Properties

Label 1050.2.b.b.251.4
Level $1050$
Weight $2$
Character 1050.251
Analytic conductor $8.384$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1050.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.38429221223\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{6})\)
Defining polynomial: \(x^{4} + 9\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 251.4
Root \(1.22474 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 1050.251
Dual form 1050.2.b.b.251.2

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +(1.22474 + 1.22474i) q^{3} -1.00000 q^{4} +(-1.22474 + 1.22474i) q^{6} +(1.00000 - 2.44949i) q^{7} -1.00000i q^{8} +3.00000i q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(1.22474 + 1.22474i) q^{3} -1.00000 q^{4} +(-1.22474 + 1.22474i) q^{6} +(1.00000 - 2.44949i) q^{7} -1.00000i q^{8} +3.00000i q^{9} +(-1.22474 - 1.22474i) q^{12} +2.44949i q^{13} +(2.44949 + 1.00000i) q^{14} +1.00000 q^{16} +4.89898 q^{17} -3.00000 q^{18} +2.44949i q^{19} +(4.22474 - 1.77526i) q^{21} +6.00000i q^{23} +(1.22474 - 1.22474i) q^{24} -2.44949 q^{26} +(-3.67423 + 3.67423i) q^{27} +(-1.00000 + 2.44949i) q^{28} +6.00000i q^{29} +1.00000i q^{32} +4.89898i q^{34} -3.00000i q^{36} +2.00000 q^{37} -2.44949 q^{38} +(-3.00000 + 3.00000i) q^{39} +4.89898 q^{41} +(1.77526 + 4.22474i) q^{42} -4.00000 q^{43} -6.00000 q^{46} +4.89898 q^{47} +(1.22474 + 1.22474i) q^{48} +(-5.00000 - 4.89898i) q^{49} +(6.00000 + 6.00000i) q^{51} -2.44949i q^{52} +6.00000i q^{53} +(-3.67423 - 3.67423i) q^{54} +(-2.44949 - 1.00000i) q^{56} +(-3.00000 + 3.00000i) q^{57} -6.00000 q^{58} +12.2474 q^{59} -12.2474i q^{61} +(7.34847 + 3.00000i) q^{63} -1.00000 q^{64} -8.00000 q^{67} -4.89898 q^{68} +(-7.34847 + 7.34847i) q^{69} +3.00000 q^{72} -9.79796i q^{73} +2.00000i q^{74} -2.44949i q^{76} +(-3.00000 - 3.00000i) q^{78} -10.0000 q^{79} -9.00000 q^{81} +4.89898i q^{82} +2.44949 q^{83} +(-4.22474 + 1.77526i) q^{84} -4.00000i q^{86} +(-7.34847 + 7.34847i) q^{87} +(6.00000 + 2.44949i) q^{91} -6.00000i q^{92} +4.89898i q^{94} +(-1.22474 + 1.22474i) q^{96} -4.89898i q^{97} +(4.89898 - 5.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{4} + 4q^{7} + O(q^{10}) \) \( 4q - 4q^{4} + 4q^{7} + 4q^{16} - 12q^{18} + 12q^{21} - 4q^{28} + 8q^{37} - 12q^{39} + 12q^{42} - 16q^{43} - 24q^{46} - 20q^{49} + 24q^{51} - 12q^{57} - 24q^{58} - 4q^{64} - 32q^{67} + 12q^{72} - 12q^{78} - 40q^{79} - 36q^{81} - 12q^{84} + 24q^{91} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 1.22474 + 1.22474i 0.707107 + 0.707107i
\(4\) −1.00000 −0.500000
\(5\) 0 0
\(6\) −1.22474 + 1.22474i −0.500000 + 0.500000i
\(7\) 1.00000 2.44949i 0.377964 0.925820i
\(8\) 1.00000i 0.353553i
\(9\) 3.00000i 1.00000i
\(10\) 0 0
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) −1.22474 1.22474i −0.353553 0.353553i
\(13\) 2.44949i 0.679366i 0.940540 + 0.339683i \(0.110320\pi\)
−0.940540 + 0.339683i \(0.889680\pi\)
\(14\) 2.44949 + 1.00000i 0.654654 + 0.267261i
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 4.89898 1.18818 0.594089 0.804400i \(-0.297513\pi\)
0.594089 + 0.804400i \(0.297513\pi\)
\(18\) −3.00000 −0.707107
\(19\) 2.44949i 0.561951i 0.959715 + 0.280976i \(0.0906580\pi\)
−0.959715 + 0.280976i \(0.909342\pi\)
\(20\) 0 0
\(21\) 4.22474 1.77526i 0.921915 0.387392i
\(22\) 0 0
\(23\) 6.00000i 1.25109i 0.780189 + 0.625543i \(0.215123\pi\)
−0.780189 + 0.625543i \(0.784877\pi\)
\(24\) 1.22474 1.22474i 0.250000 0.250000i
\(25\) 0 0
\(26\) −2.44949 −0.480384
\(27\) −3.67423 + 3.67423i −0.707107 + 0.707107i
\(28\) −1.00000 + 2.44949i −0.188982 + 0.462910i
\(29\) 6.00000i 1.11417i 0.830455 + 0.557086i \(0.188081\pi\)
−0.830455 + 0.557086i \(0.811919\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) 4.89898i 0.840168i
\(35\) 0 0
\(36\) 3.00000i 0.500000i
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) −2.44949 −0.397360
\(39\) −3.00000 + 3.00000i −0.480384 + 0.480384i
\(40\) 0 0
\(41\) 4.89898 0.765092 0.382546 0.923936i \(-0.375047\pi\)
0.382546 + 0.923936i \(0.375047\pi\)
\(42\) 1.77526 + 4.22474i 0.273928 + 0.651892i
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −6.00000 −0.884652
\(47\) 4.89898 0.714590 0.357295 0.933992i \(-0.383699\pi\)
