Properties

Label 120.2.w.b.53.1
Level $120$
Weight $2$
Character 120.53
Analytic conductor $0.958$
Analytic rank $0$
Dimension $4$
CM discriminant -24
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 120.w (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.958204824255\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(i, \sqrt{6})\)
Defining polynomial: \( x^{4} + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{4}]$

Embedding invariants

Embedding label 53.1
Root \(-1.22474 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 120.53
Dual form 120.2.w.b.77.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 - 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(-2.22474 + 0.224745i) q^{5} -2.44949 q^{6} +(1.44949 - 1.44949i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})\) \(q+(1.00000 - 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(-2.22474 + 0.224745i) q^{5} -2.44949 q^{6} +(1.44949 - 1.44949i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +(-2.00000 + 2.44949i) q^{10} +6.44949 q^{11} +(-2.44949 + 2.44949i) q^{12} -2.89898i q^{14} +(3.00000 + 2.44949i) q^{15} -4.00000 q^{16} +(3.00000 + 3.00000i) q^{18} +(0.449490 + 4.44949i) q^{20} -3.55051 q^{21} +(6.44949 - 6.44949i) q^{22} +4.89898i q^{24} +(4.89898 - 1.00000i) q^{25} +(3.67423 - 3.67423i) q^{27} +(-2.89898 - 2.89898i) q^{28} +9.34847i q^{29} +(5.44949 - 0.550510i) q^{30} -4.89898 q^{31} +(-4.00000 + 4.00000i) q^{32} +(-7.89898 - 7.89898i) q^{33} +(-2.89898 + 3.55051i) q^{35} +6.00000 q^{36} +(4.89898 + 4.00000i) q^{40} +(-3.55051 + 3.55051i) q^{42} -12.8990i q^{44} +(-0.674235 - 6.67423i) q^{45} +(4.89898 + 4.89898i) q^{48} +2.79796i q^{49} +(3.89898 - 5.89898i) q^{50} +(-2.44949 - 2.44949i) q^{53} -7.34847i q^{54} +(-14.3485 + 1.44949i) q^{55} -5.79796 q^{56} +(9.34847 + 9.34847i) q^{58} -0.651531i q^{59} +(4.89898 - 6.00000i) q^{60} +(-4.89898 + 4.89898i) q^{62} +(4.34847 + 4.34847i) q^{63} +8.00000i q^{64} -15.7980 q^{66} +(0.651531 + 6.44949i) q^{70} +(6.00000 - 6.00000i) q^{72} +(2.10102 + 2.10102i) q^{73} +(-7.22474 - 4.77526i) q^{75} +(9.34847 - 9.34847i) q^{77} -14.6969i q^{79} +(8.89898 - 0.898979i) q^{80} -9.00000 q^{81} +(-4.00000 - 4.00000i) q^{83} +7.10102i q^{84} +(11.4495 - 11.4495i) q^{87} +(-12.8990 - 12.8990i) q^{88} +(-7.34847 - 6.00000i) q^{90} +(6.00000 + 6.00000i) q^{93} +9.79796 q^{96} +(-10.7980 + 10.7980i) q^{97} +(2.79796 + 2.79796i) q^{98} +19.3485i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{2} - 4 q^{5} - 4 q^{7} - 8 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{2} - 4 q^{5} - 4 q^{7} - 8 q^{8} - 8 q^{10} + 16 q^{11} + 12 q^{15} - 16 q^{16} + 12 q^{18} - 8 q^{20} - 24 q^{21} + 16 q^{22} + 8 q^{28} + 12 q^{30} - 16 q^{32} - 12 q^{33} + 8 q^{35} + 24 q^{36} - 24 q^{42} + 12 q^{45} - 4 q^{50} - 28 q^{55} + 16 q^{56} + 8 q^{58} - 12 q^{63} - 24 q^{66} + 32 q^{70} + 24 q^{72} + 28 q^{73} - 24 q^{75} + 8 q^{77} + 16 q^{80} - 36 q^{81} - 16 q^{83} + 36 q^{87} - 32 q^{88} + 24 q^{93} - 4 q^{97} - 28 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/120\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(41\) \(61\) \(97\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 1.00000i 0.707107 0.707107i
\(3\) −1.22474 1.22474i −0.707107 0.707107i
\(4\) 2.00000i 1.00000i
\(5\) −2.22474 + 0.224745i −0.994936 + 0.100509i
\(6\) −2.44949 −1.00000
\(7\) 1.44949 1.44949i 0.547856 0.547856i −0.377964 0.925820i \(-0.623376\pi\)
0.925820 + 0.377964i \(0.123376\pi\)
\(8\) −2.00000 2.00000i −0.707107 0.707107i
\(9\) 3.00000i 1.00000i
\(10\) −2.00000 + 2.44949i −0.632456 + 0.774597i
\(11\) 6.44949 1.94459 0.972297 0.233748i \(-0.0750991\pi\)
0.972297 + 0.233748i \(0.0750991\pi\)
\(12\) −2.44949 + 2.44949i −0.707107 + 0.707107i
\(13\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(14\) 2.89898i 0.774785i
