Properties

Label 1050.2.d.b.1049.4
Level $1050$
Weight $2$
Character 1050.1049
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.d (of order \(2\), degree \(1\), not 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: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1049.4
Root \(1.22474 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 1050.1049
Dual form 1050.2.d.b.1049.3

$q$-expansion

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 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
\(7\) 2.44949 1.00000i 0.925820 0.377964i
\(8\) −1.00000 −0.353553
\(9\) 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
\(13\) 2.44949 0.679366 0.339683 0.940540i \(-0.389680\pi\)
0.339683 + 0.940540i \(0.389680\pi\)
\(14\) −2.44949 + 1.00000i −0.654654 + 0.267261i
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 4.89898i 1.18818i −0.804400 0.594089i \(-0.797513\pi\)
0.804400 0.594089i \(-0.202487\pi\)
\(18\) 3.00000i 0.707107i
\(19\) 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
\(23\) 6.00000 1.25109 0.625543 0.780189i \(-0.284877\pi\)
0.625543 + 0.780189i \(0.284877\pi\)
\(24\) −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
\(28\) 2.44949 1.00000i 0.462910 0.188982i
\(29\) 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 \(\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) 4.89898i 0.840168i
\(35\) 0 0
\(36\) 3.00000i 0.500000i
\(37\) 2.00000i 0.328798i −0.986394 0.164399i \(-0.947432\pi\)
0.986394 0.164399i \(-0.0525685\pi\)
\(38\) 2.44949i 0.397360i
\(39\) 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 \(0.375047\pi\)
\(42\) −4.22474 1.77526i −0.651892 0.273928i
\(43\) 4.00000i 0.609994i −0.952353 0.304997i \(-0.901344\pi\)
0.952353 0.304997i \(-0.0986555\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −6.00000 −0.884652
\(47\) 4.89898i 0.714590i −0.933992 0.357295i \(-0.883699\pi\)
0.933992 0.357295i \(-0.116301\pi\)
\(48\) 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
\(52\) 2.44949 0.339683
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) 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
\(58\) 6.00000i 0.787839i
\(59\) −12.2474 −1.59448 −0.797241 0.603661i \(-0.793708\pi\)
−0.797241 + 0.603661i \(0.793708\pi\)
\(60\) 0 0
\(61\) 12.2474i 1.56813i 0.620682 + 0.784063i \(0.286856\pi\)
−0.620682 + 0.784063i \(0.713144\pi\)
\(62\) 0 0
\(63\) 3.00000 + 7.34847i 0.377964 + 0.925820i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 8.00000i 0.977356i 0.872464 + 0.488678i \(0.162521\pi\)
−0.872464 + 0.488678i \(0.837479\pi\)
\(68\) 4.89898i 0.594089i
\(69\) 7.34847 + 7.34847i 0.884652 + 0.884652i
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 3.00000i 0.353553i
\(73\) −9.79796 −1.14676 −0.573382 0.819288i \(-0.694369\pi\)
−0.573382 + 0.819288i \(0.694369\pi\)
\(74\) 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 \(-0.309823\pi\)
0.562544 + 0.826767i \(0.309823\pi\)
\(80\) 0 0
\(81\) −9.00000 −1.00000
\(82\) −4.89898 −0.541002
\(83\) 2.44949i 0.268866i 0.990923 + 0.134433i \(0.0429214\pi\)
−0.990923 + 0.134433i \(0.957079\pi\)
\(84\) 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
