Properties

Label 120.2.w.a.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.a.77.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(-0.224745 + 2.22474i) q^{5} +2.44949 q^{6} +(-3.44949 + 3.44949i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})\) \(q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(-0.224745 + 2.22474i) q^{5} +2.44949 q^{6} +(-3.44949 + 3.44949i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +(-2.00000 - 2.44949i) q^{10} -1.55051 q^{11} +(-2.44949 + 2.44949i) q^{12} -6.89898i q^{14} +(3.00000 - 2.44949i) q^{15} -4.00000 q^{16} +(-3.00000 - 3.00000i) q^{18} +(4.44949 + 0.449490i) q^{20} +8.44949 q^{21} +(1.55051 - 1.55051i) q^{22} -4.89898i q^{24} +(-4.89898 - 1.00000i) q^{25} +(3.67423 - 3.67423i) q^{27} +(6.89898 + 6.89898i) q^{28} +5.34847i q^{29} +(-0.550510 + 5.44949i) q^{30} +4.89898 q^{31} +(4.00000 - 4.00000i) q^{32} +(1.89898 + 1.89898i) q^{33} +(-6.89898 - 8.44949i) q^{35} +6.00000 q^{36} +(-4.89898 + 4.00000i) q^{40} +(-8.44949 + 8.44949i) q^{42} +3.10102i q^{44} +(-6.67423 - 0.674235i) q^{45} +(4.89898 + 4.89898i) q^{48} -16.7980i q^{49} +(5.89898 - 3.89898i) q^{50} +(-2.44949 - 2.44949i) q^{53} +7.34847i q^{54} +(0.348469 - 3.44949i) q^{55} -13.7980 q^{56} +(-5.34847 - 5.34847i) q^{58} +15.3485i q^{59} +(-4.89898 - 6.00000i) q^{60} +(-4.89898 + 4.89898i) q^{62} +(-10.3485 - 10.3485i) q^{63} +8.00000i q^{64} -3.79796 q^{66} +(15.3485 + 1.55051i) q^{70} +(-6.00000 + 6.00000i) q^{72} +(11.8990 + 11.8990i) q^{73} +(4.77526 + 7.22474i) q^{75} +(5.34847 - 5.34847i) q^{77} +14.6969i q^{79} +(0.898979 - 8.89898i) q^{80} -9.00000 q^{81} +(4.00000 + 4.00000i) q^{83} -16.8990i q^{84} +(6.55051 - 6.55051i) q^{87} +(-3.10102 - 3.10102i) q^{88} +(7.34847 - 6.00000i) q^{90} +(-6.00000 - 6.00000i) q^{93} -9.79796 q^{96} +(8.79796 - 8.79796i) q^{97} +(16.7980 + 16.7980i) q^{98} -4.65153i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{2} + 4 q^{5} - 4 q^{7} + 8 q^{8}+O(q^{10}) \) 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
\(5\) −0.224745 + 2.22474i −0.100509 + 0.994936i
\(6\) 2.44949 1.00000
\(7\) −3.44949 + 3.44949i −1.30378 + 1.30378i −0.377964 + 0.925820i \(0.623376\pi\)
−0.925820 + 0.377964i \(0.876624\pi\)
\(8\) 2.00000 + 2.00000i 0.707107 + 0.707107i
\(9\) 3.00000i 1.00000i
\(10\) −2.00000 2.44949i −0.632456 0.774597i
\(11\) −1.55051 −0.467496 −0.233748 0.972297i \(-0.575099\pi\)
−0.233748 + 0.972297i \(0.575099\pi\)
\(12\) −2.44949 + 2.44949i −0.707107 + 0.707107i
\(13\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(14\) 6.89898i 1.84383i
\(15\) 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 \(0.5\pi\)
\(20\) 4.44949 + 0.449490i 0.994936 + 0.100509i
\(21\) 8.44949 1.84383
\(22\) 1.55051 1.55051i 0.330570 0.330570i
\(23\) 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
\(28\) 6.89898 + 6.89898i 1.30378 + 1.30378i
\(29\) 5.34847i 0.993186i 0.867984 + 0.496593i \(0.165416\pi\)
−0.867984 + 0.496593i \(0.834584\pi\)
\(30\) −0.550510 + 5.44949i −0.100509 + 0.994936i
\(31\) 4.89898 0.879883 0.439941 0.898027i \(-0.354999\pi\)
0.439941 + 0.898027i \(0.354999\pi\)
