(0.800241\pi\)
\(354\) 0 0
\(355\) −8.24264 + 14.2767i −0.437474 + 0.757727i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 7.72792 13.3852i 0.407864 0.706441i −0.586786 0.809742i \(-0.699607\pi\)
0.994650 + 0.103301i \(0.0329404\pi\)
\(360\) 0 0
\(361\) 8.81371 + 15.2658i 0.463879 + 0.803463i
\(362\) 0 0
\(363\) 12.3137 0.646302
\(364\) 0 0
\(365\) 10.4853 0.548825
\(366\) 0 0
\(367\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(368\) 0 0
\(369\) −1.70711 + 2.95680i −0.0888684 + 0.153925i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −18.6569 + 32.3146i −0.966015 + 1.67319i −0.259153 + 0.965836i \(0.583443\pi\)
−0.706862 + 0.707351i \(0.749890\pi\)
\(374\) 0 0
\(375\) 2.82843 + 4.89898i 0.146059 + 0.252982i
\(376\) 0 0
\(377\) 12.0000 0.618031
\(378\) 0 0
\(379\) 23.3137 1.19754 0.598772 0.800919i \(-0.295655\pi\)
0.598772 + 0.800919i \(0.295655\pi\)
\(380\) 0 0
\(381\) 3.65685 + 6.33386i 0.187346 + 0.324493i
\(382\) 0 0
\(383\) 4.48528 7.76874i 0.229187 0.396964i −0.728380 0.685173i \(-0.759727\pi\)
0.957567 + 0.288209i \(0.0930599\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −4.00000 + 6.92820i −0.203331 + 0.352180i
\(388\) 0 0
\(389\) −7.07107 12.2474i −0.358517 0.620970i 0.629196 0.777247i \(-0.283384\pi\)
−0.987713 + 0.156276i \(0.950051\pi\)
\(390\) 0 0
\(391\) 5.17157 0.261538
\(392\) 0 0
\(393\) 15.3137 0.772474
\(394\) 0 0
\(395\) 23.3137 + 40.3805i 1.17304 + 2.03176i
\(396\) 0 0
\(397\) 16.3640 28.3432i 0.821284 1.42251i −0.0834430 0.996513i \(-0.526592\pi\)
0.904727 0.425992i \(-0.140075\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −2.24264 + 3.88437i −0.111992 + 0.193976i −0.916573 0.399867i \(-0.869056\pi\)
0.804581 + 0.593843i \(0.202390\pi\)
\(402\) 0 0
\(403\) 7.65685 + 13.2621i 0.381415 + 0.660630i
\(404\) 0 0
\(405\) −3.41421 −0.169654
\(406\) 0 0
\(407\) 46.6274 2.31124
\(408\) 0 0
\(409\) 3.87868 + 6.71807i 0.191788 + 0.332187i 0.945843 0.324625i \(-0.105238\pi\)
−0.754055 + 0.656812i \(0.771905\pi\)
\(410\) 0 0
\(411\) 6.24264 10.8126i 0.307927 0.533345i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −12.4853 + 21.6251i −0.612878 + 1.06154i
\(416\) 0 0
\(417\) −4.82843 8.36308i −0.236449 0.409542i
\(418\) 0 0
\(419\) 5.17157 0.252648 0.126324 0.991989i \(-0.459682\pi\)
0.126324 + 0.991989i \(0.459682\pi\)
\(420\) 0 0
\(421\) 29.3137 1.42866 0.714331 0.699808i \(-0.246731\pi\)
0.714331 + 0.699808i \(0.246731\pi\)
\(422\) 0 0
\(423\) −0.585786 1.01461i −0.0284819 0.0493321i
\(424\) 0 0
\(425\) −20.7782 + 35.9889i −1.00789 + 1.74572i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −3.41421 + 5.91359i −0.164840 + 0.285511i
\(430\) 0 0