\(15\) 3.00000 + 2.44949i 0.774597 + 0.632456i
\(16\) −4.00000 −1.00000
\(17\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(18\) 3.00000 + 3.00000i 0.707107 + 0.707107i
\(19\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 0.449490 + 4.44949i 0.100509 + 0.994936i
\(21\) −3.55051 −0.774785
\(22\) 6.44949 6.44949i 1.37504 1.37504i
\(23\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(24\) 4.89898i 1.00000i
\(25\) 4.89898 1.00000i 0.979796 0.200000i
\(26\) 0 0
\(27\) 3.67423 3.67423i 0.707107 0.707107i
\(28\) −2.89898 2.89898i −0.547856 0.547856i
\(29\) 9.34847i 1.73597i 0.496593 + 0.867984i \(0.334584\pi\)
−0.496593 + 0.867984i \(0.665416\pi\)
\(30\) 5.44949 0.550510i 0.994936 0.100509i
\(31\) −4.89898 −0.879883 −0.439941 0.898027i \(-0.645001\pi\)
−0.439941 + 0.898027i \(0.645001\pi\)
\(32\) −4.00000 + 4.00000i −0.707107 + 0.707107i
\(33\) −7.89898 7.89898i −1.37504 1.37504i
\(34\) 0 0
\(35\) −2.89898 + 3.55051i −0.490017 + 0.600146i
\(36\) 6.00000 1.00000
\(37\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 4.89898 + 4.00000i 0.774597 + 0.632456i
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) −3.55051 + 3.55051i −0.547856 + 0.547856i
\(43\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(44\) 12.8990i 1.94459i
\(45\) −0.674235 6.67423i −0.100509 0.994936i
\(46\) 0 0
\(47\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(48\) 4.89898 + 4.89898i 0.707107 + 0.707107i
\(49\) 2.79796i 0.399708i
\(50\) 3.89898 5.89898i 0.551399 0.834242i
\(51\) 0 0
\(52\) 0 0
\(53\) −2.44949 2.44949i −0.336463 0.336463i 0.518571 0.855034i \(-0.326464\pi\)
−0.855034 + 0.518571i \(0.826464\pi\)
\(54\) 7.34847i 1.00000i
\(55\) −14.3485 + 1.44949i −1.93475 + 0.195449i
\(56\) −5.79796 −0.774785
\(57\) 0 0
\(58\) 9.34847 + 9.34847i 1.22751 + 1.22751i
\(59\) 0.651531i 0.0848221i −0.999100 0.0424110i \(-0.986496\pi\)
0.999100 0.0424110i \(-0.0135039\pi\)
\(60\) 4.89898 6.00000i 0.632456 0.774597i
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) −4.89898 + 4.89898i −0.622171 + 0.622171i
\(63\) 4.34847 + 4.34847i 0.547856 + 0.547856i
\(64\) 8.00000i 1.00000i
\(65\) 0 0
\(66\) −15.7980 −1.94459
\(67\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0.651531 + 6.44949i 0.0778728 + 0.770861i
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 6.00000 6.00000i 0.707107 0.707107i
\(73\) 2.10102 + 2.10102i 0.245906 + 0.245906i 0.819288 0.573382i \(-0.194369\pi\)
−0.573382 + 0.819288i \(0.694369\pi\)
\(74\) 0 0
\(75\) −7.22474 4.77526i −0.834242 0.551399i
\(76\) 0 0
\(77\) 9.34847 9.34847i 1.06536 1.06536i
\(78\) 0 0
\(79\) 14.6969i 1.65353i −0.562544 0.826767i \(-0.690177\pi\)
0.562544 0.826767i \(-0.309823\pi\)
\(80\) 8.89898 0.898979i 0.994936 0.100509i
\(81\) −9.00000 −1.00000
\(82\) 0 0
\(83\) −4.00000 4.00000i −0.439057 0.439057i 0.452638 0.891695i \(-0.350483\pi\)
−0.891695 + 0.452638i \(0.850483\pi\)
\(84\) 7.10102i 0.774785i
\(85\) 0 0
\(86\) 0 0
\(87\) 11.4495 11.4495i 1.22751 1.22751i
\(88\) −12.8990 12.8990i −1.37504 1.37504i
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) −7.34847 6.00000i −0.774597 0.632456i
\(91\) 0 0
\(92\) 0 0
\(93\) 6.00000 + 6.00000i 0.622171 + 0.622171i
\(94\) 0 0
\(95\) 0 0
\(96\) 9.79796 1.00000
\(97\) −10.7980 + 10.7980i −1.09637 + 1.09637i −0.101535 + 0.994832i \(0.532375\pi\)
−0.994832 + 0.101535i \(0.967625\pi\)
\(98\) 2.79796 + 2.79796i 0.282637 + 0.282637i
\(99\) 19.3485i 1.94459i
\(100\) −2.00000 9.79796i −0.200000 0.979796i
\(101\) 16.4495 1.63679 0.818393 0.574659i \(-0.194865\pi\)
0.818393 + 0.574659i \(0.194865\pi\)
\(102\) 0 0
\(103\) 14.3485 + 14.3485i 1.41380 + 1.41380i 0.724066 + 0.689730i \(0.242271\pi\)
0.689730 + 0.724066i \(0.257729\pi\)
\(104\) 0 0
\(105\) 7.89898 0.797959i 0.770861 0.0778728i