\(32\) 4.00000 4.00000i 0.707107 0.707107i
\(33\) 1.89898 + 1.89898i 0.330570 + 0.330570i
\(34\) 0 0
\(35\) −6.89898 8.44949i −1.16614 1.42822i
\(36\) 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 \(\pi\)
\(42\) −8.44949 + 8.44949i −1.30378 + 1.30378i
\(43\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(44\) 3.10102i 0.467496i
\(45\) −6.67423 0.674235i −0.994936 0.100509i
\(46\) 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
\(49\) 16.7980i 2.39971i
\(50\) 5.89898 3.89898i 0.834242 0.551399i
\(51\) 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
\(55\) 0.348469 3.44949i 0.0469876 0.465129i
\(56\) −13.7980 −1.84383
\(57\) 0 0
\(58\) −5.34847 5.34847i −0.702288 0.702288i
\(59\) 15.3485i 1.99820i 0.0424110 + 0.999100i \(0.486496\pi\)
−0.0424110 + 0.999100i \(0.513504\pi\)
\(60\) −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
\(63\) −10.3485 10.3485i −1.30378 1.30378i
\(64\) 8.00000i 1.00000i
\(65\) 0 0
\(66\) −3.79796 −0.467496
\(67\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 15.3485 + 1.55051i 1.83449 + 0.185321i
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) −6.00000 + 6.00000i −0.707107 + 0.707107i
\(73\) 11.8990 + 11.8990i 1.39267 + 1.39267i 0.819288 + 0.573382i \(0.194369\pi\)
0.573382 + 0.819288i \(0.305631\pi\)
\(74\) 0 0
\(75\) 4.77526 + 7.22474i 0.551399 + 0.834242i
\(76\) 0 0
\(77\) 5.34847 5.34847i 0.609515 0.609515i
\(78\) 0 0
\(79\) 14.6969i 1.65353i 0.562544 + 0.826767i \(0.309823\pi\)
−0.562544 + 0.826767i \(0.690177\pi\)
\(80\) 0.898979 8.89898i 0.100509 0.994936i
\(81\) −9.00000 −1.00000
\(82\) 0 0
\(83\) 4.00000 + 4.00000i 0.439057 + 0.439057i 0.891695 0.452638i \(-0.149517\pi\)
−0.452638 + 0.891695i \(0.649517\pi\)
\(84\) 16.8990i 1.84383i
\(85\) 0 0
\(86\) 0 0
\(87\) 6.55051 6.55051i 0.702288 0.702288i
\(88\) −3.10102 3.10102i −0.330570 0.330570i
\(89\) 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
\(97\) 8.79796 8.79796i 0.893297 0.893297i −0.101535 0.994832i \(-0.532375\pi\)
0.994832 + 0.101535i \(0.0323753\pi\)
\(98\) 16.7980 + 16.7980i 1.69685 + 1.69685i
\(99\) 4.65153i 0.467496i
\(100\) −2.00000 + 9.79796i −0.200000 + 0.979796i
\(101\) −11.5505 −1.14932 −0.574659 0.818393i \(-0.694865\pi\)
−0.574659 + 0.818393i \(0.694865\pi\)
\(102\) 0 0
\(103\) −0.348469 0.348469i −0.0343357 0.0343357i 0.689730 0.724066i \(-0.257729\pi\)
−0.724066 + 0.689730i \(0.757729\pi\)
\(104\) 0 0
\(105\) −1.89898 + 18.7980i −0.185321 + 1.83449i
\(106\) 4.89898 0.475831
\(107\) 8.00000 8.00000i 0.773389 0.773389i −0.205308 0.978697i \(-0.565820\pi\)
0.978697 + 0.205308i \(0.0658197\pi\)
\(108\) −7.34847 7.34847i −0.707107 0.707107i
\(109\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) 3.10102 + 3.79796i 0.295671 + 0.362121i
\(111\) 0 0
\(112\) 13.7980 13.7980i 1.30378 1.30378i
\(113\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 10.6969 0.993186
\(117\) 0 0
\(118\) −15.3485 15.3485i −1.41294 1.41294i
\(119\) 0 0
\(120\) 10.8990 + 1.10102i 0.994936 + 0.100509i
\(121\) −8.59592 −0.781447
\(122\) 0 0
\(123\) 0 0
\(124\) 9.79796i 0.879883i