\(431\) −6.75736 11.7041i −0.325491 0.563766i 0.656121 0.754656i \(-0.272196\pi\)
−0.981612 + 0.190890i \(0.938863\pi\)
\(432\) 0 0
\(433\) 10.3848 0.499061 0.249530 0.968367i \(-0.419724\pi\)
0.249530 + 0.968367i \(0.419724\pi\)
\(434\) 0 0
\(435\) 28.9706 1.38903
\(436\) 0 0
\(437\) −0.485281 0.840532i −0.0232142 0.0402081i
\(438\) 0 0
\(439\) −9.65685 + 16.7262i −0.460897 + 0.798296i −0.999006 0.0445789i \(-0.985805\pi\)
0.538109 + 0.842875i \(0.319139\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 10.7574 18.6323i 0.511098 0.885247i −0.488820 0.872385i \(-0.662572\pi\)
0.999917 0.0128621i \(-0.00409425\pi\)
\(444\) 0 0
\(445\) −25.1421 43.5475i −1.19185 2.06435i
\(446\) 0 0
\(447\) −10.0000 −0.472984
\(448\) 0 0
\(449\) −10.0000 −0.471929 −0.235965 0.971762i \(-0.575825\pi\)
−0.235965 + 0.971762i \(0.575825\pi\)
\(450\) 0 0
\(451\) 8.24264 + 14.2767i 0.388131 + 0.672262i
\(452\) 0 0
\(453\) −0.828427 + 1.43488i −0.0389229 + 0.0674164i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 12.3137 21.3280i 0.576011 0.997680i −0.419920 0.907561i \(-0.637942\pi\)
0.995931 0.0901192i \(-0.0287248\pi\)
\(458\) 0 0
\(459\) −3.12132 5.40629i −0.145691 0.252344i
\(460\) 0 0
\(461\) −9.75736 −0.454446 −0.227223 0.973843i \(-0.572965\pi\)
−0.227223 + 0.973843i \(0.572965\pi\)
\(462\) 0 0
\(463\) 12.9706 0.602793 0.301397 0.953499i \(-0.402547\pi\)
0.301397 + 0.953499i \(0.402547\pi\)
\(464\) 0 0
\(465\) 18.4853 + 32.0174i 0.857234 + 1.48477i
\(466\) 0 0
\(467\) 2.58579 4.47871i 0.119656 0.207250i −0.799975 0.600033i \(-0.795154\pi\)
0.919631 + 0.392783i \(0.128488\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 2.94975 5.10911i 0.135917 0.235415i
\(472\) 0 0
\(473\) 19.3137 + 33.4523i 0.888045 + 1.53814i
\(474\) 0 0
\(475\) 7.79899 0.357842
\(476\) 0 0
\(477\) 9.31371 0.426445
\(478\) 0 0
\(479\) −9.55635 16.5521i −0.436641 0.756284i 0.560787 0.827960i \(-0.310499\pi\)
−0.997428 + 0.0716760i \(0.977165\pi\)
\(480\) 0 0
\(481\) −6.82843 + 11.8272i −0.311349 + 0.539273i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 27.7279 48.0262i 1.25906 2.18076i
\(486\) 0 0
\(487\) 6.48528 + 11.2328i 0.293876 + 0.509008i 0.974723 0.223418i \(-0.0717213\pi\)
−0.680847 + 0.732426i \(0.738388\pi\)
\(488\) 0 0
\(489\) 2.34315 0.105961
\(490\) 0 0
\(491\) 4.14214 0.186932 0.0934660 0.995622i \(-0.470205\pi\)
0.0934660 + 0.995622i \(0.470205\pi\)
\(492\) 0 0
\(493\) 26.4853 + 45.8739i 1.19284 + 2.06605i
\(494\) 0 0
\(495\) −8.24264 + 14.2767i −0.370479 + 0.641689i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 14.1421 24.4949i 0.633089 1.09654i −0.353828 0.935311i \(-0.615120\pi\)
0.986917 0.161232i \(-0.0515466\pi\)