\(106\) −4.89898 −0.475831
\(107\) −8.00000 + 8.00000i −0.773389 + 0.773389i −0.978697 0.205308i \(-0.934180\pi\)
0.205308 + 0.978697i \(0.434180\pi\)
\(108\) −7.34847 7.34847i −0.707107 0.707107i
\(109\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) −12.8990 + 15.7980i −1.22987 + 1.50628i
\(111\) 0 0
\(112\) −5.79796 + 5.79796i −0.547856 + 0.547856i
\(113\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 18.6969 1.73597
\(117\) 0 0
\(118\) −0.651531 0.651531i −0.0599783 0.0599783i
\(119\) 0 0
\(120\) −1.10102 10.8990i −0.100509 0.994936i
\(121\) 30.5959 2.78145
\(122\) 0 0
\(123\) 0 0
\(124\) 9.79796i 0.879883i
\(125\) −10.6742 + 3.32577i −0.954733 + 0.297465i
\(126\) 8.69694 0.774785
\(127\) −8.55051 + 8.55051i −0.758735 + 0.758735i −0.976092 0.217357i \(-0.930256\pi\)
0.217357 + 0.976092i \(0.430256\pi\)
\(128\) 8.00000 + 8.00000i 0.707107 + 0.707107i
\(129\) 0 0
\(130\) 0 0
\(131\) −13.5505 −1.18391 −0.591957 0.805970i \(-0.701644\pi\)
−0.591957 + 0.805970i \(0.701644\pi\)
\(132\) −15.7980 + 15.7980i −1.37504 + 1.37504i
\(133\) 0 0
\(134\) 0 0
\(135\) −7.34847 + 9.00000i −0.632456 + 0.774597i
\(136\) 0 0
\(137\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 7.10102 + 5.79796i 0.600146 + 0.490017i
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 12.0000i 1.00000i
\(145\) −2.10102 20.7980i −0.174480 1.72718i
\(146\) 4.20204 0.347763
\(147\) 3.42679 3.42679i 0.282637 0.282637i
\(148\) 0 0
\(149\) 15.1464i 1.24084i −0.784268 0.620422i \(-0.786961\pi\)
0.784268 0.620422i \(-0.213039\pi\)
\(150\) −12.0000 + 2.44949i −0.979796 + 0.200000i
\(151\) 2.00000 0.162758 0.0813788 0.996683i \(-0.474068\pi\)
0.0813788 + 0.996683i \(0.474068\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 18.6969i 1.50664i
\(155\) 10.8990 1.10102i 0.875427 0.0884361i
\(156\) 0 0
\(157\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(158\) −14.6969 14.6969i −1.16923 1.16923i
\(159\) 6.00000i 0.475831i
\(160\) 8.00000 9.79796i 0.632456 0.774597i
\(161\) 0 0
\(162\) −9.00000 + 9.00000i −0.707107 + 0.707107i
\(163\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(164\) 0 0
\(165\) 19.3485 + 15.7980i 1.50628 + 1.22987i
\(166\) −8.00000 −0.620920
\(167\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(168\) 7.10102 + 7.10102i 0.547856 + 0.547856i
\(169\) 13.0000i 1.00000i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −14.0000 14.0000i −1.06440 1.06440i −0.997778 0.0666220i \(-0.978778\pi\)
−0.0666220 0.997778i \(-0.521222\pi\)
\(174\) 22.8990i 1.73597i
\(175\) 5.65153 8.55051i 0.427216 0.646358i
\(176\) −25.7980 −1.94459
\(177\) −0.797959 + 0.797959i −0.0599783 + 0.0599783i
\(178\) 0 0
\(179\) 25.1464i 1.87953i −0.341818 0.939766i \(-0.611043\pi\)
0.341818 0.939766i \(-0.388957\pi\)
\(180\) −13.3485 + 1.34847i −0.994936 + 0.100509i
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 12.0000 0.879883
\(187\) 0 0
\(188\) 0 0
\(189\) 10.6515i 0.774785i
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) 9.79796 9.79796i 0.707107 0.707107i
\(193\) −17.8990 17.8990i −1.28840 1.28840i −0.935760 0.352636i \(-0.885285\pi\)
−0.352636 0.935760i \(-0.614715\pi\)
\(194\) 21.5959i 1.55050i
\(195\) 0 0
\(196\) 5.59592 0.399708
\(197\) −17.1464 + 17.1464i −1.22163 + 1.22163i −0.254581 + 0.967051i \(0.581938\pi\)
−0.967051 + 0.254581i \(0.918062\pi\)
\(198\) 19.3485 + 19.3485i 1.37504 + 1.37504i
\(199\) 14.0000i 0.992434i −0.868199 0.496217i \(-0.834722\pi\)
0.868199 0.496217i \(-0.165278\pi\)
\(200\) −11.7980 7.79796i −0.834242 0.551399i
\(201\) 0 0
\(202\) 16.4495 16.4495i 1.15738 1.15738i
\(203\) 13.5505 + 13.5505i 0.951059 + 0.951059i
\(204\) 0 0
\(205\) 0 0
\(206\) 28.6969 1.99941
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 7.10102 8.69694i 0.490017 0.600146i