\(125\) 3.32577 10.6742i 0.297465 0.954733i
\(126\) 20.6969 1.84383
\(127\) −13.4495 + 13.4495i −1.19345 + 1.19345i −0.217357 + 0.976092i \(0.569744\pi\)
−0.976092 + 0.217357i \(0.930256\pi\)
\(128\) −8.00000 8.00000i −0.707107 0.707107i
\(129\) 0 0
\(130\) 0 0
\(131\) 18.4495 1.61194 0.805970 0.591957i \(-0.201644\pi\)
0.805970 + 0.591957i \(0.201644\pi\)
\(132\) 3.79796 3.79796i 0.330570 0.330570i
\(133\) 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 \(0.5\pi\)
\(140\) −16.8990 + 13.7980i −1.42822 + 1.16614i
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 12.0000i 1.00000i
\(145\) −11.8990 1.20204i −0.988156 0.0998241i
\(146\) −23.7980 −1.96953
\(147\) −20.5732 + 20.5732i −1.69685 + 1.69685i
\(148\) 0 0
\(149\) 19.1464i 1.56854i −0.620422 0.784268i \(-0.713039\pi\)
0.620422 0.784268i \(-0.286961\pi\)
\(150\) −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
\(154\) 10.6969i 0.861984i
\(155\) −1.10102 + 10.8990i −0.0884361 + 0.875427i
\(156\) 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
\(165\) −4.65153 + 3.79796i −0.362121 + 0.295671i
\(166\) −8.00000 −0.620920
\(167\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(168\) 16.8990 + 16.8990i 1.30378 + 1.30378i
\(169\) 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 \(0.0212222\pi\)
0.0666220 + 0.997778i \(0.478778\pi\)
\(174\) 13.1010i 0.993186i
\(175\) 20.3485 13.4495i 1.53820 1.01669i
\(176\) 6.20204 0.467496
\(177\) 18.7980 18.7980i 1.41294 1.41294i
\(178\) 0 0
\(179\) 9.14643i 0.683636i −0.939766 0.341818i \(-0.888957\pi\)
0.939766 0.341818i \(-0.111043\pi\)
\(180\) −1.34847 + 13.3485i −0.100509 + 0.994936i
\(181\) 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
\(189\) 25.3485i 1.84383i
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) 9.79796 9.79796i 0.707107 0.707107i
\(193\) −8.10102 8.10102i −0.583124 0.583124i 0.352636 0.935760i \(-0.385285\pi\)
−0.935760 + 0.352636i \(0.885285\pi\)
\(194\) 17.5959i 1.26331i
\(195\) 0 0
\(196\) −33.5959 −2.39971
\(197\) −17.1464 + 17.1464i −1.22163 + 1.22163i −0.254581 + 0.967051i \(0.581938\pi\)
−0.967051 + 0.254581i \(0.918062\pi\)
\(198\) 4.65153 + 4.65153i 0.330570 + 0.330570i
\(199\) 14.0000i 0.992434i −0.868199 0.496217i \(-0.834722\pi\)
0.868199 0.496217i \(-0.165278\pi\)
\(200\) −7.79796 11.7980i −0.551399 0.834242i
\(201\) 0 0
\(202\) 11.5505 11.5505i 0.812691 0.812691i
\(203\) −18.4495 18.4495i −1.29490 1.29490i
\(204\) 0 0
\(205\) 0 0
\(206\) 0.696938 0.0485580
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) −16.8990 20.6969i −1.16614 1.42822i
\(211\) 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
\(217\) −16.8990 + 16.8990i −1.14718 + 1.14718i
\(218\) 0 0
\(219\) 29.1464i 1.96953i
\(220\) −6.89898 0.696938i −0.465129 0.0469876i
\(221\) 0 0
\(222\) 0 0
\(223\) −20.3485 20.3485i −1.36263 1.36263i −0.870544 0.492090i \(-0.836233\pi\)
−0.492090 0.870544i \(-0.663767\pi\)
\(224\) 27.5959i 1.84383i
\(225\) 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
\(231\) −13.1010 −0.861984
\(232\) −10.6969 + 10.6969i −0.702288 + 0.702288i