\(500\) 0 0
\(501\) −3.41421 5.91359i −0.152536 0.264200i
\(502\) 0 0
\(503\) 30.6274 1.36561 0.682805 0.730601i \(-0.260760\pi\)
0.682805 + 0.730601i \(0.260760\pi\)
\(504\) 0 0
\(505\) 2.00000 0.0889988
\(506\) 0 0
\(507\) 5.50000 + 9.52628i 0.244264 + 0.423077i
\(508\) 0 0
\(509\) 11.4645 19.8570i 0.508154 0.880148i −0.491802 0.870707i \(-0.663662\pi\)
0.999955 0.00944061i \(-0.00300508\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −0.585786 + 1.01461i −0.0258631 + 0.0447962i
\(514\) 0 0
\(515\) 8.82843 + 15.2913i 0.389027 + 0.673814i
\(516\) 0 0
\(517\) −5.65685 −0.248788
\(518\) 0 0
\(519\) 0.585786 0.0257132
\(520\) 0 0
\(521\) 2.63604 + 4.56575i 0.115487 + 0.200029i 0.917974 0.396640i \(-0.129824\pi\)
−0.802487 + 0.596669i \(0.796490\pi\)
\(522\) 0 0
\(523\) 0.828427 1.43488i 0.0362246 0.0627428i −0.847345 0.531043i \(-0.821800\pi\)
0.883569 + 0.468300i \(0.155133\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −33.7990 + 58.5416i −1.47231 + 2.55011i
\(528\) 0 0
\(529\) 11.1569 + 19.3242i 0.485081 + 0.840184i
\(530\) 0 0
\(531\) 10.8284 0.469914
\(532\) 0 0
\(533\) −4.82843 −0.209142
\(534\) 0 0
\(535\) 4.24264 + 7.34847i 0.183425 + 0.317702i
\(536\) 0 0
\(537\) −10.8995 + 18.8785i −0.470348 + 0.814667i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 4.31371 7.47156i 0.185461 0.321228i −0.758271 0.651940i \(-0.773956\pi\)
0.943732 + 0.330712i \(0.107289\pi\)
\(542\) 0 0
\(543\) 4.94975 + 8.57321i 0.212414 + 0.367912i
\(544\) 0 0
\(545\) −38.6274 −1.65462
\(546\) 0 0
\(547\) 4.97056 0.212526 0.106263 0.994338i \(-0.466111\pi\)
0.106263 + 0.994338i \(0.466111\pi\)
\(548\) 0 0
\(549\) −2.94975 5.10911i −0.125892 0.218052i
\(550\) 0 0
\(551\) 4.97056 8.60927i 0.211753 0.366767i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −16.4853 + 28.5533i −0.699761 + 1.21202i
\(556\) 0 0
\(557\) −21.9706 38.0541i −0.930923 1.61241i −0.781748 0.623594i \(-0.785672\pi\)
−0.149175 0.988811i \(-0.547662\pi\)
\(558\) 0 0
\(559\) −11.3137 −0.478519
\(560\) 0 0
\(561\) −30.1421 −1.27260
\(562\) 0 0
\(563\) −13.4142 23.2341i −0.565342 0.979201i −0.997018 0.0771719i \(-0.975411\pi\)
0.431676 0.902029i \(-0.357922\pi\)
\(564\) 0 0
\(565\) 10.2426 17.7408i 0.430911 0.746360i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −3.41421 + 5.91359i −0.143131 + 0.247911i −0.928674 0.370897i \(-0.879050\pi\)
0.785543 + 0.618807i \(0.212384\pi\)
\(570\) 0 0
\(571\) 20.1421 + 34.8872i 0.842922 + 1.45998i 0.887414 + 0.460974i \(0.152500\pi\)
−0.0444914 + 0.999010i \(0.514167\pi\)
\(572\) 0 0
\(573\) −20.8284 −0.870120
\(574\) 0 0
\(575\) 5.51472 0.229980
\(576\) 0 0