0.357295 + 0.933992i \(0.383699\pi\)
\(48\) 1.22474 + 1.22474i 0.176777 + 0.176777i
\(49\) −5.00000 4.89898i −0.714286 0.699854i
\(50\) 0 0
\(51\) 6.00000 + 6.00000i 0.840168 + 0.840168i
\(52\) 2.44949i 0.339683i
\(53\) 6.00000i 0.824163i 0.911147 + 0.412082i \(0.135198\pi\)
−0.911147 + 0.412082i \(0.864802\pi\)
\(54\) −3.67423 3.67423i −0.500000 0.500000i
\(55\) 0 0
\(56\) −2.44949 1.00000i −0.327327 0.133631i
\(57\) −3.00000 + 3.00000i −0.397360 + 0.397360i
\(58\) −6.00000 −0.787839
\(59\) 12.2474 1.59448 0.797241 0.603661i \(-0.206292\pi\)
0.797241 + 0.603661i \(0.206292\pi\)
\(60\) 0 0
\(61\) 12.2474i 1.56813i −0.620682 0.784063i \(-0.713144\pi\)
0.620682 0.784063i \(-0.286856\pi\)
\(62\) 0 0
\(63\) 7.34847 + 3.00000i 0.925820 + 0.377964i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −8.00000 −0.977356 −0.488678 0.872464i \(-0.662521\pi\)
−0.488678 + 0.872464i \(0.662521\pi\)
\(68\) −4.89898 −0.594089
\(69\) −7.34847 + 7.34847i −0.884652 + 0.884652i
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 3.00000 0.353553
\(73\) 9.79796i 1.14676i −0.819288 0.573382i \(-0.805631\pi\)
0.819288 0.573382i \(-0.194369\pi\)
\(74\) 2.00000i 0.232495i
\(75\) 0 0
\(76\) 2.44949i 0.280976i
\(77\) 0 0
\(78\) −3.00000 3.00000i −0.339683 0.339683i
\(79\) −10.0000 −1.12509 −0.562544 0.826767i \(-0.690177\pi\)
−0.562544 + 0.826767i \(0.690177\pi\)
\(80\) 0 0
\(81\) −9.00000 −1.00000
\(82\) 4.89898i 0.541002i
\(83\) 2.44949 0.268866 0.134433 0.990923i \(-0.457079\pi\)
0.134433 + 0.990923i \(0.457079\pi\)
\(84\) −4.22474 + 1.77526i −0.460957 + 0.193696i
\(85\) 0 0
\(86\) 4.00000i 0.431331i
\(87\) −7.34847 + 7.34847i −0.787839 + 0.787839i
\(88\) 0 0
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 0 0
\(91\) 6.00000 + 2.44949i 0.628971 + 0.256776i
\(92\) 6.00000i 0.625543i
\(93\) 0 0
\(94\) 4.89898i 0.505291i
\(95\) 0 0
\(96\) −1.22474 + 1.22474i −0.125000 + 0.125000i
\(97\) 4.89898i 0.497416i −0.968579 0.248708i \(-0.919994\pi\)
0.968579 0.248708i \(-0.0800060\pi\)
\(98\) 4.89898 5.00000i 0.494872 0.505076i
\(99\) 0 0
\(100\) 0 0
\(101\) −7.34847 −0.731200 −0.365600 0.930772i \(-0.619136\pi\)
−0.365600 + 0.930772i \(0.619136\pi\)
\(102\) −6.00000 + 6.00000i −0.594089 + 0.594089i
\(103\) 9.79796i 0.965422i −0.875780 0.482711i \(-0.839652\pi\)
0.875780 0.482711i \(-0.160348\pi\)
\(104\) 2.44949 0.240192
\(105\) 0 0
\(106\) −6.00000 −0.582772
\(107\) 12.0000i 1.16008i −0.814587 0.580042i \(-0.803036\pi\)
0.814587 0.580042i \(-0.196964\pi\)
\(108\) 3.67423 3.67423i 0.353553 0.353553i
\(109\) 10.0000 0.957826 0.478913 0.877862i \(-0.341031\pi\)
0.478913 + 0.877862i \(0.341031\pi\)
\(110\) 0 0
\(111\) 2.44949 + 2.44949i 0.232495 + 0.232495i
\(112\) 1.00000 2.44949i 0.0944911 0.231455i
\(113\) 6.00000i 0.564433i 0.959351 + 0.282216i \(0.0910696\pi\)
−0.959351 + 0.282216i \(0.908930\pi\)
\(114\) −3.00000 3.00000i −0.280976 0.280976i
\(115\) 0 0
\(116\) 6.00000i 0.557086i
\(117\) −7.34847 −0.679366
\(118\) 12.2474i 1.12747i
\(119\) 4.89898 12.0000i 0.449089 1.10004i
\(120\) 0 0
\(121\) 11.0000 1.00000
\(122\) 12.2474 1.10883
\(123\) 6.00000 + 6.00000i 0.541002 + 0.541002i
\(124\) 0 0
\(125\) 0 0
\(126\) −3.00000 + 7.34847i −0.267261 + 0.654654i
\(127\) −8.00000 −0.709885 −0.354943 0.934888i \(-0.615500\pi\)
−0.354943 + 0.934888i \(0.615500\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −4.89898 4.89898i −0.431331 0.431331i
\(130\) 0 0
\(131\) −7.34847 −0.642039 −0.321019 0.947073i \(-0.604025\pi\)
−0.321019 + 0.947073i \(0.604025\pi\)
\(132\) 0 0
\(133\) 6.00000 + 2.44949i 0.520266 + 0.212398i
\(134\) 8.00000i 0.691095i
\(135\) 0 0
\(136\) 4.89898i 0.420084i
\(137\) 12.0000i 1.02523i −0.858619 0.512615i \(-0.828677\pi\)
0.858619 0.512615i \(-0.171323\pi\)
\(138\) −7.34847 7.34847i −0.625543 0.625543i
\(139\) 2.44949i 0.207763i 0.994590 + 0.103882i \(0.0331263\pi\)
−0.994590 + 0.103882i \(0.966874\pi\)
\(140\) 0 0
\(141\) 6.00000 + 6.00000i 0.505291 + 0.505291i
\(142\) 0 0
\(143\) 0 0
\(144\) 3.00000i 0.250000i
\(145\) 0 0
\(146\) 9.79796 0.810885
\(147\) −0.123724 12.1237i −0.0102046 0.999948i
\(148\) −2.00000 −0.164399
\(149\) 6.00000i 0.491539i 0.969328 + 0.245770i \(0.0790407\pi\)
−0.969328 + 0.245770i \(0.920959\pi\)