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) −4.89898 + 4.89898i −0.336463 + 0.336463i
\(213\) 0 0
\(214\) 16.0000i 1.09374i
\(215\) 0 0
\(216\) −14.6969 −1.00000
\(217\) −7.10102 + 7.10102i −0.482049 + 0.482049i
\(218\) 0 0
\(219\) 5.14643i 0.347763i
\(220\) 2.89898 + 28.6969i 0.195449 + 1.93475i
\(221\) 0 0
\(222\) 0 0
\(223\) −5.65153 5.65153i −0.378454 0.378454i 0.492090 0.870544i \(-0.336233\pi\)
−0.870544 + 0.492090i \(0.836233\pi\)
\(224\) 11.5959i 0.774785i
\(225\) 3.00000 + 14.6969i 0.200000 + 0.979796i
\(226\) 0 0
\(227\) 7.34847 7.34847i 0.487735 0.487735i −0.419856 0.907591i \(-0.637919\pi\)
0.907591 + 0.419856i \(0.137919\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(230\) 0 0
\(231\) −22.8990 −1.50664
\(232\) 18.6969 18.6969i 1.22751 1.22751i
\(233\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −1.30306 −0.0848221
\(237\) −18.0000 + 18.0000i −1.16923 + 1.16923i
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) −12.0000 9.79796i −0.774597 0.632456i
\(241\) −29.3939 −1.89343 −0.946713 0.322078i \(-0.895619\pi\)
−0.946713 + 0.322078i \(0.895619\pi\)
\(242\) 30.5959 30.5959i 1.96678 1.96678i
\(243\) 11.0227 + 11.0227i 0.707107 + 0.707107i
\(244\) 0 0
\(245\) −0.628827 6.22474i −0.0401743 0.397684i
\(246\) 0 0
\(247\) 0 0
\(248\) 9.79796 + 9.79796i 0.622171 + 0.622171i
\(249\) 9.79796i 0.620920i
\(250\) −7.34847 + 14.0000i −0.464758 + 0.885438i
\(251\) −18.0454 −1.13902 −0.569508 0.821986i \(-0.692866\pi\)
−0.569508 + 0.821986i \(0.692866\pi\)
\(252\) 8.69694 8.69694i 0.547856 0.547856i
\(253\) 0 0
\(254\) 17.1010i 1.07301i
\(255\) 0 0
\(256\) 16.0000 1.00000
\(257\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −28.0454 −1.73597
\(262\) −13.5505 + 13.5505i −0.837153 + 0.837153i
\(263\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(264\) 31.5959i 1.94459i
\(265\) 6.00000 + 4.89898i 0.368577 + 0.300942i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 29.3485i 1.78941i 0.446660 + 0.894704i \(0.352613\pi\)
−0.446660 + 0.894704i \(0.647387\pi\)
\(270\) 1.65153 + 16.3485i 0.100509 + 0.994936i
\(271\) 22.0000 1.33640 0.668202 0.743980i \(-0.267064\pi\)
0.668202 + 0.743980i \(0.267064\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 31.5959 6.44949i 1.90531 0.388919i
\(276\) 0 0
\(277\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(278\) 0 0
\(279\) 14.6969i 0.879883i
\(280\) 12.8990 1.30306i 0.770861 0.0778728i
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −12.0000 12.0000i −0.707107 0.707107i
\(289\) 17.0000i 1.00000i
\(290\) −22.8990 18.6969i −1.34467 1.09792i
\(291\) 26.4495 1.55050
\(292\) 4.20204 4.20204i 0.245906 0.245906i
\(293\) 22.0454 + 22.0454i 1.28791 + 1.28791i 0.936056 + 0.351850i \(0.114447\pi\)
0.351850 + 0.936056i \(0.385553\pi\)
\(294\) 6.85357i 0.399708i
\(295\) 0.146428 + 1.44949i 0.00852538 + 0.0843926i
\(296\) 0 0
\(297\) 23.6969 23.6969i 1.37504 1.37504i
\(298\) −15.1464 15.1464i −0.877409 0.877409i
\(299\) 0 0
\(300\) −9.55051 + 14.4495i −0.551399 + 0.834242i
\(301\) 0 0
\(302\) 2.00000 2.00000i 0.115087 0.115087i
\(303\) −20.1464 20.1464i −1.15738 1.15738i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(308\) −18.6969 18.6969i −1.06536 1.06536i
\(309\) 35.1464i 1.99941i
\(310\) 9.79796 12.0000i 0.556487 0.681554i
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) 12.1010 + 12.1010i 0.683990 + 0.683990i 0.960897 0.276907i \(-0.0893093\pi\)
−0.276907 + 0.960897i \(0.589309\pi\)
\(314\) 0 0
\(315\) −10.6515 8.69694i −0.600146 0.490017i
\(316\) −29.3939 −1.65353
\(317\) 22.0000 22.0000i 1.23564 1.23564i 0.273879 0.961764i \(-0.411693\pi\)
0.961764 0.273879i \(-0.0883068\pi\)
\(318\) 6.00000 + 6.00000i 0.336463 + 0.336463i
\(319\) 60.2929i 3.37575i
\(320\) −1.79796 17.7980i −0.100509 0.994936i
\(321\) 19.5959 1.09374
\(322\) 0 0
\(323\) 0 0