\(233\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 30.6969 1.99820
\(237\) 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 \(-0.104381\pi\)
0.946713 + 0.322078i \(0.104381\pi\)
\(242\) 8.59592 8.59592i 0.552567 0.552567i
\(243\) 11.0227 + 11.0227i 0.707107 + 0.707107i
\(244\) 0 0
\(245\) 37.3712 + 3.77526i 2.38756 + 0.241192i
\(246\) 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
\(251\) −26.0454 −1.64397 −0.821986 0.569508i \(-0.807134\pi\)
−0.821986 + 0.569508i \(0.807134\pi\)
\(252\) −20.6969 + 20.6969i −1.30378 + 1.30378i
\(253\) 0 0
\(254\) 26.8990i 1.68779i
\(255\) 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
\(261\) −16.0454 −0.993186
\(262\) −18.4495 + 18.4495i −1.13981 + 1.13981i
\(263\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(264\) 7.59592i 0.467496i
\(265\) 6.00000 4.89898i 0.368577 0.300942i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 14.6515i 0.893320i −0.894704 0.446660i \(-0.852613\pi\)
0.894704 0.446660i \(-0.147387\pi\)
\(270\) −16.3485 1.65153i −0.994936 0.100509i
\(271\) 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
\(275\) 7.59592 + 1.55051i 0.458051 + 0.0934993i
\(276\) 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
\(280\) 3.10102 30.6969i 0.185321 1.83449i
\(281\) 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
\(290\) 13.1010 10.6969i 0.769318 0.628146i
\(291\) −21.5505 −1.26331
\(292\) 23.7980 23.7980i 1.39267 1.39267i
\(293\) 22.0454 + 22.0454i 1.28791 + 1.28791i 0.936056 + 0.351850i \(0.114447\pi\)
0.351850 + 0.936056i \(0.385553\pi\)
\(294\) 41.1464i 2.39971i
\(295\) −34.1464 3.44949i −1.98808 0.200837i
\(296\) 0 0
\(297\) −5.69694 + 5.69694i −0.330570 + 0.330570i
\(298\) 19.1464 + 19.1464i 1.10912 + 1.10912i
\(299\) 0 0
\(300\) 14.4495 9.55051i 0.834242 0.551399i
\(301\) 0 0
\(302\) −2.00000 + 2.00000i −0.115087 + 0.115087i
\(303\) 14.1464 + 14.1464i 0.812691 + 0.812691i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(308\) −10.6969 10.6969i −0.609515 0.609515i
\(309\) 0.853572i 0.0485580i
\(310\) −9.79796 12.0000i −0.556487 0.681554i
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) 21.8990 + 21.8990i 1.23780 + 1.23780i 0.960897 + 0.276907i \(0.0893093\pi\)
0.276907 + 0.960897i \(0.410691\pi\)
\(314\) 0 0
\(315\) 25.3485 20.6969i 1.42822 1.16614i
\(316\) 29.3939 1.65353
\(317\) −22.0000 + 22.0000i −1.23564 + 1.23564i −0.273879 + 0.961764i \(0.588307\pi\)
−0.961764 + 0.273879i \(0.911693\pi\)
\(318\) −6.00000 6.00000i −0.336463 0.336463i
\(319\) 8.29286i 0.464311i
\(320\) −17.7980 1.79796i −0.994936 0.100509i
\(321\) −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
\(330\) 0.853572 8.44949i 0.0469876 0.465129i
\(331\) 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
\(336\) −33.7980 −1.84383
\(337\) −25.6969 + 25.6969i −1.39980 + 1.39980i −0.599208 + 0.800593i \(0.704518\pi\)
−0.800593 + 0.599208i \(0.795482\pi\)
\(338\) −13.0000 13.0000i −0.707107 0.707107i
\(339\) 0 0
\(340\) 0 0
\(341\) −7.59592 −0.411342
\(342\) 0 0
\(343\) 33.7980 + 33.7980i 1.82492 + 1.82492i
\(344\) 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 \(0.475596\pi\)