\(150\) 0 0
\(151\) −8.00000 −0.651031 −0.325515 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) 2.44949 0.198680
\(153\) 14.6969i 1.18818i
\(154\) 0 0
\(155\) 0 0
\(156\) 3.00000 3.00000i 0.240192 0.240192i
\(157\) 7.34847i 0.586472i 0.956040 + 0.293236i \(0.0947321\pi\)
−0.956040 + 0.293236i \(0.905268\pi\)
\(158\) 10.0000i 0.795557i
\(159\) −7.34847 + 7.34847i −0.582772 + 0.582772i
\(160\) 0 0
\(161\) 14.6969 + 6.00000i 1.15828 + 0.472866i
\(162\) 9.00000i 0.707107i
\(163\) 16.0000 1.25322 0.626608 0.779334i \(-0.284443\pi\)
0.626608 + 0.779334i \(0.284443\pi\)
\(164\) −4.89898 −0.382546
\(165\) 0 0
\(166\) 2.44949i 0.190117i
\(167\) 4.89898 0.379094 0.189547 0.981872i \(-0.439298\pi\)
0.189547 + 0.981872i \(0.439298\pi\)
\(168\) −1.77526 4.22474i −0.136964 0.325946i
\(169\) 7.00000 0.538462
\(170\) 0 0
\(171\) −7.34847 −0.561951
\(172\) 4.00000 0.304997
\(173\) −22.0454 −1.67608 −0.838041 0.545608i \(-0.816299\pi\)
−0.838041 + 0.545608i \(0.816299\pi\)
\(174\) −7.34847 7.34847i −0.557086 0.557086i
\(175\) 0 0
\(176\) 0 0
\(177\) 15.0000 + 15.0000i 1.12747 + 1.12747i
\(178\) 0 0
\(179\) 24.0000i 1.79384i −0.442189 0.896922i \(-0.645798\pi\)
0.442189 0.896922i \(-0.354202\pi\)
\(180\) 0 0
\(181\) 12.2474i 0.910346i 0.890403 + 0.455173i \(0.150423\pi\)
−0.890403 + 0.455173i \(0.849577\pi\)
\(182\) −2.44949 + 6.00000i −0.181568 + 0.444750i
\(183\) 15.0000 15.0000i 1.10883 1.10883i
\(184\) 6.00000 0.442326
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) −4.89898 −0.357295
\(189\) 5.32577 + 12.6742i 0.387392 + 0.921915i
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) −1.22474 1.22474i −0.0883883 0.0883883i
\(193\) −4.00000 −0.287926 −0.143963 0.989583i \(-0.545985\pi\)
−0.143963 + 0.989583i \(0.545985\pi\)
\(194\) 4.89898 0.351726
\(195\) 0 0
\(196\) 5.00000 + 4.89898i 0.357143 + 0.349927i
\(197\) 18.0000i 1.28245i 0.767354 + 0.641223i \(0.221573\pi\)
−0.767354 + 0.641223i \(0.778427\pi\)
\(198\) 0 0
\(199\) 9.79796i 0.694559i −0.937762 0.347279i \(-0.887106\pi\)
0.937762 0.347279i \(-0.112894\pi\)
\(200\) 0 0
\(201\) −9.79796 9.79796i −0.691095 0.691095i
\(202\) 7.34847i 0.517036i
\(203\) 14.6969 + 6.00000i 1.03152 + 0.421117i
\(204\) −6.00000 6.00000i −0.420084 0.420084i
\(205\) 0 0
\(206\) 9.79796 0.682656
\(207\) −18.0000 −1.25109
\(208\) 2.44949i 0.169842i
\(209\) 0 0
\(210\) 0 0
\(211\) −8.00000 −0.550743 −0.275371 0.961338i \(-0.588801\pi\)
−0.275371 + 0.961338i \(0.588801\pi\)
\(212\) 6.00000i 0.412082i
\(213\) 0 0
\(214\) 12.0000 0.820303
\(215\) 0 0
\(216\) 3.67423 + 3.67423i 0.250000 + 0.250000i
\(217\) 0 0
\(218\) 10.0000i 0.677285i
\(219\) 12.0000 12.0000i 0.810885 0.810885i
\(220\) 0 0
\(221\) 12.0000i 0.807207i
\(222\) −2.44949 + 2.44949i −0.164399 + 0.164399i
\(223\) 14.6969i 0.984180i 0.870544 + 0.492090i \(0.163767\pi\)
−0.870544 + 0.492090i \(0.836233\pi\)
\(224\) 2.44949 + 1.00000i 0.163663 + 0.0668153i
\(225\) 0 0
\(226\) −6.00000 −0.399114
\(227\) −7.34847 −0.487735 −0.243868 0.969809i \(-0.578416\pi\)
−0.243868 + 0.969809i \(0.578416\pi\)
\(228\) 3.00000 3.00000i 0.198680 0.198680i
\(229\) 22.0454i 1.45680i −0.685151 0.728401i \(-0.740264\pi\)
0.685151 0.728401i \(-0.259736\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 6.00000 0.393919
\(233\) 24.0000i 1.57229i −0.618041 0.786146i \(-0.712073\pi\)
0.618041 0.786146i \(-0.287927\pi\)
\(234\) 7.34847i 0.480384i
\(235\) 0 0
\(236\) −12.2474 −0.797241
\(237\) −12.2474 12.2474i −0.795557 0.795557i
\(238\) 12.0000 + 4.89898i 0.777844 + 0.317554i
\(239\) 6.00000i 0.388108i 0.980991 + 0.194054i \(0.0621637\pi\)
−0.980991 + 0.194054i \(0.937836\pi\)
\(240\) 0 0
\(241\) 24.4949i 1.57786i 0.614486 + 0.788928i \(0.289363\pi\)
−0.614486 + 0.788928i \(0.710637\pi\)
\(242\) 11.0000i 0.707107i
\(243\) −11.0227 11.0227i −0.707107 0.707107i
\(244\) 12.2474i 0.784063i
\(245\) 0 0
\(246\) −6.00000 + 6.00000i −0.382546 + 0.382546i
\(247\) −6.00000 −0.381771
\(248\) 0 0
\(249\) 3.00000 + 3.00000i 0.190117 + 0.190117i
\(250\) 0 0
\(251\) 17.1464 1.08227 0.541136 0.840935i \(-0.317994\pi\)
0.541136 + 0.840935i \(0.317994\pi\)
\(252\) −7.34847 3.00000i −0.462910 0.188982i
\(253\) 0 0