\(324\) 18.0000i 1.00000i
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 35.1464 3.55051i 1.93475 0.195449i
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) −8.00000 + 8.00000i −0.439057 + 0.439057i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 14.2020 0.774785
\(337\) 3.69694 3.69694i 0.201385 0.201385i −0.599208 0.800593i \(-0.704518\pi\)
0.800593 + 0.599208i \(0.204518\pi\)
\(338\) 13.0000 + 13.0000i 0.707107 + 0.707107i
\(339\) 0 0
\(340\) 0 0
\(341\) −31.5959 −1.71101
\(342\) 0 0
\(343\) 14.2020 + 14.2020i 0.766838 + 0.766838i
\(344\) 0 0
\(345\) 0 0
\(346\) −28.0000 −1.50529
\(347\) −17.1464 + 17.1464i −0.920468 + 0.920468i −0.997062 0.0765939i \(-0.975596\pi\)
0.0765939 + 0.997062i \(0.475596\pi\)
\(348\) −22.8990 22.8990i −1.22751 1.22751i
\(349\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(350\) −2.89898 14.2020i −0.154957 0.759131i
\(351\) 0 0
\(352\) −25.7980 + 25.7980i −1.37504 + 1.37504i
\(353\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(354\) 1.59592i 0.0848221i
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) −25.1464 25.1464i −1.32903 1.32903i
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) −12.0000 + 14.6969i −0.632456 + 0.774597i
\(361\) −19.0000 −1.00000
\(362\) 0 0
\(363\) −37.4722 37.4722i −1.96678 1.96678i
\(364\) 0 0
\(365\) −5.14643 4.20204i −0.269376 0.219945i
\(366\) 0 0
\(367\) 21.4495 21.4495i 1.11965 1.11965i 0.127862 0.991792i \(-0.459188\pi\)
0.991792 0.127862i \(-0.0408116\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −7.10102 −0.368667
\(372\) 12.0000 12.0000i 0.622171 0.622171i
\(373\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(374\) 0 0
\(375\) 17.1464 + 9.00000i 0.885438 + 0.464758i
\(376\) 0 0
\(377\) 0 0
\(378\) −10.6515 10.6515i −0.547856 0.547856i
\(379\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) 0 0
\(381\) 20.9444 1.07301
\(382\) 0 0
\(383\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(384\) 19.5959i 1.00000i
\(385\) −18.6969 + 22.8990i −0.952884 + 1.16704i
\(386\) −35.7980 −1.82207
\(387\) 0 0
\(388\) 21.5959 + 21.5959i 1.09637 + 1.09637i
\(389\) 4.85357i 0.246086i 0.992401 + 0.123043i \(0.0392653\pi\)
−0.992401 + 0.123043i \(0.960735\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 5.59592 5.59592i 0.282637 0.282637i
\(393\) 16.5959 + 16.5959i 0.837153 + 0.837153i
\(394\) 34.2929i 1.72765i
\(395\) 3.30306 + 32.6969i 0.166195 + 1.64516i
\(396\) 38.6969 1.94459
\(397\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(398\) −14.0000 14.0000i −0.701757 0.701757i
\(399\) 0 0
\(400\) −19.5959 + 4.00000i −0.979796 + 0.200000i
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 32.8990i 1.63679i
\(405\) 20.0227 2.02270i 0.994936 0.100509i
\(406\) 27.1010 1.34500
\(407\) 0 0
\(408\) 0 0
\(409\) 39.1918i 1.93791i −0.247234 0.968956i \(-0.579522\pi\)
0.247234 0.968956i \(-0.420478\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 28.6969 28.6969i 1.41380 1.41380i
\(413\) −0.944387 0.944387i −0.0464703 0.0464703i
\(414\) 0 0
\(415\) 9.79796 + 8.00000i 0.480963 + 0.392705i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 20.6515i 1.00889i −0.863443 0.504447i \(-0.831697\pi\)
0.863443 0.504447i \(-0.168303\pi\)
\(420\) −1.59592 15.7980i −0.0778728 0.770861i
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 9.79796i 0.475831i
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 16.0000 + 16.0000i 0.773389 + 0.773389i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) −14.6969 + 14.6969i −0.707107 + 0.707107i
\(433\) 26.5959 + 26.5959i 1.27812 + 1.27812i 0.941720 + 0.336399i \(0.109209\pi\)
0.336399 + 0.941720i \(0.390791\pi\)
\(434\) 14.2020i 0.681720i
\(435\) −22.8990 + 28.0454i −1.09792 + 1.34467i
\(436\) 0 0
\(437\) 0 0
\(438\) −5.14643 5.14643i −0.245906 0.245906i