\(348\) −13.1010 13.1010i −0.702288 0.702288i
\(349\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(350\) −6.89898 + 33.7980i −0.368766 + 1.80658i
\(351\) 0 0
\(352\) −6.20204 + 6.20204i −0.330570 + 0.330570i
\(353\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(354\) 37.5959i 1.99820i
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 9.14643 + 9.14643i 0.483404 + 0.483404i
\(359\) 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
\(363\) 10.5278 + 10.5278i 0.552567 + 0.552567i
\(364\) 0 0
\(365\) −29.1464 + 23.7980i −1.52559 + 1.24564i
\(366\) 0 0
\(367\) 16.5505 16.5505i 0.863930 0.863930i −0.127862 0.991792i \(-0.540812\pi\)
0.991792 + 0.127862i \(0.0408116\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 16.8990 0.877351
\(372\) −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
\(378\) −25.3485 25.3485i −1.30378 1.30378i
\(379\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) 0 0
\(381\) 32.9444 1.68779
\(382\) 0 0
\(383\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(384\) 19.5959i 1.00000i
\(385\) 10.6969 + 13.1010i 0.545166 + 0.667690i
\(386\) 16.2020 0.824662
\(387\) 0 0
\(388\) −17.5959 17.5959i −0.893297 0.893297i
\(389\) 39.1464i 1.98480i −0.123043 0.992401i \(-0.539265\pi\)
0.123043 0.992401i \(-0.460735\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 33.5959 33.5959i 1.69685 1.69685i
\(393\) −22.5959 22.5959i −1.13981 1.13981i
\(394\) 34.2929i 1.72765i
\(395\) −32.6969 3.30306i −1.64516 0.166195i
\(396\) −9.30306 −0.467496
\(397\) 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
\(404\) 23.1010i 1.14932i
\(405\) 2.02270 20.0227i 0.100509 0.994936i
\(406\) 36.8990 1.83127
\(407\) 0 0
\(408\) 0 0
\(409\) 39.1918i 1.93791i 0.247234 + 0.968956i \(0.420478\pi\)
−0.247234 + 0.968956i \(0.579522\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −0.696938 + 0.696938i −0.0343357 + 0.0343357i
\(413\) −52.9444 52.9444i −2.60522 2.60522i
\(414\) 0 0
\(415\) −9.79796 + 8.00000i −0.480963 + 0.392705i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 35.3485i 1.72689i 0.504447 + 0.863443i \(0.331697\pi\)
−0.504447 + 0.863443i \(0.668303\pi\)
\(420\) 37.5959 + 3.79796i 1.83449 + 0.185321i
\(421\) 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
\(433\) −12.5959 12.5959i −0.605321 0.605321i 0.336399 0.941720i \(-0.390791\pi\)
−0.941720 + 0.336399i \(0.890791\pi\)
\(434\) 33.7980i 1.62235i
\(435\) 13.1010 + 16.0454i 0.628146 + 0.769318i
\(436\) 0 0
\(437\) 0 0
\(438\) 29.1464 + 29.1464i 1.39267 + 1.39267i
\(439\) 34.0000i 1.62273i −0.584539 0.811366i \(-0.698725\pi\)
0.584539 0.811366i \(-0.301275\pi\)
\(440\) 7.59592 6.20204i 0.362121 0.295671i
\(441\) 50.3939 2.39971
\(442\) 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
\(446\) 40.6969 1.92706
\(447\) −23.4495 + 23.4495i −1.10912 + 1.10912i
\(448\) −27.5959 27.5959i −1.30378 1.30378i
\(449\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(450\) 11.6969 + 17.6969i 0.551399 + 0.834242i
\(451\) 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