\(254\) 8.00000i 0.501965i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 29.3939 1.83354 0.916770 0.399416i \(-0.130787\pi\)
0.916770 + 0.399416i \(0.130787\pi\)
\(258\) 4.89898 4.89898i 0.304997 0.304997i
\(259\) 2.00000 4.89898i 0.124274 0.304408i
\(260\) 0 0
\(261\) −18.0000 −1.11417
\(262\) 7.34847i 0.453990i
\(263\) 24.0000i 1.47990i −0.672660 0.739952i \(-0.734848\pi\)
0.672660 0.739952i \(-0.265152\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −2.44949 + 6.00000i −0.150188 + 0.367884i
\(267\) 0 0
\(268\) 8.00000 0.488678
\(269\) 12.2474 0.746740 0.373370 0.927682i \(-0.378202\pi\)
0.373370 + 0.927682i \(0.378202\pi\)
\(270\) 0 0
\(271\) 24.4949i 1.48796i −0.668202 0.743980i \(-0.732936\pi\)
0.668202 0.743980i \(-0.267064\pi\)
\(272\) 4.89898 0.297044
\(273\) 4.34847 + 10.3485i 0.263181 + 0.626318i
\(274\) 12.0000 0.724947
\(275\) 0 0
\(276\) 7.34847 7.34847i 0.442326 0.442326i
\(277\) 22.0000 1.32185 0.660926 0.750451i \(-0.270164\pi\)
0.660926 + 0.750451i \(0.270164\pi\)
\(278\) −2.44949 −0.146911
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) −6.00000 + 6.00000i −0.357295 + 0.357295i
\(283\) 22.0454i 1.31046i −0.755428 0.655232i \(-0.772571\pi\)
0.755428 0.655232i \(-0.227429\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 4.89898 12.0000i 0.289178 0.708338i
\(288\) −3.00000 −0.176777
\(289\) 7.00000 0.411765
\(290\) 0 0
\(291\) 6.00000 6.00000i 0.351726 0.351726i
\(292\) 9.79796i 0.573382i
\(293\) 2.44949 0.143101 0.0715504 0.997437i \(-0.477205\pi\)
0.0715504 + 0.997437i \(0.477205\pi\)
\(294\) 12.1237 0.123724i 0.707070 0.00721575i
\(295\) 0 0
\(296\) 2.00000i 0.116248i
\(297\) 0 0
\(298\) −6.00000 −0.347571
\(299\) −14.6969 −0.849946
\(300\) 0 0
\(301\) −4.00000 + 9.79796i −0.230556 + 0.564745i
\(302\) 8.00000i 0.460348i
\(303\) −9.00000 9.00000i −0.517036 0.517036i
\(304\) 2.44949i 0.140488i
\(305\) 0 0
\(306\) −14.6969 −0.840168
\(307\) 7.34847i 0.419399i 0.977766 + 0.209700i \(0.0672486\pi\)
−0.977766 + 0.209700i \(0.932751\pi\)
\(308\) 0 0
\(309\) 12.0000 12.0000i 0.682656 0.682656i
\(310\) 0 0
\(311\) −19.5959 −1.11118 −0.555591 0.831456i \(-0.687508\pi\)
−0.555591 + 0.831456i \(0.687508\pi\)
\(312\) 3.00000 + 3.00000i 0.169842 + 0.169842i
\(313\) 34.2929i 1.93835i −0.246380 0.969173i \(-0.579241\pi\)
0.246380 0.969173i \(-0.420759\pi\)
\(314\) −7.34847 −0.414698
\(315\) 0 0
\(316\) 10.0000 0.562544
\(317\) 18.0000i 1.01098i 0.862832 + 0.505490i \(0.168688\pi\)
−0.862832 + 0.505490i \(0.831312\pi\)
\(318\) −7.34847 7.34847i −0.412082 0.412082i
\(319\) 0 0
\(320\) 0 0
\(321\) 14.6969 14.6969i 0.820303 0.820303i
\(322\) −6.00000 + 14.6969i −0.334367 + 0.819028i
\(323\) 12.0000i 0.667698i
\(324\) 9.00000 0.500000
\(325\) 0 0
\(326\) 16.0000i 0.886158i
\(327\) 12.2474 + 12.2474i 0.677285 + 0.677285i
\(328\) 4.89898i 0.270501i
\(329\) 4.89898 12.0000i 0.270089 0.661581i
\(330\) 0 0
\(331\) −8.00000 −0.439720 −0.219860 0.975531i \(-0.570560\pi\)
−0.219860 + 0.975531i \(0.570560\pi\)
\(332\) −2.44949 −0.134433
\(333\) 6.00000i 0.328798i
\(334\) 4.89898i 0.268060i
\(335\) 0 0
\(336\) 4.22474 1.77526i 0.230479 0.0968481i
\(337\) 32.0000 1.74315 0.871576 0.490261i \(-0.163099\pi\)
0.871576 + 0.490261i \(0.163099\pi\)
\(338\) 7.00000i 0.380750i
\(339\) −7.34847 + 7.34847i −0.399114 + 0.399114i
\(340\) 0 0
\(341\) 0 0
\(342\) 7.34847i 0.397360i
\(343\) −17.0000 + 7.34847i −0.917914 + 0.396780i
\(344\) 4.00000i 0.215666i
\(345\) 0 0
\(346\) 22.0454i 1.18517i
\(347\) 12.0000i 0.644194i −0.946707 0.322097i \(-0.895612\pi\)
0.946707 0.322097i \(-0.104388\pi\)
\(348\) 7.34847 7.34847i 0.393919 0.393919i
\(349\) 2.44949i 0.131118i 0.997849 + 0.0655591i \(0.0208831\pi\)
−0.997849 + 0.0655591i \(0.979117\pi\)
\(350\) 0 0
\(351\) −9.00000 9.00000i −0.480384 0.480384i
\(352\) 0 0
\(353\) −9.79796 −0.521493 −0.260746 0.965407i \(-0.583969\pi\)
−0.260746 + 0.965407i \(0.583969\pi\)
\(354\) −15.0000 + 15.0000i −0.797241 + 0.797241i
\(355\) 0 0
\(356\) 0 0
\(357\) 20.6969 8.69694i 1.09540 0.460291i
\(358\) 24.0000 1.26844
\(359\) 6.00000i 0.316668i 0.987386 + 0.158334i \(0.0506123\pi\)
−0.987386 + 0.158334i \(0.949388\pi\)
\(360\) 0 0
\(361\) 13.0000 0.684211
\(362\) −12.2474 −0.643712
\(363\) 13.4722 + 13.4722i 0.707107 + 0.707107i