\(92\) 6.00000 0.625543
\(93\) 0 0
\(94\) 4.89898i 0.505291i
\(95\) 0 0
\(96\) −1.22474 1.22474i −0.125000 0.125000i
\(97\) 4.89898 0.497416 0.248708 0.968579i \(-0.419994\pi\)
0.248708 + 0.968579i \(0.419994\pi\)
\(98\) −5.00000 + 4.89898i −0.505076 + 0.494872i
\(99\) 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
\(103\) −9.79796 −0.965422 −0.482711 0.875780i \(-0.660348\pi\)
−0.482711 + 0.875780i \(0.660348\pi\)
\(104\) −2.44949 −0.240192
\(105\) 0 0
\(106\) −6.00000 −0.582772
\(107\) 12.0000 1.16008 0.580042 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) −3.67423 + 3.67423i −0.353553 + 0.353553i
\(109\) −10.0000 −0.957826 −0.478913 0.877862i \(-0.658969\pi\)
−0.478913 + 0.877862i \(0.658969\pi\)
\(110\) 0 0
\(111\) 2.44949 2.44949i 0.232495 0.232495i
\(112\) 2.44949 1.00000i 0.231455 0.0944911i
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 3.00000 3.00000i 0.280976 0.280976i
\(115\) 0 0
\(116\) 6.00000i 0.557086i
\(117\) 7.34847i 0.679366i
\(118\) 12.2474 1.12747
\(119\) −4.89898 12.0000i −0.449089 1.10004i
\(120\) 0 0
\(121\) 11.0000 1.00000
\(122\) 12.2474i 1.10883i
\(123\) 6.00000 + 6.00000i 0.541002 + 0.541002i
\(124\) 0 0
\(125\) 0 0
\(126\) −3.00000 7.34847i −0.267261 0.654654i
\(127\) 8.00000i 0.709885i 0.934888 + 0.354943i \(0.115500\pi\)
−0.934888 + 0.354943i \(0.884500\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 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
\(133\) 2.44949 + 6.00000i 0.212398 + 0.520266i
\(134\) 8.00000i 0.691095i
\(135\) 0 0
\(136\) 4.89898i 0.420084i
\(137\) 12.0000 1.02523 0.512615 0.858619i \(-0.328677\pi\)
0.512615 + 0.858619i \(0.328677\pi\)
\(138\) −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
\(147\) 12.1237 + 0.123724i 0.999948 + 0.0102046i
\(148\) 2.00000i 0.164399i
\(149\) 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 \(0.605538\pi\)
\(152\) 2.44949i 0.198680i
\(153\) 14.6969 1.18818
\(154\) 0 0
\(155\) 0 0
\(156\) 3.00000 + 3.00000i 0.240192 + 0.240192i
\(157\) −7.34847 −0.586472 −0.293236 0.956040i \(-0.594732\pi\)
−0.293236 + 0.956040i \(0.594732\pi\)
\(158\) −10.0000 −0.795557
\(159\) 7.34847 + 7.34847i 0.582772 + 0.582772i
\(160\) 0 0
\(161\) 14.6969 6.00000i 1.15828 0.472866i
\(162\) 9.00000 0.707107
\(163\) 16.0000i 1.25322i 0.779334 + 0.626608i \(0.215557\pi\)
−0.779334 + 0.626608i \(0.784443\pi\)
\(164\) 4.89898 0.382546
\(165\) 0 0
\(166\) 2.44949i 0.190117i
\(167\) 4.89898i 0.379094i −0.981872 0.189547i \(-0.939298\pi\)
0.981872 0.189547i \(-0.0607020\pi\)
\(168\) −4.22474 1.77526i −0.325946 0.136964i
\(169\) −7.00000 −0.538462
\(170\) 0 0
\(171\) −7.34847 −0.561951
\(172\) 4.00000i 0.304997i
\(173\) 22.0454i 1.67608i −0.545608 0.838041i \(-0.683701\pi\)
0.545608 0.838041i \(-0.316299\pi\)
\(174\) 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 \(-0.849577\pi\)
0.890403 0.455173i \(-0.150423\pi\)
\(182\) −6.00000 + 2.44949i −0.444750 + 0.181568i
\(183\) −15.0000 + 15.0000i −1.10883 + 1.10883i
\(184\) −6.00000 −0.442326
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 4.89898i 0.357295i
\(189\) −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