\(457\) 28.7980 28.7980i 1.34711 1.34711i 0.458329 0.888783i \(-0.348448\pi\)
0.888783 0.458329i \(-0.151552\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 12.9444 0.602880 0.301440 0.953485i \(-0.402533\pi\)
0.301440 + 0.953485i \(0.402533\pi\)
\(462\) 13.1010 13.1010i 0.609515 0.609515i
\(463\) 4.14643 + 4.14643i 0.192701 + 0.192701i 0.796862 0.604161i \(-0.206492\pi\)
−0.604161 + 0.796862i \(0.706492\pi\)
\(464\) 21.3939i 0.993186i
\(465\) 14.6969 12.0000i 0.681554 0.556487i
\(466\) 0 0
\(467\) 28.0000 28.0000i 1.29569 1.29569i 0.364471 0.931215i \(-0.381250\pi\)
0.931215 0.364471i \(-0.118750\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −30.6969 + 30.6969i −1.41294 + 1.41294i
\(473\) 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 \(0.5\pi\)
\(480\) 2.20204 21.7980i 0.100509 0.994936i
\(481\) 0 0
\(482\) −29.3939 + 29.3939i −1.33885 + 1.33885i
\(483\) 0 0
\(484\) 17.1918i 0.781447i
\(485\) 17.5959 + 21.5505i 0.798989 + 0.978558i
\(486\) −22.0454 −1.00000
\(487\) 21.0454 21.0454i 0.953658 0.953658i −0.0453143 0.998973i \(-0.514429\pi\)
0.998973 + 0.0453143i \(0.0144289\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) −41.1464 + 33.5959i −1.85881 + 1.51771i
\(491\) 42.9444 1.93805 0.969027 0.246957i \(-0.0794305\pi\)
0.969027 + 0.246957i \(0.0794305\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 10.3485 + 1.04541i 0.465129 + 0.0469876i
\(496\) −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 \(0.5\pi\)
\(500\) −21.3485 6.65153i −0.954733 0.297465i
\(501\) 0 0
\(502\) 26.0454 26.0454i 1.16246 1.16246i
\(503\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(504\) 41.3939i 1.84383i
\(505\) 2.59592 25.6969i 0.115517 1.14350i
\(506\) 0 0
\(507\) 15.9217 15.9217i 0.707107 0.707107i
\(508\) 26.8990 + 26.8990i 1.19345 + 1.19345i
\(509\) 29.8434i 1.32278i 0.750040 + 0.661392i \(0.230034\pi\)
−0.750040 + 0.661392i \(0.769966\pi\)
\(510\) 0 0
\(511\) −82.0908 −3.63148
\(512\) −16.0000 + 16.0000i −0.707107 + 0.707107i
\(513\) 0 0
\(514\) 0 0
\(515\) 0.853572 0.696938i 0.0376129 0.0307108i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 34.2929i 1.50529i
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 16.0454 16.0454i 0.702288 0.702288i
\(523\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(524\) 36.8990i 1.61194i
\(525\) −41.3939 8.44949i −1.80658 0.368766i
\(526\) 0 0
\(527\) 0 0
\(528\) −7.59592 7.59592i −0.330570 0.330570i
\(529\) 23.0000i 1.00000i
\(530\) −1.10102 + 10.8990i −0.0478253 + 0.473421i
\(531\) −46.0454 −1.99820
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 16.0000 + 19.5959i 0.691740 + 0.847205i
\(536\) 0 0
\(537\) −11.2020 + 11.2020i −0.483404 + 0.483404i
\(538\) 14.6515 + 14.6515i 0.631672 + 0.631672i
\(539\) 26.0454i 1.12186i
\(540\) 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
\(550\) −9.14643 + 6.04541i −0.390005 + 0.257777i
\(551\) 0 0
\(552\) 0 0
\(553\) −50.6969 50.6969i −2.15585 2.15585i
\(554\) 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
\(560\) 27.5959 + 33.7980i 1.16614 + 1.42822i
\(561\) 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