\(364\) −6.00000 2.44949i −0.314485 0.128388i
\(365\) 0 0
\(366\) 15.0000 + 15.0000i 0.784063 + 0.784063i
\(367\) 4.89898i 0.255725i −0.991792 0.127862i \(-0.959188\pi\)
0.991792 0.127862i \(-0.0408116\pi\)
\(368\) 6.00000i 0.312772i
\(369\) 14.6969i 0.765092i
\(370\) 0 0
\(371\) 14.6969 + 6.00000i 0.763027 + 0.311504i
\(372\) 0 0
\(373\) −14.0000 −0.724893 −0.362446 0.932005i \(-0.618058\pi\)
−0.362446 + 0.932005i \(0.618058\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 4.89898i 0.252646i
\(377\) −14.6969 −0.756931
\(378\) −12.6742 + 5.32577i −0.651892 + 0.273928i
\(379\) −20.0000 −1.02733 −0.513665 0.857991i \(-0.671713\pi\)
−0.513665 + 0.857991i \(0.671713\pi\)
\(380\) 0 0
\(381\) −9.79796 9.79796i −0.501965 0.501965i
\(382\) 0 0
\(383\) −34.2929 −1.75228 −0.876142 0.482054i \(-0.839891\pi\)
−0.876142 + 0.482054i \(0.839891\pi\)
\(384\) 1.22474 1.22474i 0.0625000 0.0625000i
\(385\) 0 0
\(386\) 4.00000i 0.203595i
\(387\) 12.0000i 0.609994i
\(388\) 4.89898i 0.248708i
\(389\) 6.00000i 0.304212i 0.988364 + 0.152106i \(0.0486055\pi\)
−0.988364 + 0.152106i \(0.951394\pi\)
\(390\) 0 0
\(391\) 29.3939i 1.48651i
\(392\) −4.89898 + 5.00000i −0.247436 + 0.252538i
\(393\) −9.00000 9.00000i −0.453990 0.453990i
\(394\) −18.0000 −0.906827
\(395\) 0 0
\(396\) 0 0
\(397\) 7.34847i 0.368809i 0.982850 + 0.184405i \(0.0590357\pi\)
−0.982850 + 0.184405i \(0.940964\pi\)
\(398\) 9.79796 0.491127
\(399\) 4.34847 + 10.3485i 0.217696 + 0.518071i
\(400\) 0 0
\(401\) 30.0000i 1.49813i −0.662497 0.749064i \(-0.730503\pi\)
0.662497 0.749064i \(-0.269497\pi\)
\(402\) 9.79796 9.79796i 0.488678 0.488678i
\(403\) 0 0
\(404\) 7.34847 0.365600
\(405\) 0 0
\(406\) −6.00000 + 14.6969i −0.297775 + 0.729397i
\(407\) 0 0
\(408\) 6.00000 6.00000i 0.297044 0.297044i
\(409\) 34.2929i 1.69567i −0.530258 0.847836i \(-0.677905\pi\)
0.530258 0.847836i \(-0.322095\pi\)
\(410\) 0 0
\(411\) 14.6969 14.6969i 0.724947 0.724947i
\(412\) 9.79796i 0.482711i
\(413\) 12.2474 30.0000i 0.602658 1.47620i
\(414\) 18.0000i 0.884652i
\(415\) 0 0
\(416\) −2.44949 −0.120096
\(417\) −3.00000 + 3.00000i −0.146911 + 0.146911i
\(418\) 0 0
\(419\) −12.2474 −0.598327 −0.299164 0.954202i \(-0.596708\pi\)
−0.299164 + 0.954202i \(0.596708\pi\)
\(420\) 0 0
\(421\) 2.00000 0.0974740 0.0487370 0.998812i \(-0.484480\pi\)
0.0487370 + 0.998812i \(0.484480\pi\)
\(422\) 8.00000i 0.389434i
\(423\) 14.6969i 0.714590i
\(424\) 6.00000 0.291386
\(425\) 0 0
\(426\) 0 0
\(427\) −30.0000 12.2474i −1.45180 0.592696i
\(428\) 12.0000i 0.580042i
\(429\) 0 0
\(430\) 0 0
\(431\) 30.0000i 1.44505i −0.691345 0.722525i \(-0.742982\pi\)
0.691345 0.722525i \(-0.257018\pi\)
\(432\) −3.67423 + 3.67423i −0.176777 + 0.176777i
\(433\) 14.6969i 0.706290i 0.935569 + 0.353145i \(0.114888\pi\)
−0.935569 + 0.353145i \(0.885112\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −10.0000 −0.478913
\(437\) −14.6969 −0.703050
\(438\) 12.0000 + 12.0000i 0.573382 + 0.573382i
\(439\) 14.6969i 0.701447i 0.936479 + 0.350723i \(0.114064\pi\)
−0.936479 + 0.350723i \(0.885936\pi\)
\(440\) 0 0
\(441\) 14.6969 15.0000i 0.699854 0.714286i
\(442\) −12.0000 −0.570782
\(443\) 36.0000i 1.71041i 0.518289 + 0.855206i \(0.326569\pi\)
−0.518289 + 0.855206i \(0.673431\pi\)
\(444\) −2.44949 2.44949i −0.116248 0.116248i
\(445\) 0 0
\(446\) −14.6969 −0.695920
\(447\) −7.34847 + 7.34847i −0.347571 + 0.347571i
\(448\) −1.00000 + 2.44949i −0.0472456 + 0.115728i
\(449\) 36.0000i 1.69895i 0.527633 + 0.849473i \(0.323080\pi\)
−0.527633 + 0.849473i \(0.676920\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 6.00000i 0.282216i
\(453\) −9.79796 9.79796i −0.460348 0.460348i
\(454\) 7.34847i 0.344881i
\(455\) 0 0
\(456\) 3.00000 + 3.00000i 0.140488 + 0.140488i
\(457\) −28.0000 −1.30978 −0.654892 0.755722i \(-0.727286\pi\)
−0.654892 + 0.755722i \(0.727286\pi\)
\(458\) 22.0454 1.03011
\(459\) −18.0000 + 18.0000i −0.840168 + 0.840168i
\(460\) 0 0
\(461\) −31.8434 −1.48309 −0.741547 0.670901i \(-0.765907\pi\)
−0.741547 + 0.670901i \(0.765907\pi\)
\(462\) 0 0
\(463\) −14.0000 −0.650635 −0.325318 0.945605i \(-0.605471\pi\)
−0.325318 + 0.945605i \(0.605471\pi\)
\(464\) 6.00000i 0.278543i
\(465\) 0 0
\(466\) 24.0000 1.11178