\(193\) 4.00000i 0.287926i −0.989583 0.143963i \(-0.954015\pi\)
0.989583 0.143963i \(-0.0459847\pi\)
\(194\) −4.89898 −0.351726
\(195\) 0 0
\(196\) 5.00000 4.89898i 0.357143 0.349927i
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) 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
\(202\) 7.34847 0.517036
\(203\) 6.00000 + 14.6969i 0.421117 + 1.03152i
\(204\) 6.00000 6.00000i 0.420084 0.420084i
\(205\) 0 0
\(206\) 9.79796 0.682656
\(207\) 18.0000i 1.25109i
\(208\) 2.44949 0.169842
\(209\) 0 0
\(210\) 0 0
\(211\) −8.00000 −0.550743 −0.275371 0.961338i \(-0.588801\pi\)
−0.275371 + 0.961338i \(0.588801\pi\)
\(212\) 6.00000 0.412082
\(213\) 0 0
\(214\) −12.0000 −0.820303
\(215\) 0 0
\(216\) 3.67423 3.67423i 0.250000 0.250000i
\(217\) 0 0
\(218\) 10.0000 0.677285
\(219\) −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
\(223\) 14.6969 0.984180 0.492090 0.870544i \(-0.336233\pi\)
0.492090 + 0.870544i \(0.336233\pi\)
\(224\) −2.44949 + 1.00000i −0.163663 + 0.0668153i
\(225\) 0 0
\(226\) −6.00000 −0.399114
\(227\) 7.34847i 0.487735i 0.969809 + 0.243868i \(0.0784162\pi\)
−0.969809 + 0.243868i \(0.921584\pi\)
\(228\) −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
\(232\) 6.00000i 0.393919i
\(233\) −24.0000 −1.57229 −0.786146 0.618041i \(-0.787927\pi\)
−0.786146 + 0.618041i \(0.787927\pi\)
\(234\) 7.34847i 0.480384i
\(235\) 0 0
\(236\) −12.2474 −0.797241
\(237\) 12.2474 + 12.2474i 0.795557 + 0.795557i
\(238\) 4.89898 + 12.0000i 0.317554 + 0.777844i
\(239\) 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 \(-0.710637\pi\)
0.614486 0.788928i \(-0.289363\pi\)
\(242\) −11.0000 −0.707107
\(243\) −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
\(247\) 6.00000i 0.381771i
\(248\) 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 \(0.317994\pi\)
\(252\) 3.00000 + 7.34847i 0.188982 + 0.462910i
\(253\) 0 0
\(254\) 8.00000i 0.501965i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 29.3939i 1.83354i −0.399416 0.916770i \(-0.630787\pi\)
0.399416 0.916770i \(-0.369213\pi\)
\(258\) −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
\(262\) 7.34847 0.453990
\(263\) −24.0000 −1.47990 −0.739952 0.672660i \(-0.765152\pi\)
−0.739952 + 0.672660i \(0.765152\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −2.44949 6.00000i −0.150188 0.367884i
\(267\) 0 0
\(268\) 8.00000i 0.488678i
\(269\) −12.2474 −0.746740 −0.373370 0.927682i \(-0.621798\pi\)
−0.373370 + 0.927682i \(0.621798\pi\)
\(270\) 0 0
\(271\) 24.4949i 1.48796i 0.668202 + 0.743980i \(0.267064\pi\)
−0.668202 + 0.743980i \(0.732936\pi\)
\(272\) 4.89898i 0.297044i
\(273\) 10.3485 + 4.34847i 0.626318 + 0.263181i
\(274\) −12.0000 −0.724947
\(275\) 0 0
\(276\) 7.34847 + 7.34847i 0.442326 + 0.442326i
\(277\) 22.0000i 1.32185i −0.750451 0.660926i \(-0.770164\pi\)
0.750451 0.660926i \(-0.229836\pi\)
\(278\) 2.44949i 0.146911i
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) −6.00000 + 6.00000i −0.357295 + 0.357295i
\(283\) −22.0454 −1.31046 −0.655232 0.755428i \(-0.727429\pi\)
−0.655232 + 0.755428i \(0.727429\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 12.0000 4.89898i 0.708338 0.289178i
\(288\) 3.00000i 0.176777i