\(577\) −4.70711 8.15295i −0.195959 0.339412i 0.751255 0.660012i \(-0.229449\pi\)
−0.947215 + 0.320600i \(0.896115\pi\)
\(578\) 0 0
\(579\) 10.3137 17.8639i 0.428623 0.742397i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 22.4853 38.9456i 0.931245 1.61296i
\(584\) 0 0
\(585\) −2.41421 4.18154i −0.0998154 0.172885i
\(586\) 0 0
\(587\) −26.8284 −1.10733 −0.553664 0.832740i \(-0.686771\pi\)
−0.553664 + 0.832740i \(0.686771\pi\)
\(588\) 0 0
\(589\) 12.6863 0.522730
\(590\) 0 0
\(591\) −1.00000 1.73205i −0.0411345 0.0712470i
\(592\) 0 0
\(593\) 14.5355 25.1763i 0.596903 1.03387i −0.396372 0.918090i \(-0.629731\pi\)
0.993275 0.115776i \(-0.0369356\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 2.82843 4.89898i 0.115760 0.200502i
\(598\) 0 0
\(599\) 8.07107 + 13.9795i 0.329775 + 0.571187i 0.982467 0.186436i \(-0.0596938\pi\)
−0.652692 + 0.757623i \(0.726360\pi\)
\(600\) 0 0
\(601\) 12.2426 0.499388 0.249694 0.968325i \(-0.419670\pi\)
0.249694 + 0.968325i \(0.419670\pi\)
\(602\) 0 0
\(603\) 8.00000 0.325785
\(604\) 0 0
\(605\) 21.0208 + 36.4091i 0.854618 + 1.48024i
\(606\) 0 0
\(607\) −15.7990 + 27.3647i −0.641261 + 1.11070i 0.343890 + 0.939010i \(0.388255\pi\)
−0.985152 + 0.171687i \(0.945078\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0.828427 1.43488i 0.0335146 0.0580489i
\(612\) 0 0
\(613\) 1.17157 + 2.02922i 0.0473194 + 0.0819596i 0.888715 0.458460i \(-0.151599\pi\)
−0.841396 + 0.540420i \(0.818265\pi\)
\(614\) 0 0
\(615\) −11.6569 −0.470050
\(616\) 0 0
\(617\) 21.4558 0.863780 0.431890 0.901926i \(-0.357847\pi\)
0.431890 + 0.901926i \(0.357847\pi\)
\(618\) 0 0
\(619\) 20.1421 + 34.8872i 0.809581 + 1.40224i 0.913155 + 0.407613i \(0.133639\pi\)
−0.103574 + 0.994622i \(0.533028\pi\)
\(620\) 0 0
\(621\) −0.414214 + 0.717439i −0.0166218 + 0.0287898i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 6.98528 12.0989i 0.279411 0.483954i
\(626\) 0 0
\(627\) 2.82843 + 4.89898i 0.112956 + 0.195646i
\(628\) 0 0
\(629\) −60.2843 −2.40369
\(630\) 0 0
\(631\) 8.28427 0.329792 0.164896 0.986311i \(-0.447271\pi\)
0.164896 + 0.986311i \(0.447271\pi\)
\(632\) 0 0
\(633\) −12.8284 22.2195i −0.509884 0.883145i
\(634\) 0 0
\(635\) −12.4853 + 21.6251i −0.495463 + 0.858168i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 2.41421 4.18154i 0.0955048 0.165419i
\(640\) 0 0
\(641\) −12.5858 21.7992i −0.497109 0.861017i 0.502886 0.864353i \(-0.332272\pi\)
−0.999994 + 0.00333540i \(0.998938\pi\)
\(642\) 0 0
\(643\) 19.5147 0.769585 0.384793 0.923003i \(-0.374273\pi\)
0.384793 + 0.923003i \(0.374273\pi\)
\(644\) 0 0
\(645\) −27.3137 −1.07548
\(646\) 0 0
\(647\) −7.41421 12.8418i −0.291483 0.504863i 0.682678 0.730720i \(-0.260815\pi\)