\(439\) 34.0000i 1.62273i −0.584539 0.811366i \(-0.698725\pi\)
0.584539 0.811366i \(-0.301275\pi\)
\(440\) 31.5959 + 25.7980i 1.50628 + 1.22987i
\(441\) −8.39388 −0.399708
\(442\) 0 0
\(443\) 22.0454 + 22.0454i 1.04741 + 1.04741i 0.998819 + 0.0485901i \(0.0154728\pi\)
0.0485901 + 0.998819i \(0.484527\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −11.3031 −0.535215
\(447\) −18.5505 + 18.5505i −0.877409 + 0.877409i
\(448\) 11.5959 + 11.5959i 0.547856 + 0.547856i
\(449\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(450\) 17.6969 + 11.6969i 0.834242 + 0.551399i
\(451\) 0 0
\(452\) 0 0
\(453\) −2.44949 2.44949i −0.115087 0.115087i
\(454\) 14.6969i 0.689761i
\(455\) 0 0
\(456\) 0 0
\(457\) 9.20204 9.20204i 0.430453 0.430453i −0.458329 0.888783i \(-0.651552\pi\)
0.888783 + 0.458329i \(0.151552\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 40.9444 1.90697 0.953485 0.301440i \(-0.0974673\pi\)
0.953485 + 0.301440i \(0.0974673\pi\)
\(462\) −22.8990 + 22.8990i −1.06536 + 1.06536i
\(463\) −30.1464 30.1464i −1.40102 1.40102i −0.796862 0.604161i \(-0.793508\pi\)
−0.604161 0.796862i \(-0.706492\pi\)
\(464\) 37.3939i 1.73597i
\(465\) −14.6969 12.0000i −0.681554 0.556487i
\(466\) 0 0
\(467\) −28.0000 + 28.0000i −1.29569 + 1.29569i −0.364471 + 0.931215i \(0.618750\pi\)
−0.931215 + 0.364471i \(0.881250\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −1.30306 + 1.30306i −0.0599783 + 0.0599783i
\(473\) 0 0
\(474\) 36.0000i 1.65353i
\(475\) 0 0
\(476\) 0 0
\(477\) 7.34847 7.34847i 0.336463 0.336463i
\(478\) 0 0
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) −21.7980 + 2.20204i −0.994936 + 0.100509i
\(481\) 0 0
\(482\) −29.3939 + 29.3939i −1.33885 + 1.33885i
\(483\) 0 0
\(484\) 61.1918i 2.78145i
\(485\) 21.5959 26.4495i 0.980620 1.20101i
\(486\) 22.0454 1.00000
\(487\) −23.0454 + 23.0454i −1.04429 + 1.04429i −0.0453143 + 0.998973i \(0.514429\pi\)
−0.998973 + 0.0453143i \(0.985571\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) −6.85357 5.59592i −0.309613 0.252798i
\(491\) 10.9444 0.493913 0.246957 0.969027i \(-0.420569\pi\)
0.246957 + 0.969027i \(0.420569\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) −4.34847 43.0454i −0.195449 1.93475i
\(496\) 19.5959 0.879883
\(497\) 0 0
\(498\) 9.79796 + 9.79796i 0.439057 + 0.439057i
\(499\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(500\) 6.65153 + 21.3485i 0.297465 + 0.954733i
\(501\) 0 0
\(502\) −18.0454 + 18.0454i −0.805406 + 0.805406i
\(503\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(504\) 17.3939i 0.774785i
\(505\) −36.5959 + 3.69694i −1.62850 + 0.164512i
\(506\) 0 0
\(507\) 15.9217 15.9217i 0.707107 0.707107i
\(508\) 17.1010 + 17.1010i 0.758735 + 0.758735i
\(509\) 33.8434i 1.50008i 0.661392 + 0.750040i \(0.269966\pi\)
−0.661392 + 0.750040i \(0.730034\pi\)
\(510\) 0 0
\(511\) 6.09082 0.269442
\(512\) 16.0000 16.0000i 0.707107 0.707107i
\(513\) 0 0
\(514\) 0 0
\(515\) −35.1464 28.6969i −1.54874 1.26454i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 34.2929i 1.50529i
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) −28.0454 + 28.0454i −1.22751 + 1.22751i
\(523\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(524\) 27.1010i 1.18391i
\(525\) −17.3939 + 3.55051i −0.759131 + 0.154957i
\(526\) 0 0
\(527\) 0 0
\(528\) 31.5959 + 31.5959i 1.37504 + 1.37504i
\(529\) 23.0000i 1.00000i
\(530\) 10.8990 1.10102i 0.473421 0.0478253i
\(531\) 1.95459 0.0848221
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 16.0000 19.5959i 0.691740 0.847205i
\(536\) 0 0
\(537\) −30.7980 + 30.7980i −1.32903 + 1.32903i
\(538\) 29.3485 + 29.3485i 1.26530 + 1.26530i
\(539\) 18.0454i 0.777271i
\(540\) 18.0000 + 14.6969i 0.774597 + 0.632456i
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 22.0000 22.0000i 0.944981 0.944981i