\(289\) −7.00000 −0.411765
\(290\) 0 0
\(291\) 6.00000 + 6.00000i 0.351726 + 0.351726i
\(292\) −9.79796 −0.573382
\(293\) 2.44949i 0.143101i 0.997437 + 0.0715504i \(0.0227947\pi\)
−0.997437 + 0.0715504i \(0.977205\pi\)
\(294\) −12.1237 0.123724i −0.707070 0.00721575i
\(295\) 0 0
\(296\) 2.00000i 0.116248i
\(297\) 0 0
\(298\) 6.00000i 0.347571i
\(299\) 14.6969 0.849946
\(300\) 0 0
\(301\) −4.00000 9.79796i −0.230556 0.564745i
\(302\) 8.00000 0.460348
\(303\) −9.00000 9.00000i −0.517036 0.517036i
\(304\) 2.44949i 0.140488i
\(305\) 0 0
\(306\) −14.6969 −0.840168
\(307\) −7.34847 −0.419399 −0.209700 0.977766i \(-0.567249\pi\)
−0.209700 + 0.977766i \(0.567249\pi\)
\(308\) 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
\(313\) −34.2929 −1.93835 −0.969173 0.246380i \(-0.920759\pi\)
−0.969173 + 0.246380i \(0.920759\pi\)
\(314\) 7.34847 0.414698
\(315\) 0 0
\(316\) 10.0000 0.562544
\(317\) −18.0000 −1.01098 −0.505490 0.862832i \(-0.668688\pi\)
−0.505490 + 0.862832i \(0.668688\pi\)
\(318\) −7.34847 7.34847i −0.412082 0.412082i
\(319\) 0 0
\(320\) 0 0
\(321\) 14.6969 + 14.6969i 0.820303 + 0.820303i
\(322\) −14.6969 + 6.00000i −0.819028 + 0.334367i
\(323\) 12.0000 0.667698
\(324\) −9.00000 −0.500000
\(325\) 0 0
\(326\) 16.0000i 0.886158i
\(327\) −12.2474 12.2474i −0.677285 0.677285i
\(328\) −4.89898 −0.270501
\(329\) −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 \(0.570560\pi\)
\(332\) 2.44949i 0.134433i
\(333\) 6.00000 0.328798
\(334\) 4.89898i 0.268060i
\(335\) 0 0
\(336\) 4.22474 + 1.77526i 0.230479 + 0.0968481i
\(337\) 32.0000i 1.74315i −0.490261 0.871576i \(-0.663099\pi\)
0.490261 0.871576i \(-0.336901\pi\)
\(338\) 7.00000 0.380750
\(339\) 7.34847 + 7.34847i 0.399114 + 0.399114i
\(340\) 0 0
\(341\) 0 0
\(342\) 7.34847 0.397360
\(343\) 7.34847 17.0000i 0.396780 0.917914i
\(344\) 4.00000i 0.215666i
\(345\) 0 0
\(346\) 22.0454i 1.18517i
\(347\) 12.0000 0.644194 0.322097 0.946707i \(-0.395612\pi\)
0.322097 + 0.946707i \(0.395612\pi\)
\(348\) −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
\(353\) 9.79796i 0.521493i −0.965407 0.260746i \(-0.916031\pi\)
0.965407 0.260746i \(-0.0839686\pi\)
\(354\) 15.0000 + 15.0000i 0.797241 + 0.797241i
\(355\) 0 0
\(356\) 0 0
\(357\) 8.69694 20.6969i 0.460291 1.09540i
\(358\) 24.0000i 1.26844i
\(359\) 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
\(362\) 12.2474i 0.643712i
\(363\) 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
\(367\) 4.89898 0.255725 0.127862 0.991792i \(-0.459188\pi\)
0.127862 + 0.991792i \(0.459188\pi\)
\(368\) 6.00000 0.312772
\(369\) 14.6969i 0.765092i
\(370\) 0 0
\(371\) 14.6969 6.00000i 0.763027 0.311504i
\(372\) 0 0
\(373\) 14.0000i 0.724893i −0.932005 0.362446i \(-0.881942\pi\)
0.932005 0.362446i \(-0.118058\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 4.89898i 0.252646i
\(377\) 14.6969i 0.756931i
\(378\) 5.32577 12.6742i 0.273928 0.651892i
\(379\) 20.0000 1.02733 0.513665 0.857991i \(-0.328287\pi\)
0.513665 + 0.857991i \(0.328287\pi\)
\(380\) 0 0
\(381\) −9.79796 + 9.79796i −0.501965 + 0.501965i
\(382\) 0 0
\(383\) 34.2929i 1.75228i −0.482054 0.876142i \(-0.660109\pi\)
0.482054 0.876142i \(-0.339891\pi\)