\(467\) −7.34847 −0.340047 −0.170023 0.985440i \(-0.554384\pi\)
−0.170023 + 0.985440i \(0.554384\pi\)
\(468\) 7.34847 0.339683
\(469\) −8.00000 + 19.5959i −0.369406 + 0.904855i
\(470\) 0 0
\(471\) −9.00000 + 9.00000i −0.414698 + 0.414698i
\(472\) 12.2474i 0.563735i
\(473\) 0 0
\(474\) 12.2474 12.2474i 0.562544 0.562544i
\(475\) 0 0
\(476\) −4.89898 + 12.0000i −0.224544 + 0.550019i
\(477\) −18.0000 −0.824163
\(478\) −6.00000 −0.274434
\(479\) −24.4949 −1.11920 −0.559600 0.828763i \(-0.689045\pi\)
−0.559600 + 0.828763i \(0.689045\pi\)
\(480\) 0 0
\(481\) 4.89898i 0.223374i
\(482\) −24.4949 −1.11571
\(483\) 10.6515 + 25.3485i 0.484661 + 1.15340i
\(484\) −11.0000 −0.500000
\(485\) 0 0
\(486\) 11.0227 11.0227i 0.500000 0.500000i
\(487\) 32.0000 1.45006 0.725029 0.688718i \(-0.241826\pi\)
0.725029 + 0.688718i \(0.241826\pi\)
\(488\) −12.2474 −0.554416
\(489\) 19.5959 + 19.5959i 0.886158 + 0.886158i
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) −6.00000 6.00000i −0.270501 0.270501i
\(493\) 29.3939i 1.32383i
\(494\) 6.00000i 0.269953i
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) −3.00000 + 3.00000i −0.134433 + 0.134433i
\(499\) −20.0000 −0.895323 −0.447661 0.894203i \(-0.647743\pi\)
−0.447661 + 0.894203i \(0.647743\pi\)
\(500\) 0 0
\(501\) 6.00000 + 6.00000i 0.268060 + 0.268060i
\(502\) 17.1464i 0.765283i
\(503\) 39.1918 1.74748 0.873739 0.486395i \(-0.161689\pi\)
0.873739 + 0.486395i \(0.161689\pi\)
\(504\) 3.00000 7.34847i 0.133631 0.327327i
\(505\) 0 0
\(506\) 0 0
\(507\) 8.57321 + 8.57321i 0.380750 + 0.380750i
\(508\) 8.00000 0.354943
\(509\) 12.2474 0.542859 0.271429 0.962458i \(-0.412504\pi\)
0.271429 + 0.962458i \(0.412504\pi\)
\(510\) 0 0
\(511\) −24.0000 9.79796i −1.06170 0.433436i
\(512\) 1.00000i 0.0441942i
\(513\) −9.00000 9.00000i −0.397360 0.397360i
\(514\) 29.3939i 1.29651i
\(515\) 0 0
\(516\) 4.89898 + 4.89898i 0.215666 + 0.215666i
\(517\) 0 0
\(518\) 4.89898 + 2.00000i 0.215249 + 0.0878750i
\(519\) −27.0000 27.0000i −1.18517 1.18517i
\(520\) 0 0
\(521\) 4.89898 0.214628 0.107314 0.994225i \(-0.465775\pi\)
0.107314 + 0.994225i \(0.465775\pi\)
\(522\) 18.0000i 0.787839i
\(523\) 2.44949i 0.107109i 0.998565 + 0.0535544i \(0.0170550\pi\)
−0.998565 + 0.0535544i \(0.982945\pi\)
\(524\) 7.34847 0.321019
\(525\) 0 0
\(526\) 24.0000 1.04645
\(527\) 0 0
\(528\) 0 0
\(529\) −13.0000 −0.565217
\(530\) 0 0
\(531\) 36.7423i 1.59448i
\(532\) −6.00000 2.44949i −0.260133 0.106199i
\(533\) 12.0000i 0.519778i
\(534\) 0 0
\(535\) 0 0
\(536\) 8.00000i 0.345547i
\(537\) 29.3939 29.3939i 1.26844 1.26844i
\(538\) 12.2474i 0.528025i
\(539\) 0 0
\(540\) 0 0
\(541\) 2.00000 0.0859867 0.0429934 0.999075i \(-0.486311\pi\)
0.0429934 + 0.999075i \(0.486311\pi\)
\(542\) 24.4949 1.05215
\(543\) −15.0000 + 15.0000i −0.643712 + 0.643712i
\(544\) 4.89898i 0.210042i
\(545\) 0 0
\(546\) −10.3485 + 4.34847i −0.442874 + 0.186097i
\(547\) −8.00000 −0.342055 −0.171028 0.985266i \(-0.554709\pi\)
−0.171028 + 0.985266i \(0.554709\pi\)
\(548\) 12.0000i 0.512615i
\(549\) 36.7423 1.56813
\(550\) 0 0
\(551\) −14.6969 −0.626111
\(552\) 7.34847 + 7.34847i 0.312772 + 0.312772i
\(553\) −10.0000 + 24.4949i −0.425243 + 1.04163i
\(554\) 22.0000i 0.934690i
\(555\) 0 0
\(556\) 2.44949i 0.103882i
\(557\) 18.0000i 0.762684i 0.924434 + 0.381342i \(0.124538\pi\)
−0.924434 + 0.381342i \(0.875462\pi\)
\(558\) 0 0
\(559\) 9.79796i 0.414410i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −22.0454 −0.929103 −0.464552 0.885546i \(-0.653784\pi\)
−0.464552 + 0.885546i \(0.653784\pi\)
\(564\) −6.00000 6.00000i −0.252646 0.252646i
\(565\) 0 0
\(566\) 22.0454 0.926638
\(567\) −9.00000 + 22.0454i −0.377964 + 0.925820i
\(568\) 0 0
\(569\) 6.00000i 0.251533i 0.992060 + 0.125767i \(0.0401390\pi\)
−0.992060 + 0.125767i \(0.959861\pi\)
\(570\) 0 0
\(571\) 32.0000 1.33916 0.669579 0.742741i \(-0.266474\pi\)
0.669579 + 0.742741i \(0.266474\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 12.0000 + 4.89898i 0.500870 + 0.204479i
\(575\) 0 0
\(576\) 3.00000i 0.125000i
\(577\) 19.5959i 0.815789i 0.913029 + 0.407894i \(0.133737\pi\)
−0.913029 + 0.407894i \(0.866263\pi\)
\(578\) 7.00000i 0.291162i
\(579\) −4.89898 4.89898i −0.203595 0.203595i
\(580\) 0 0