−0.974161 + 0.225857i \(0.927482\pi\)
\(648\) 0 0
\(649\) 26.1421 45.2795i 1.02617 1.77738i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −1.41421 + 2.44949i −0.0553425 + 0.0958559i −0.892369 0.451306i \(-0.850958\pi\)
0.837027 + 0.547162i \(0.184292\pi\)
\(654\) 0 0
\(655\) 26.1421 + 45.2795i 1.02146 + 1.76922i
\(656\) 0 0
\(657\) −3.07107 −0.119814
\(658\) 0 0
\(659\) −25.5147 −0.993912 −0.496956 0.867776i \(-0.665549\pi\)
−0.496956 + 0.867776i \(0.665549\pi\)
\(660\) 0 0
\(661\) −11.6777 20.2263i −0.454209 0.786713i 0.544434 0.838804i \(-0.316745\pi\)
−0.998642 + 0.0520914i \(0.983411\pi\)
\(662\) 0 0
\(663\) 4.41421 7.64564i 0.171434 0.296932i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 3.51472 6.08767i 0.136090 0.235716i
\(668\) 0 0
\(669\) 1.17157 + 2.02922i 0.0452956 + 0.0784543i
\(670\) 0 0
\(671\) −28.4853 −1.09966
\(672\) 0 0
\(673\) 15.3137 0.590300 0.295150 0.955451i \(-0.404630\pi\)
0.295150 + 0.955451i \(0.404630\pi\)
\(674\) 0 0
\(675\) −3.32843 5.76500i −0.128111 0.221895i
\(676\) 0 0
\(677\) −0.778175 + 1.34784i −0.0299077 + 0.0518016i −0.880592 0.473876i \(-0.842855\pi\)
0.850684 + 0.525677i \(0.176188\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −9.89949 + 17.1464i −0.379349 + 0.657053i
\(682\) 0 0
\(683\) 6.07107 + 10.5154i 0.232303 + 0.402361i 0.958485 0.285141i \(-0.0920406\pi\)
−0.726182 + 0.687502i \(0.758707\pi\)
\(684\) 0 0
\(685\) 42.6274 1.62871
\(686\) 0 0
\(687\) −0.928932 −0.0354410
\(688\) 0 0
\(689\) 6.58579 + 11.4069i 0.250898 + 0.434569i
\(690\) 0 0
\(691\) −14.0000 + 24.2487i −0.532585 + 0.922464i 0.466691 + 0.884420i \(0.345446\pi\)
−0.999276 + 0.0380440i \(0.987887\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 16.4853 28.5533i 0.625322 1.08309i
\(696\) 0 0
\(697\) −10.6569 18.4582i −0.403657 0.699155i
\(698\) 0 0
\(699\) −11.5147 −0.435527
\(700\) 0 0
\(701\) −10.8284 −0.408984 −0.204492 0.978868i \(-0.565554\pi\)
−0.204492 + 0.978868i \(0.565554\pi\)
\(702\) 0 0
\(703\) 5.65685 + 9.79796i 0.213352 + 0.369537i
\(704\) 0 0
\(705\) 2.00000 3.46410i 0.0753244 0.130466i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 4.00000 6.92820i 0.150223 0.260194i −0.781086 0.624423i \(-0.785334\pi\)
0.931309 + 0.364229i \(0.118667\pi\)
\(710\) 0 0
\(711\) −6.82843 11.8272i −0.256086 0.443554i
\(712\) 0 0
\(713\) 8.97056 0.335950
\(714\) 0 0
\(715\) −23.3137 −0.871883
\(716\) 0 0
\(717\) −4.41421 7.64564i −0.164852 0.285532i
\(718\) 0 0
\(719\) 13.6569 23.6544i 0.509315 0.882159i −0.490627 0.871370i \(-0.663232\pi\)
0.999942 0.0107893i \(-0.00343441\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −1.05025 + 1.81909i −0.0390593 + 0.0676527i