\(384\) −1.22474 1.22474i −0.0625000 0.0625000i
\(385\) 0 0
\(386\) 4.00000i 0.203595i
\(387\) 12.0000 0.609994
\(388\) 4.89898 0.248708
\(389\) 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
\(392\) −5.00000 + 4.89898i −0.252538 + 0.247436i
\(393\) −9.00000 9.00000i −0.453990 0.453990i
\(394\) 18.0000 0.906827
\(395\) 0 0
\(396\) 0 0
\(397\) −7.34847 −0.368809 −0.184405 0.982850i \(-0.559036\pi\)
−0.184405 + 0.982850i \(0.559036\pi\)
\(398\) 9.79796i 0.491127i
\(399\) −4.34847 + 10.3485i −0.217696 + 0.518071i
\(400\) 0 0
\(401\) 30.0000i 1.49813i 0.662497 + 0.749064i \(0.269497\pi\)
−0.662497 + 0.749064i \(0.730503\pi\)
\(402\) 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
\(412\) −9.79796 −0.482711
\(413\) −30.0000 + 12.2474i −1.47620 + 0.602658i
\(414\) 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 \(-0.403292\pi\)
0.299164 + 0.954202i \(0.403292\pi\)
\(420\) 0 0
\(421\) 2.00000 0.0974740 0.0487370 0.998812i \(-0.484480\pi\)
0.0487370 + 0.998812i \(0.484480\pi\)
\(422\) 8.00000 0.389434
\(423\) 14.6969 0.714590
\(424\) −6.00000 −0.291386
\(425\) 0 0
\(426\) 0 0
\(427\) 12.2474 + 30.0000i 0.592696 + 1.45180i
\(428\) 12.0000 0.580042
\(429\) 0 0
\(430\) 0 0
\(431\) 30.0000i 1.44505i 0.691345 + 0.722525i \(0.257018\pi\)
−0.691345 + 0.722525i \(0.742982\pi\)
\(432\) −3.67423 + 3.67423i −0.176777 + 0.176777i
\(433\) 14.6969 0.706290 0.353145 0.935569i \(-0.385112\pi\)
0.353145 + 0.935569i \(0.385112\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −10.0000 −0.478913
\(437\) 14.6969i 0.703050i
\(438\) 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
\(442\) 12.0000i 0.570782i
\(443\) 36.0000 1.71041 0.855206 0.518289i \(-0.173431\pi\)
0.855206 + 0.518289i \(0.173431\pi\)
\(444\) 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
\(448\) 2.44949 1.00000i 0.115728 0.0472456i
\(449\) 36.0000i 1.69895i 0.527633 + 0.849473i \(0.323080\pi\)
−0.527633 + 0.849473i \(0.676920\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 6.00000 0.282216
\(453\) −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
\(457\) 28.0000i 1.30978i 0.755722 + 0.654892i \(0.227286\pi\)
−0.755722 + 0.654892i \(0.772714\pi\)
\(458\) 22.0454i 1.03011i
\(459\) 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
\(463\) 14.0000i 0.650635i −0.945605 0.325318i \(-0.894529\pi\)
0.945605 0.325318i \(-0.105471\pi\)
\(464\) 6.00000i 0.278543i
\(465\) 0 0
\(466\) 24.0000 1.11178
\(467\) 7.34847i 0.340047i 0.985440 + 0.170023i \(0.0543843\pi\)
−0.985440 + 0.170023i \(0.945616\pi\)
\(468\) 7.34847i 0.339683i
\(469\) 8.00000 + 19.5959i 0.369406 + 0.904855i
\(470\) 0 0
\(471\) −9.00000 9.00000i −0.414698 0.414698i
\(472\) 12.2474 0.563735
\(473\) 0 0
\(474\) −12.2474 12.2474i −0.562544 0.562544i
\(475\) 0 0
\(476\) −4.89898 12.0000i −0.224544 0.550019i
\(477\) 18.0000i 0.824163i
\(478\) 6.00000i 0.274434i
\(479\) 24.4949 1.11920 0.559600 0.828763i \(-0.310955\pi\)
0.559600 + 0.828763i \(0.310955\pi\)
\(480\) 0 0
\(481\) 4.89898i 0.223374i
\(482\) 24.4949i 1.11571i
\(483\) 25.3485 + 10.6515i 1.15340 + 0.484661i
\(484\) 11.0000 0.500000
\(485\) 0 0
\(486\) 11.0227 + 11.0227i 0.500000 + 0.500000i