\(581\) 2.44949 6.00000i 0.101622 0.248922i
\(582\) 6.00000 + 6.00000i 0.248708 + 0.248708i
\(583\) 0 0
\(584\) −9.79796 −0.405442
\(585\) 0 0
\(586\) 2.44949i 0.101187i
\(587\) −7.34847 −0.303304 −0.151652 0.988434i \(-0.548459\pi\)
−0.151652 + 0.988434i \(0.548459\pi\)
\(588\) 0.123724 + 12.1237i 0.00510231 + 0.499974i
\(589\) 0 0
\(590\) 0 0
\(591\) −22.0454 + 22.0454i −0.906827 + 0.906827i
\(592\) 2.00000 0.0821995
\(593\) 39.1918 1.60942 0.804708 0.593671i \(-0.202322\pi\)
0.804708 + 0.593671i \(0.202322\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 6.00000i 0.245770i
\(597\) 12.0000 12.0000i 0.491127 0.491127i
\(598\) 14.6969i 0.601003i
\(599\) 24.0000i 0.980613i −0.871550 0.490307i \(-0.836885\pi\)
0.871550 0.490307i \(-0.163115\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) −9.79796 4.00000i −0.399335 0.163028i
\(603\) 24.0000i 0.977356i
\(604\) 8.00000 0.325515
\(605\) 0 0
\(606\) 9.00000 9.00000i 0.365600 0.365600i
\(607\) 4.89898i 0.198843i −0.995045 0.0994217i \(-0.968301\pi\)
0.995045 0.0994217i \(-0.0316993\pi\)
\(608\) −2.44949 −0.0993399
\(609\) 10.6515 + 25.3485i 0.431622 + 1.02717i
\(610\) 0 0
\(611\) 12.0000i 0.485468i
\(612\) 14.6969i 0.594089i
\(613\) −14.0000 −0.565455 −0.282727 0.959200i \(-0.591239\pi\)
−0.282727 + 0.959200i \(0.591239\pi\)
\(614\) −7.34847 −0.296560
\(615\) 0 0
\(616\) 0 0
\(617\) 18.0000i 0.724653i 0.932051 + 0.362326i \(0.118017\pi\)
−0.932051 + 0.362326i \(0.881983\pi\)
\(618\) 12.0000 + 12.0000i 0.482711 + 0.482711i
\(619\) 26.9444i 1.08299i 0.840705 + 0.541493i \(0.182141\pi\)
−0.840705 + 0.541493i \(0.817859\pi\)
\(620\) 0 0
\(621\) −22.0454 22.0454i −0.884652 0.884652i
\(622\) 19.5959i 0.785725i
\(623\) 0 0
\(624\) −3.00000 + 3.00000i −0.120096 + 0.120096i
\(625\) 0 0
\(626\) 34.2929 1.37062
\(627\) 0 0
\(628\) 7.34847i 0.293236i
\(629\) 9.79796 0.390670
\(630\) 0 0
\(631\) 2.00000 0.0796187 0.0398094 0.999207i \(-0.487325\pi\)
0.0398094 + 0.999207i \(0.487325\pi\)
\(632\) 10.0000i 0.397779i
\(633\) −9.79796 9.79796i −0.389434 0.389434i
\(634\) −18.0000 −0.714871
\(635\) 0 0
\(636\) 7.34847 7.34847i 0.291386 0.291386i
\(637\) 12.0000 12.2474i 0.475457 0.485262i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 30.0000i 1.18493i 0.805597 + 0.592464i \(0.201845\pi\)
−0.805597 + 0.592464i \(0.798155\pi\)
\(642\) 14.6969 + 14.6969i 0.580042 + 0.580042i
\(643\) 22.0454i 0.869386i −0.900579 0.434693i \(-0.856857\pi\)
0.900579 0.434693i \(-0.143143\pi\)
\(644\) −14.6969 6.00000i −0.579141 0.236433i
\(645\) 0 0
\(646\) −12.0000 −0.472134
\(647\) −44.0908 −1.73339 −0.866694 0.498839i \(-0.833760\pi\)
−0.866694 + 0.498839i \(0.833760\pi\)
\(648\) 9.00000i 0.353553i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −16.0000 −0.626608
\(653\) 6.00000i 0.234798i 0.993085 + 0.117399i \(0.0374557\pi\)
−0.993085 + 0.117399i \(0.962544\pi\)
\(654\) −12.2474 + 12.2474i −0.478913 + 0.478913i
\(655\) 0 0
\(656\) 4.89898 0.191273
\(657\) 29.3939 1.14676
\(658\) 12.0000 + 4.89898i 0.467809 + 0.190982i
\(659\) 36.0000i 1.40236i 0.712984 + 0.701180i \(0.247343\pi\)
−0.712984 + 0.701180i \(0.752657\pi\)
\(660\) 0 0
\(661\) 12.2474i 0.476371i 0.971220 + 0.238185i \(0.0765525\pi\)
−0.971220 + 0.238185i \(0.923447\pi\)
\(662\) 8.00000i 0.310929i
\(663\) −14.6969 + 14.6969i −0.570782 + 0.570782i
\(664\) 2.44949i 0.0950586i
\(665\) 0 0
\(666\) −6.00000 −0.232495
\(667\) −36.0000 −1.39393
\(668\) −4.89898 −0.189547
\(669\) −18.0000 + 18.0000i −0.695920 + 0.695920i
\(670\) 0 0
\(671\) 0 0
\(672\) 1.77526 + 4.22474i 0.0684820 + 0.162973i
\(673\) −34.0000 −1.31060 −0.655302 0.755367i \(-0.727459\pi\)
−0.655302 + 0.755367i \(0.727459\pi\)
\(674\) 32.0000i 1.23259i
\(675\) 0 0
\(676\) −7.00000 −0.269231
\(677\) −7.34847 −0.282425 −0.141212 0.989979i \(-0.545100\pi\)
−0.141212 + 0.989979i \(0.545100\pi\)
\(678\) −7.34847 7.34847i −0.282216 0.282216i
\(679\) −12.0000 4.89898i −0.460518 0.188006i
\(680\) 0 0
\(681\) −9.00000 9.00000i −0.344881 0.344881i
\(682\) 0 0
\(683\) 24.0000i 0.918334i −0.888350 0.459167i \(-0.848148\pi\)
0.888350 0.459167i \(-0.151852\pi\)
\(684\) 7.34847 0.280976
\(685\) 0 0
\(686\) −7.34847 17.0000i −0.280566 0.649063i
\(687\) 27.0000 27.0000i 1.03011 1.03011i