\(567\) 31.0454 31.0454i 1.30378 1.30378i
\(568\) 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
\(577\) 4.30306 4.30306i 0.179139 0.179139i −0.611842 0.790980i \(-0.709571\pi\)
0.790980 + 0.611842i \(0.209571\pi\)
\(578\) 17.0000 + 17.0000i 0.707107 + 0.707107i
\(579\) 19.8434i 0.824662i
\(580\) −2.40408 + 23.7980i −0.0998241 + 0.988156i
\(581\) −27.5959 −1.14487
\(582\) 21.5505 21.5505i 0.893297 0.893297i
\(583\) 3.79796 + 3.79796i 0.157295 + 0.157295i
\(584\) 47.5959i 1.96953i
\(585\) 0 0
\(586\) −44.0908 −1.82137
\(587\) −32.0000 + 32.0000i −1.32078 + 1.32078i −0.407638 + 0.913144i \(0.633647\pi\)
−0.913144 + 0.407638i \(0.866353\pi\)
\(588\) 41.1464 + 41.1464i 1.69685 + 1.69685i
\(589\) 0 0
\(590\) 37.5959 30.6969i 1.54780 1.26377i
\(591\) 42.0000 1.72765
\(592\) 0 0
\(593\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(594\) 11.3939i 0.467496i
\(595\) 0 0
\(596\) −38.2929 −1.56854
\(597\) −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
\(605\) 1.93189 19.1237i 0.0785424 0.777490i
\(606\) −28.2929 −1.14932
\(607\) 11.0454 11.0454i 0.448319 0.448319i −0.446476 0.894795i \(-0.647321\pi\)
0.894795 + 0.446476i \(0.147321\pi\)
\(608\) 0 0
\(609\) 45.1918i 1.83127i
\(610\) 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
\(616\) 21.3939 0.861984
\(617\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(618\) −0.853572 0.853572i −0.0343357 0.0343357i
\(619\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(620\) 21.7980 + 2.20204i 0.875427 + 0.0884361i
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 23.0000 + 9.79796i 0.920000 + 0.391918i
\(626\) −43.7980 −1.75052
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) −4.65153 + 46.0454i −0.185321 + 1.83449i
\(631\) 4.89898 0.195025 0.0975126 0.995234i \(-0.468911\pi\)
0.0975126 + 0.995234i \(0.468911\pi\)
\(632\) −29.3939 + 29.3939i −1.16923 + 1.16923i
\(633\) 0 0
\(634\) 44.0000i 1.74746i
\(635\) −26.8990 32.9444i −1.06745 1.30736i
\(636\) 12.0000 0.475831
\(637\) 0 0
\(638\) 8.29286 + 8.29286i 0.328317 + 0.328317i
\(639\) 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
\(649\) 23.7980i 0.934152i
\(650\) 0 0
\(651\) 41.3939 1.62235
\(652\) 0 0
\(653\) 34.0000 + 34.0000i 1.33052 + 1.33052i 0.904901 + 0.425622i \(0.139945\pi\)
0.425622 + 0.904901i \(0.360055\pi\)
\(654\) 0 0
\(655\) −4.14643 + 41.0454i −0.162014 + 1.60378i
\(656\) 0 0
\(657\) −35.6969 + 35.6969i −1.39267 + 1.39267i
\(658\) 0 0
\(659\) 49.1464i 1.91447i −0.289307 0.957237i \(-0.593425\pi\)
0.289307 0.957237i \(-0.406575\pi\)
\(660\) 7.59592 + 9.30306i 0.295671 + 0.362121i
\(661\) 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
\(669\) 49.8434i 1.92706i
\(670\) 0 0
\(671\) 0 0
\(672\) 33.7980 33.7980i 1.30378 1.30378i
\(673\) −2.59592 2.59592i −0.100065 0.100065i 0.655302 0.755367i \(-0.272541\pi\)
−0.755367 + 0.655302i \(0.772541\pi\)
\(674\) 51.3939i 1.97962i
\(675\) −21.6742 + 14.3258i −0.834242 + 0.551399i
\(676\) 26.0000 1.00000
\(677\) −2.00000 + 2.00000i −0.0768662 + 0.0768662i −0.744495 0.667628i \(-0.767310\pi\)
0.667628 + 0.744495i \(0.267310\pi\)