\(487\) 32.0000i 1.45006i −0.688718 0.725029i \(-0.741826\pi\)
0.688718 0.725029i \(-0.258174\pi\)
\(488\) 12.2474i 0.554416i
\(489\) −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
\(493\) 29.3939 1.32383
\(494\) 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 \(-0.352257\pi\)
0.447661 + 0.894203i \(0.352257\pi\)
\(500\) 0 0
\(501\) 6.00000 6.00000i 0.268060 0.268060i
\(502\) −17.1464 −0.765283
\(503\) 39.1918i 1.74748i 0.486395 + 0.873739i \(0.338311\pi\)
−0.486395 + 0.873739i \(0.661689\pi\)
\(504\) −3.00000 7.34847i −0.133631 0.327327i
\(505\) 0 0
\(506\) 0 0
\(507\) −8.57321 8.57321i −0.380750 0.380750i
\(508\) 8.00000i 0.354943i
\(509\) −12.2474 −0.542859 −0.271429 0.962458i \(-0.587496\pi\)
−0.271429 + 0.962458i \(0.587496\pi\)
\(510\) 0 0
\(511\) −24.0000 + 9.79796i −1.06170 + 0.433436i
\(512\) −1.00000 −0.0441942
\(513\) −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
\(518\) 2.00000 + 4.89898i 0.0878750 + 0.215249i
\(519\) 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 \(0.465775\pi\)
\(522\) 18.0000 0.787839
\(523\) 2.44949 0.107109 0.0535544 0.998565i \(-0.482945\pi\)
0.0535544 + 0.998565i \(0.482945\pi\)
\(524\) −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
\(532\) 2.44949 + 6.00000i 0.106199 + 0.260133i
\(533\) 12.0000 0.519778
\(534\) 0 0
\(535\) 0 0
\(536\) 8.00000i 0.345547i
\(537\) 29.3939 29.3939i 1.26844 1.26844i
\(538\) 12.2474 0.528025
\(539\) 0 0
\(540\) 0 0
\(541\) 2.00000 0.0859867 0.0429934 0.999075i \(-0.486311\pi\)
0.0429934 + 0.999075i \(0.486311\pi\)
\(542\) 24.4949i 1.05215i
\(543\) 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
\(547\) 8.00000i 0.342055i 0.985266 + 0.171028i \(0.0547087\pi\)
−0.985266 + 0.171028i \(0.945291\pi\)
\(548\) 12.0000 0.512615
\(549\) −36.7423 −1.56813
\(550\) 0 0
\(551\) −14.6969 −0.626111
\(552\) −7.34847 7.34847i −0.312772 0.312772i
\(553\) 24.4949 10.0000i 1.04163 0.425243i
\(554\) 22.0000i 0.934690i
\(555\) 0 0
\(556\) 2.44949i 0.103882i
\(557\) −18.0000 −0.762684 −0.381342 0.924434i \(-0.624538\pi\)
−0.381342 + 0.924434i \(0.624538\pi\)
\(558\) 0 0
\(559\) 9.79796i 0.414410i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 22.0454i 0.929103i −0.885546 0.464552i \(-0.846216\pi\)
0.885546 0.464552i \(-0.153784\pi\)
\(564\) 6.00000 6.00000i 0.252646 0.252646i
\(565\) 0 0
\(566\) 22.0454 0.926638
\(567\) −22.0454 + 9.00000i −0.925820 + 0.377964i
\(568\) 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
\(577\) −19.5959 −0.815789 −0.407894 0.913029i \(-0.633737\pi\)
−0.407894 + 0.913029i \(0.633737\pi\)
\(578\) 7.00000 0.291162
\(579\) 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
\(587\) 7.34847i 0.303304i 0.988434 + 0.151652i \(0.0484593\pi\)
−0.988434 + 0.151652i \(0.951541\pi\)
\(588\) 12.1237 + 0.123724i 0.499974 + 0.00510231i
\(589\) 0 0
\(590\) 0 0
\(591\) −22.0454 22.0454i −0.906827 0.906827i
\(592\) 2.00000i 0.0821995i
\(593\) 39.1918i 1.60942i 0.593671 + 0.804708i \(0.297678\pi\)
−0.593671 + 0.804708i \(0.702322\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 6.00000i 0.245770i
\(597\) 12.0000 12.0000i 0.491127 0.491127i