\(724\) 0 0
\(725\) 28.2426 + 48.9177i 1.04891 + 1.81676i
\(726\) 0 0
\(727\) −25.4558 −0.944105 −0.472052 0.881570i \(-0.656487\pi\)
−0.472052 + 0.881570i \(0.656487\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −24.9706 43.2503i −0.923570 1.59967i
\(732\) 0 0
\(733\) 10.1213 17.5306i 0.373839 0.647509i −0.616313 0.787501i \(-0.711374\pi\)
0.990153 + 0.139992i \(0.0447078\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 19.3137 33.4523i 0.711430 1.23223i
\(738\) 0 0
\(739\) −18.1421 31.4231i −0.667369 1.15592i −0.978637 0.205595i \(-0.934087\pi\)
0.311268 0.950322i \(-0.399246\pi\)
\(740\) 0 0
\(741\) −1.65685 −0.0608661
\(742\) 0 0
\(743\) 16.8284 0.617375 0.308688 0.951163i \(-0.400110\pi\)
0.308688 + 0.951163i \(0.400110\pi\)
\(744\) 0 0
\(745\) −17.0711 29.5680i −0.625436 1.08329i
\(746\) 0 0
\(747\) 3.65685 6.33386i 0.133797 0.231744i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 9.17157 15.8856i 0.334675 0.579675i −0.648747 0.761004i \(-0.724707\pi\)
0.983422 + 0.181329i \(0.0580400\pi\)
\(752\) 0 0
\(753\) 4.24264 + 7.34847i 0.154610 + 0.267793i
\(754\) 0 0
\(755\) −5.65685 −0.205874
\(756\) 0 0
\(757\) 11.3137 0.411204 0.205602 0.978636i \(-0.434085\pi\)
0.205602 + 0.978636i \(0.434085\pi\)
\(758\) 0 0
\(759\) 2.00000 + 3.46410i 0.0725954 + 0.125739i
\(760\) 0 0
\(761\) −9.12132 + 15.7986i −0.330648 + 0.572698i −0.982639 0.185528i \(-0.940600\pi\)
0.651991 + 0.758226i \(0.273934\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 10.6569 18.4582i 0.385299 0.667358i
\(766\) 0 0
\(767\) 7.65685 + 13.2621i 0.276473 + 0.478865i
\(768\) 0 0
\(769\) −0.928932 −0.0334982 −0.0167491 0.999860i \(-0.505332\pi\)
−0.0167491 + 0.999860i \(0.505332\pi\)
\(770\) 0 0
\(771\) 21.7574 0.783572
\(772\) 0 0
\(773\) −0.292893 0.507306i −0.0105346 0.0182465i 0.860710 0.509096i \(-0.170020\pi\)
−0.871245 + 0.490849i \(0.836687\pi\)
\(774\) 0 0
\(775\) −36.0416 + 62.4259i −1.29465 + 2.24241i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −2.00000 + 3.46410i −0.0716574 + 0.124114i
\(780\) 0 0
\(781\) −11.6569 20.1903i −0.417115 0.722464i
\(782\) 0 0
\(783\) −8.48528 −0.303239
\(784\) 0 0
\(785\) 20.1421 0.718904
\(786\) 0 0
\(787\) −17.3137 29.9882i −0.617167 1.06896i −0.990000 0.141066i \(-0.954947\pi\)
0.372833 0.927898i \(-0.378386\pi\)
\(788\) 0 0
\(789\) 9.58579 16.6031i 0.341263 0.591085i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 4.17157 7.22538i 0.148137 0.256581i
\(794\) 0 0
\(795\) 15.8995 + 27.5387i 0.563897 + 0.976698i
\(796\) 0 0
\(797\) 0.786797 0.0278698 0.0139349 0.999903i \(-0.495564\pi\)
0.0139349 + 0.999903i \(0.495564\pi\)
\(798\) 0 0
\(799\) 7.31371 0.258740
\(800\) 0