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 25.1464 38.0454i 1.07225 1.62226i
\(551\) 0 0
\(552\) 0 0
\(553\) −21.3031 21.3031i −0.905898 0.905898i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 31.8434 31.8434i 1.34925 1.34925i 0.462767 0.886480i \(-0.346857\pi\)
0.886480 0.462767i \(-0.153143\pi\)
\(558\) −14.6969 14.6969i −0.622171 0.622171i
\(559\) 0 0
\(560\) 11.5959 14.2020i 0.490017 0.600146i
\(561\) 0 0
\(562\) 0 0
\(563\) −26.9444 26.9444i −1.13557 1.13557i −0.989235 0.146336i \(-0.953252\pi\)
−0.146336 0.989235i \(-0.546748\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −13.0454 + 13.0454i −0.547856 + 0.547856i
\(568\) 0 0
\(569\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −24.0000 −1.00000
\(577\) 33.6969 33.6969i 1.40282 1.40282i 0.611842 0.790980i \(-0.290429\pi\)
0.790980 0.611842i \(-0.209571\pi\)
\(578\) −17.0000 17.0000i −0.707107 0.707107i
\(579\) 43.8434i 1.82207i
\(580\) −41.5959 + 4.20204i −1.72718 + 0.174480i
\(581\) −11.5959 −0.481080
\(582\) 26.4495 26.4495i 1.09637 1.09637i
\(583\) −15.7980 15.7980i −0.654285 0.654285i
\(584\) 8.40408i 0.347763i
\(585\) 0 0
\(586\) 44.0908 1.82137
\(587\) 32.0000 32.0000i 1.32078 1.32078i 0.407638 0.913144i \(-0.366353\pi\)
0.913144 0.407638i \(-0.133647\pi\)
\(588\) −6.85357 6.85357i −0.282637 0.282637i
\(589\) 0 0
\(590\) 1.59592 + 1.30306i 0.0657029 + 0.0536462i
\(591\) 42.0000 1.72765
\(592\) 0 0
\(593\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(594\) 47.3939i 1.94459i
\(595\) 0 0
\(596\) −30.2929 −1.24084
\(597\) −17.1464 + 17.1464i −0.701757 + 0.701757i
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 4.89898 + 24.0000i 0.200000 + 0.979796i
\(601\) 2.00000 0.0815817 0.0407909 0.999168i \(-0.487012\pi\)
0.0407909 + 0.999168i \(0.487012\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 4.00000i 0.162758i
\(605\) −68.0681 + 6.87628i −2.76736 + 0.279560i
\(606\) −40.2929 −1.63679
\(607\) −33.0454 + 33.0454i −1.34127 + 1.34127i −0.446476 + 0.894795i \(0.647321\pi\)
−0.894795 + 0.446476i \(0.852679\pi\)
\(608\) 0 0
\(609\) 33.1918i 1.34500i
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) −37.3939 −1.50664
\(617\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(618\) −35.1464 35.1464i −1.41380 1.41380i
\(619\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(620\) −2.20204 21.7980i −0.0884361 0.875427i
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 23.0000 9.79796i 0.920000 0.391918i
\(626\) 24.2020 0.967308
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) −19.3485 + 1.95459i −0.770861 + 0.0778728i
\(631\) −4.89898 −0.195025 −0.0975126 0.995234i \(-0.531089\pi\)
−0.0975126 + 0.995234i \(0.531089\pi\)
\(632\) −29.3939 + 29.3939i −1.16923 + 1.16923i
\(633\) 0 0
\(634\) 44.0000i 1.74746i
\(635\) 17.1010 20.9444i 0.678633 0.831153i
\(636\) 12.0000 0.475831
\(637\) 0 0
\(638\) 60.2929 + 60.2929i 2.38702 + 2.38702i
\(639\) 0 0
\(640\) −19.5959 16.0000i −0.774597 0.632456i
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 19.5959 19.5959i 0.773389 0.773389i
\(643\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(648\) 18.0000 + 18.0000i 0.707107 + 0.707107i
\(649\) 4.20204i 0.164945i
\(650\) 0 0
\(651\) 17.3939 0.681720
\(652\) 0 0
\(653\) −34.0000 34.0000i −1.33052 1.33052i −0.904901 0.425622i \(-0.860055\pi\)
−0.425622 0.904901i \(-0.639945\pi\)
\(654\) 0 0
\(655\) 30.1464 3.04541i 1.17792 0.118994i
\(656\) 0 0
\(657\) −6.30306 + 6.30306i −0.245906 + 0.245906i
\(658\) 0 0
\(659\) 14.8536i 0.578613i 0.957237 + 0.289307i \(0.0934247\pi\)
−0.957237 + 0.289307i \(0.906575\pi\)
\(660\) 31.5959 38.6969i 1.22987 1.50628i
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 16.0000i 0.620920i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 13.8434i 0.535215i
\(670\) 0 0