\(598\) −14.6969 −0.601003
\(599\) 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 \(\pi\)
\(602\) 4.00000 + 9.79796i 0.163028 + 0.399335i
\(603\) −24.0000 −0.977356
\(604\) −8.00000 −0.325515
\(605\) 0 0
\(606\) 9.00000 + 9.00000i 0.365600 + 0.365600i
\(607\) 4.89898 0.198843 0.0994217 0.995045i \(-0.468301\pi\)
0.0994217 + 0.995045i \(0.468301\pi\)
\(608\) 2.44949i 0.0993399i
\(609\) −10.6515 + 25.3485i −0.431622 + 1.02717i
\(610\) 0 0
\(611\) 12.0000i 0.485468i
\(612\) 14.6969 0.594089
\(613\) 14.0000i 0.565455i −0.959200 0.282727i \(-0.908761\pi\)
0.959200 0.282727i \(-0.0912392\pi\)
\(614\) 7.34847 0.296560
\(615\) 0 0
\(616\) 0 0
\(617\) −18.0000 −0.724653 −0.362326 0.932051i \(-0.618017\pi\)
−0.362326 + 0.932051i \(0.618017\pi\)
\(618\) 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
\(622\) 19.5959 0.785725
\(623\) 0 0
\(624\) 3.00000 + 3.00000i 0.120096 + 0.120096i
\(625\) 0 0
\(626\) 34.2929 1.37062
\(627\) 0 0
\(628\) −7.34847 −0.293236
\(629\) −9.79796 −0.390670
\(630\) 0 0
\(631\) 2.00000 0.0796187 0.0398094 0.999207i \(-0.487325\pi\)
0.0398094 + 0.999207i \(0.487325\pi\)
\(632\) −10.0000 −0.397779
\(633\) −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
\(637\) 12.2474 12.0000i 0.485262 0.475457i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 30.0000i 1.18493i −0.805597 0.592464i \(-0.798155\pi\)
0.805597 0.592464i \(-0.201845\pi\)
\(642\) −14.6969 14.6969i −0.580042 0.580042i
\(643\) −22.0454 −0.869386 −0.434693 0.900579i \(-0.643143\pi\)
−0.434693 + 0.900579i \(0.643143\pi\)
\(644\) 14.6969 6.00000i 0.579141 0.236433i
\(645\) 0 0
\(646\) −12.0000 −0.472134
\(647\) 44.0908i 1.73339i 0.498839 + 0.866694i \(0.333760\pi\)
−0.498839 + 0.866694i \(0.666240\pi\)
\(648\) 9.00000 0.353553
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 16.0000i 0.626608i
\(653\) 6.00000 0.234798 0.117399 0.993085i \(-0.462544\pi\)
0.117399 + 0.993085i \(0.462544\pi\)
\(654\) 12.2474 + 12.2474i 0.478913 + 0.478913i
\(655\) 0 0
\(656\) 4.89898 0.191273
\(657\) 29.3939i 1.14676i
\(658\) 4.89898 + 12.0000i 0.190982 + 0.467809i
\(659\) 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 \(-0.923447\pi\)
0.971220 0.238185i \(-0.0765525\pi\)
\(662\) 8.00000 0.310929
\(663\) 14.6969 14.6969i 0.570782 0.570782i
\(664\) 2.44949i 0.0950586i
\(665\) 0 0
\(666\) −6.00000 −0.232495
\(667\) 36.0000i 1.39393i
\(668\) 4.89898i 0.189547i
\(669\) 18.0000 + 18.0000i 0.695920 + 0.695920i
\(670\) 0 0
\(671\) 0 0
\(672\) −4.22474 1.77526i −0.162973 0.0684820i
\(673\) 34.0000i 1.31060i −0.755367 0.655302i \(-0.772541\pi\)
0.755367 0.655302i \(-0.227459\pi\)
\(674\) 32.0000i 1.23259i
\(675\) 0 0
\(676\) −7.00000 −0.269231
\(677\) 7.34847i 0.282425i 0.989979 + 0.141212i \(0.0451000\pi\)
−0.989979 + 0.141212i \(0.954900\pi\)
\(678\) −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
\(683\) −24.0000 −0.918334 −0.459167 0.888350i \(-0.651852\pi\)
−0.459167 + 0.888350i \(0.651852\pi\)
\(684\) −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
\(688\) 4.00000i 0.152499i
\(689\) 14.6969 0.559909
\(690\) 0 0
\(691\) 36.7423i 1.39774i 0.715246 + 0.698872i \(0.246314\pi\)
−0.715246 + 0.698872i \(0.753686\pi\)