\(688\) −4.00000 −0.152499
\(689\) −14.6969 −0.559909
\(690\) 0 0
\(691\) 36.7423i 1.39774i −0.715246 0.698872i \(-0.753686\pi\)
0.715246 0.698872i \(-0.246314\pi\)
\(692\) 22.0454 0.838041
\(693\) 0 0
\(694\) 12.0000 0.455514
\(695\) 0 0
\(696\) 7.34847 + 7.34847i 0.278543 + 0.278543i
\(697\) 24.0000 0.909065
\(698\) −2.44949 −0.0927146
\(699\) 29.3939 29.3939i 1.11178 1.11178i
\(700\) 0 0
\(701\) 30.0000i 1.13308i −0.824033 0.566542i \(-0.808281\pi\)
0.824033 0.566542i \(-0.191719\pi\)
\(702\) 9.00000 9.00000i 0.339683 0.339683i
\(703\) 4.89898i 0.184769i
\(704\) 0 0
\(705\) 0 0
\(706\) 9.79796i 0.368751i
\(707\) −7.34847 + 18.0000i −0.276368 + 0.676960i
\(708\) −15.0000 15.0000i −0.563735 0.563735i
\(709\) 10.0000 0.375558 0.187779 0.982211i \(-0.439871\pi\)
0.187779 + 0.982211i \(0.439871\pi\)
\(710\) 0 0
\(711\) 30.0000i 1.12509i
\(712\) 0 0
\(713\) 0 0
\(714\) 8.69694 + 20.6969i 0.325475 + 0.774563i
\(715\) 0 0
\(716\) 24.0000i 0.896922i
\(717\) −7.34847 + 7.34847i −0.274434 + 0.274434i
\(718\) −6.00000 −0.223918
\(719\) −24.4949 −0.913506 −0.456753 0.889594i \(-0.650988\pi\)
−0.456753 + 0.889594i \(0.650988\pi\)
\(720\) 0 0
\(721\) −24.0000 9.79796i −0.893807 0.364895i
\(722\) 13.0000i 0.483810i
\(723\) −30.0000 + 30.0000i −1.11571 + 1.11571i
\(724\) 12.2474i 0.455173i
\(725\) 0 0
\(726\) −13.4722 + 13.4722i −0.500000 + 0.500000i
\(727\) 29.3939i 1.09016i −0.838385 0.545079i \(-0.816500\pi\)
0.838385 0.545079i \(-0.183500\pi\)
\(728\) 2.44949 6.00000i 0.0907841 0.222375i
\(729\) 27.0000i 1.00000i
\(730\) 0 0
\(731\) −19.5959 −0.724781
\(732\) −15.0000 + 15.0000i −0.554416 + 0.554416i
\(733\) 22.0454i 0.814266i −0.913369 0.407133i \(-0.866529\pi\)
0.913369 0.407133i \(-0.133471\pi\)
\(734\) 4.89898 0.180825
\(735\) 0 0
\(736\) −6.00000 −0.221163
\(737\) 0 0
\(738\) −14.6969 −0.541002
\(739\) 20.0000 0.735712 0.367856 0.929883i \(-0.380092\pi\)
0.367856 + 0.929883i \(0.380092\pi\)
\(740\) 0 0
\(741\) −7.34847 7.34847i −0.269953 0.269953i
\(742\) −6.00000 + 14.6969i −0.220267 + 0.539542i
\(743\) 6.00000i 0.220119i 0.993925 + 0.110059i \(0.0351041\pi\)
−0.993925 + 0.110059i \(0.964896\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 14.0000i 0.512576i
\(747\) 7.34847i 0.268866i
\(748\) 0 0
\(749\) −29.3939 12.0000i −1.07403 0.438470i
\(750\) 0 0
\(751\) −8.00000 −0.291924 −0.145962 0.989290i \(-0.546628\pi\)
−0.145962 + 0.989290i \(0.546628\pi\)
\(752\) 4.89898 0.178647
\(753\) 21.0000 + 21.0000i 0.765283 + 0.765283i
\(754\) 14.6969i 0.535231i
\(755\) 0 0
\(756\) −5.32577 12.6742i −0.193696 0.460957i
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) 20.0000i 0.726433i
\(759\) 0 0
\(760\) 0 0
\(761\) 4.89898 0.177588 0.0887939 0.996050i \(-0.471699\pi\)
0.0887939 + 0.996050i \(0.471699\pi\)
\(762\) 9.79796 9.79796i 0.354943 0.354943i
\(763\) 10.0000 24.4949i 0.362024 0.886775i
\(764\) 0 0
\(765\) 0 0
\(766\) 34.2929i 1.23905i
\(767\) 30.0000i 1.08324i
\(768\) 1.22474 + 1.22474i 0.0441942 + 0.0441942i
\(769\) 34.2929i 1.23663i −0.785930 0.618316i \(-0.787815\pi\)
0.785930 0.618316i \(-0.212185\pi\)
\(770\) 0 0
\(771\) 36.0000 + 36.0000i 1.29651 + 1.29651i
\(772\) 4.00000 0.143963
\(773\) 26.9444 0.969122 0.484561 0.874757i \(-0.338979\pi\)
0.484561 + 0.874757i \(0.338979\pi\)
\(774\) 12.0000 0.431331
\(775\) 0 0
\(776\) −4.89898 −0.175863
\(777\) 8.44949 3.55051i 0.303124 0.127374i
\(778\) −6.00000 −0.215110
\(779\) 12.0000i 0.429945i
\(780\) 0 0
\(781\) 0 0
\(782\) −29.3939 −1.05112
\(783\) −22.0454 22.0454i −0.787839 0.787839i
\(784\) −5.00000 4.89898i −0.178571 0.174964i
\(785\) 0 0
\(786\) 9.00000 9.00000i 0.321019 0.321019i
\(787\) 31.8434i 1.13509i 0.823341 + 0.567547i \(0.192107\pi\)
−0.823341 + 0.567547i \(0.807893\pi\)
\(788\) 18.0000i 0.641223i
\(789\) 29.3939 29.3939i 1.04645 1.04645i
\(790\) 0 0
\(791\) 14.6969 + 6.00000i 0.522563 + 0.213335i
\(792\) 0 0
\(793\) 30.0000 1.06533
\(794\) −7.34847 −0.260787
\(795\) 0 0
\(796\) 9.79796i 0.347279i
\(797\) −7.34847 −0.260296 −0.130148 0.991495i \(-0.541545\pi\)
−0.130148 + 0.991495i \(0.541545\pi\)
\(798\) −10.3485 + 4.34847i −0.366332 + 0.153934i
\(799\) 24.0000 0.849059
\(800\) 0 0
\(801\) 0 0
\(802\) 30.0000 1.05934
\(803\) 0 0
\(804\) 9.79796