\(671\) 0 0
\(672\) 14.2020 14.2020i 0.547856 0.547856i
\(673\) 36.5959 + 36.5959i 1.41067 + 1.41067i 0.755367 + 0.655302i \(0.227459\pi\)
0.655302 + 0.755367i \(0.272541\pi\)
\(674\) 7.39388i 0.284801i
\(675\) 14.3258 21.6742i 0.551399 0.834242i
\(676\) 26.0000 1.00000
\(677\) 2.00000 2.00000i 0.0768662 0.0768662i −0.667628 0.744495i \(-0.732690\pi\)
0.744495 + 0.667628i \(0.232690\pi\)
\(678\) 0 0
\(679\) 31.3031i 1.20130i
\(680\) 0 0
\(681\) −18.0000 −0.689761
\(682\) −31.5959 + 31.5959i −1.20987 + 1.20987i
\(683\) −4.00000 4.00000i −0.153056 0.153056i 0.626426 0.779481i \(-0.284517\pi\)
−0.779481 + 0.626426i \(0.784517\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 28.4041 1.08447
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) −28.0000 + 28.0000i −1.06440 + 1.06440i
\(693\) 28.0454 + 28.0454i 1.06536 + 1.06536i
\(694\) 34.2929i 1.30174i
\(695\) 0 0
\(696\) −45.7980 −1.73597
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −17.1010 11.3031i −0.646358 0.427216i
\(701\) 0.944387 0.0356690 0.0178345 0.999841i \(-0.494323\pi\)
0.0178345 + 0.999841i \(0.494323\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 51.5959i 1.94459i
\(705\) 0 0
\(706\) 0 0
\(707\) 23.8434 23.8434i 0.896722 0.896722i
\(708\) 1.59592 + 1.59592i 0.0599783 + 0.0599783i
\(709\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(710\) 0 0
\(711\) 44.0908 1.65353
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −50.2929 −1.87953
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 2.69694 + 26.6969i 0.100509 + 0.994936i
\(721\) 41.5959 1.54911
\(722\) −19.0000 + 19.0000i −0.707107 + 0.707107i
\(723\) 36.0000 + 36.0000i 1.33885 + 1.33885i
\(724\) 0 0
\(725\) 9.34847 + 45.7980i 0.347193 + 1.70089i
\(726\) −74.9444 −2.78145
\(727\) 25.9444 25.9444i 0.962224 0.962224i −0.0370879 0.999312i \(-0.511808\pi\)
0.999312 + 0.0370879i \(0.0118082\pi\)
\(728\) 0 0
\(729\) 27.0000i 1.00000i
\(730\) −9.34847 + 0.944387i −0.346002 + 0.0349533i
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(734\) 42.8990i 1.58343i
\(735\) −6.85357 + 8.39388i −0.252798 + 0.309613i
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −7.10102 + 7.10102i −0.260687 + 0.260687i
\(743\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(744\) 24.0000i 0.879883i
\(745\) 3.40408 + 33.6969i 0.124716 + 1.23456i
\(746\) 0 0
\(747\) 12.0000 12.0000i 0.439057 0.439057i
\(748\) 0 0
\(749\) 23.1918i 0.847411i
\(750\) 26.1464 8.14643i 0.954733 0.297465i
\(751\) −53.8888 −1.96643 −0.983215 0.182453i \(-0.941596\pi\)
−0.983215 + 0.182453i \(0.941596\pi\)
\(752\) 0 0
\(753\) 22.1010 + 22.1010i 0.805406 + 0.805406i
\(754\) 0 0
\(755\) −4.44949 + 0.449490i −0.161934 + 0.0163586i
\(756\) −21.3031 −0.774785
\(757\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 20.9444 20.9444i 0.758735 0.758735i
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −19.5959 19.5959i −0.707107 0.707107i
\(769\) 26.0000i 0.937584i 0.883309 + 0.468792i \(0.155311\pi\)
−0.883309 + 0.468792i \(0.844689\pi\)
\(770\) 4.20204 + 41.5959i 0.151431 + 1.49901i
\(771\) 0 0
\(772\) −35.7980 + 35.7980i −1.28840 + 1.28840i
\(773\) −14.0000 14.0000i −0.503545 0.503545i 0.408993 0.912538i \(-0.365880\pi\)
−0.912538 + 0.408993i \(0.865880\pi\)
\(774\) 0 0
\(775\) −24.0000 + 4.89898i −0.862105 + 0.175977i
\(776\) 43.1918 1.55050
\(777\) 0 0
\(778\) 4.85357 + 4.85357i 0.174009 + 0.174009i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 34.3485 + 34.3485i 1.22751 + 1.22751i
\(784\) 11.1918i 0.399708i
\(785\) 0 0
\(786\) 33.1918 1.18391
\(787\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(788\) 34.2929 + 34.2929i 1.22163 + 1.22163i
\(789\) 0 0
\(790\) 36.0000 + 29.3939i 1.28082 + 1.04579i
\(791\) 0 0
\(792\) 38.6969 38.6969i 1.37504 1.37504i
\(793\) 0 0
\(794\) 0 0
\(795\) &