\(678\) 0 0
\(679\) 60.6969i 2.32933i
\(680\) 0 0
\(681\) −18.0000 −0.689761
\(682\) 7.59592 7.59592i 0.290863 0.290863i
\(683\) 4.00000 + 4.00000i 0.153056 + 0.153056i 0.779481 0.626426i \(-0.215483\pi\)
−0.626426 + 0.779481i \(0.715483\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −67.5959 −2.58082
\(687\) 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
\(693\) 16.0454 + 16.0454i 0.609515 + 0.609515i
\(694\) 34.2929i 1.30174i
\(695\) 0 0
\(696\) 26.2020 0.993186
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −26.8990 40.6969i −1.01669 1.53820i
\(701\) 52.9444 1.99968 0.999841 0.0178345i \(-0.00567720\pi\)
0.999841 + 0.0178345i \(0.00567720\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 12.4041i 0.467496i
\(705\) 0 0
\(706\) 0 0
\(707\) 39.8434 39.8434i 1.49846 1.49846i
\(708\) −37.5959 37.5959i −1.41294 1.41294i
\(709\) 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
\(716\) −18.2929 −0.683636
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 26.6969 + 2.69694i 0.994936 + 0.100509i
\(721\) 2.40408 0.0895327
\(722\) 19.0000 19.0000i 0.707107 0.707107i
\(723\) −36.0000 36.0000i −1.33885 1.33885i
\(724\) 0 0
\(725\) 5.34847 26.2020i 0.198637 0.973119i
\(726\) −21.0556 −0.781447
\(727\) −27.9444 + 27.9444i −1.03640 + 1.03640i −0.0370879 + 0.999312i \(0.511808\pi\)
−0.999312 + 0.0370879i \(0.988192\pi\)
\(728\) 0 0
\(729\) 27.0000i 1.00000i
\(730\) 5.34847 52.9444i 0.197956 1.95956i
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(734\) 33.1010i 1.22178i
\(735\) −41.1464 50.3939i −1.51771 1.85881i
\(736\) 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
\(742\) −16.8990 + 16.8990i −0.620381 + 0.620381i
\(743\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(744\) 24.0000i 0.879883i
\(745\) 42.5959 + 4.30306i 1.56059 + 0.157652i
\(746\) 0 0
\(747\) −12.0000 + 12.0000i −0.439057 + 0.439057i
\(748\) 0 0
\(749\) 55.1918i 2.01667i
\(750\) 8.14643 26.1464i 0.297465 0.954733i
\(751\) 53.8888 1.96643 0.983215 0.182453i \(-0.0584036\pi\)
0.983215 + 0.182453i \(0.0584036\pi\)
\(752\) 0 0
\(753\) 31.8990 + 31.8990i 1.16246 + 1.16246i
\(754\) 0 0
\(755\) −0.449490 + 4.44949i −0.0163586 + 0.161934i
\(756\) 50.6969 1.84383
\(757\) 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 \(\pi\)
\(762\) −32.9444 + 32.9444i −1.19345 + 1.19345i
\(763\) 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 \(0.844689\pi\)
\(770\) −23.7980 2.40408i −0.857619 0.0866371i
\(771\) 0 0
\(772\) −16.2020 + 16.2020i −0.583124 + 0.583124i
\(773\) 14.0000 + 14.0000i 0.503545 + 0.503545i 0.912538 0.408993i \(-0.134120\pi\)
−0.408993 + 0.912538i \(0.634120\pi\)
\(774\) 0 0
\(775\) −24.0000 4.89898i −0.862105 0.175977i
\(776\) 35.1918 1.26331
\(777\) 0 0
\(778\) 39.1464 + 39.1464i 1.40347 + 1.40347i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 19.6515 + 19.6515i 0.702288 + 0.702288i
\(784\) 67.1918i 2.39971i
\(785\) 0 0
\(786\) 45.1918 1.61194
\(787\) 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
\(792\) 9.30306 9.30306i 0.330570 0.330570i
\(793\) 0 0
\(794\) 0 0
\(795\) −13.3485