\(692\) 22.0454i 0.838041i
\(693\) 0 0
\(694\) −12.0000 −0.455514
\(695\) 0 0
\(696\) 7.34847 7.34847i 0.278543 0.278543i
\(697\) 24.0000i 0.909065i
\(698\) 2.44949i 0.0927146i
\(699\) −29.3939 29.3939i −1.11178 1.11178i
\(700\) 0 0
\(701\) 30.0000i 1.13308i 0.824033 + 0.566542i \(0.191719\pi\)
−0.824033 + 0.566542i \(0.808281\pi\)
\(702\) 9.00000 9.00000i 0.339683 0.339683i
\(703\) 4.89898 0.184769
\(704\) 0 0
\(705\) 0 0
\(706\) 9.79796i 0.368751i
\(707\) −18.0000 + 7.34847i −0.676960 + 0.276368i
\(708\) −15.0000 15.0000i −0.563735 0.563735i
\(709\) −10.0000 −0.375558 −0.187779 0.982211i \(-0.560129\pi\)
−0.187779 + 0.982211i \(0.560129\pi\)
\(710\) 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
\(718\) 6.00000i 0.223918i
\(719\) 24.4949 0.913506 0.456753 0.889594i \(-0.349012\pi\)
0.456753 + 0.889594i \(0.349012\pi\)
\(720\) 0 0
\(721\) −24.0000 + 9.79796i −0.893807 + 0.364895i
\(722\) −13.0000 −0.483810
\(723\) 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
\(727\) 29.3939 1.09016 0.545079 0.838385i \(-0.316500\pi\)
0.545079 + 0.838385i \(0.316500\pi\)
\(728\) −6.00000 + 2.44949i −0.222375 + 0.0907841i
\(729\) 27.0000i 1.00000i
\(730\) 0 0
\(731\) −19.5959 −0.724781
\(732\) −15.0000 + 15.0000i −0.554416 + 0.554416i
\(733\) −22.0454 −0.814266 −0.407133 0.913369i \(-0.633471\pi\)
−0.407133 + 0.913369i \(0.633471\pi\)
\(734\) −4.89898 −0.180825
\(735\) 0 0
\(736\) −6.00000 −0.221163
\(737\) 0 0
\(738\) 14.6969i 0.541002i
\(739\) −20.0000 −0.735712 −0.367856 0.929883i \(-0.619908\pi\)
−0.367856 + 0.929883i \(0.619908\pi\)
\(740\) 0 0
\(741\) −7.34847 + 7.34847i −0.269953 + 0.269953i
\(742\) −14.6969 + 6.00000i −0.539542 + 0.220267i
\(743\) 6.00000 0.220119 0.110059 0.993925i \(-0.464896\pi\)
0.110059 + 0.993925i \(0.464896\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 14.0000i 0.512576i
\(747\) −7.34847 −0.268866
\(748\) 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 \(0.546628\pi\)
\(752\) 4.89898i 0.178647i
\(753\) 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
\(757\) 2.00000i 0.0726912i −0.999339 0.0363456i \(-0.988428\pi\)
0.999339 0.0363456i \(-0.0115717\pi\)
\(758\) −20.0000 −0.726433
\(759\) 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
\(763\) −24.4949 + 10.0000i −0.886775 + 0.362024i
\(764\) 0 0
\(765\) 0 0
\(766\) 34.2929i 1.23905i
\(767\) −30.0000 −1.08324
\(768\) 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
\(772\) 4.00000i 0.143963i
\(773\) 26.9444i 0.969122i 0.874757 + 0.484561i \(0.161021\pi\)
−0.874757 + 0.484561i \(0.838979\pi\)
\(774\) −12.0000 −0.431331
\(775\) 0 0
\(776\) −4.89898 −0.175863
\(777\) 3.55051 8.44949i 0.127374 0.303124i
\(778\) 6.00000i 0.215110i
\(779\) 12.0000i 0.429945i
\(780\) 0 0
\(781\) 0 0
\(782\) 29.3939i 1.05112i
\(783\) −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
\(787\) −31.8434 −1.13509 −0.567547 0.823341i \(-0.692107\pi\)
−0.567547 + 0.823341i \(0.692107\pi\)
\(788\) −18.0000 −0.641223
\(789\) −29.3939 29.3939i −1.04645 1.04645i
\(790\) 0 0
\(791\) 14.6969 6.00000i 0.522563 0.213335i
\(792\) 0 0
\(793\) 30.0000i 1.06533i
\(794\) 7.34847 0.260787
\(795\) 0 0