Properties

Label 1680.2.f.e.881.2
Level $1680$
Weight $2$
Character 1680.881
Analytic conductor $13.415$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1680.f (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.4148675396\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{5})\)
Defining polynomial: \(x^{4} + 3 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 881.2
Root \(1.61803i\) of defining polynomial
Character \(\chi\) \(=\) 1680.881
Dual form 1680.2.f.e.881.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.61803 + 0.618034i) q^{3} -1.00000 q^{5} +(-2.61803 - 0.381966i) q^{7} +(2.23607 - 2.00000i) q^{9} +O(q^{10})\) \(q+(-1.61803 + 0.618034i) q^{3} -1.00000 q^{5} +(-2.61803 - 0.381966i) q^{7} +(2.23607 - 2.00000i) q^{9} +4.47214i q^{11} -1.23607i q^{13} +(1.61803 - 0.618034i) q^{15} -5.23607 q^{17} -8.47214i q^{19} +(4.47214 - 1.00000i) q^{21} -4.00000i q^{23} +1.00000 q^{25} +(-2.38197 + 4.61803i) q^{27} +7.70820i q^{29} +2.76393i q^{31} +(-2.76393 - 7.23607i) q^{33} +(2.61803 + 0.381966i) q^{35} +0.763932 q^{37} +(0.763932 + 2.00000i) q^{39} +2.47214 q^{41} +4.94427 q^{43} +(-2.23607 + 2.00000i) q^{45} -6.47214 q^{47} +(6.70820 + 2.00000i) q^{49} +(8.47214 - 3.23607i) q^{51} -0.472136i q^{53} -4.47214i q^{55} +(5.23607 + 13.7082i) q^{57} +4.47214 q^{59} +7.23607i q^{61} +(-6.61803 + 4.38197i) q^{63} +1.23607i q^{65} +12.0000 q^{67} +(2.47214 + 6.47214i) q^{69} -7.23607i q^{71} -11.2361i q^{73} +(-1.61803 + 0.618034i) q^{75} +(1.70820 - 11.7082i) q^{77} +8.94427 q^{79} +(1.00000 - 8.94427i) q^{81} +14.6525 q^{83} +5.23607 q^{85} +(-4.76393 - 12.4721i) q^{87} +5.52786 q^{89} +(-0.472136 + 3.23607i) q^{91} +(-1.70820 - 4.47214i) q^{93} +8.47214i q^{95} +0.763932i q^{97} +(8.94427 + 10.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{3} - 4q^{5} - 6q^{7} + O(q^{10}) \) \( 4q - 2q^{3} - 4q^{5} - 6q^{7} + 2q^{15} - 12q^{17} + 4q^{25} - 14q^{27} - 20q^{33} + 6q^{35} + 12q^{37} + 12q^{39} - 8q^{41} - 16q^{43} - 8q^{47} + 16q^{51} + 12q^{57} - 22q^{63} + 48q^{67} - 8q^{69} - 2q^{75} - 20q^{77} + 4q^{81} - 4q^{83} + 12q^{85} - 28q^{87} + 40q^{89} + 16q^{91} + 20q^{93} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times\).

\(n\) \(241\) \(337\) \(421\) \(1121\) \(1471\)
\(\chi(n)\) \(-1\) \(1\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.61803 + 0.618034i −0.934172 + 0.356822i
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −2.61803 0.381966i −0.989524 0.144370i
\(8\) 0 0
\(9\) 2.23607 2.00000i 0.745356 0.666667i
\(10\) 0 0
\(11\) 4.47214i 1.34840i 0.738549 + 0.674200i \(0.235511\pi\)
−0.738549 + 0.674200i \(0.764489\pi\)
\(12\) 0 0
\(13\) 1.23607i 0.342824i −0.985199 0.171412i \(-0.945167\pi\)
0.985199 0.171412i \(-0.0548329\pi\)
\(14\) 0 0
\(15\) 1.61803 0.618034i 0.417775 0.159576i
\(16\) 0 0
\(17\) −5.23607 −1.26993 −0.634967 0.772540i \(-0.718986\pi\)
−0.634967 + 0.772540i \(0.718986\pi\)
\(18\) 0 0
\(19\) 8.47214i 1.94364i −0.235722 0.971821i \(-0.575745\pi\)
0.235722 0.971821i \(-0.424255\pi\)
\(20\) 0 0
\(21\) 4.47214 1.00000i 0.975900 0.218218i
\(22\) 0 0
\(23\) 4.00000i 0.834058i −0.908893 0.417029i \(-0.863071\pi\)
0.908893 0.417029i \(-0.136929\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −2.38197 + 4.61803i −0.458410 + 0.888741i
\(28\) 0 0
\(29\) 7.70820i 1.43138i 0.698419 + 0.715689i \(0.253887\pi\)
−0.698419 + 0.715689i \(0.746113\pi\)
\(30\) 0 0
\(31\) 2.76393i 0.496417i 0.968707 + 0.248208i \(0.0798418\pi\)
−0.968707 + 0.248208i \(0.920158\pi\)
\(32\) 0 0
\(33\) −2.76393 7.23607i −0.481139 1.25964i
\(34\) 0 0
\(35\) 2.61803 + 0.381966i 0.442529 + 0.0645640i
\(36\) 0 0
\(37\) 0.763932 0.125590 0.0627948 0.998026i \(-0.479999\pi\)
0.0627948 + 0.998026i \(0.479999\pi\)
\(38\) 0 0
\(39\) 0.763932 + 2.00000i 0.122327 + 0.320256i
\(40\) 0 0
\(41\) 2.47214 0.386083 0.193041 0.981191i \(-0.438165\pi\)
0.193041 + 0.981191i \(0.438165\pi\)
\(42\) 0 0
\(43\) 4.94427 0.753994 0.376997 0.926214i \(-0.376957\pi\)
0.376997 + 0.926214i \(0.376957\pi\)
\(44\) 0 0
\(45\) −2.23607 + 2.00000i −0.333333 + 0.298142i
\(46\) 0 0
\(47\) −6.47214 −0.944058 −0.472029 0.881583i \(-0.656478\pi\)
−0.472029 + 0.881583i \(0.656478\pi\)
\(48\) 0 0
\(49\) 6.70820 + 2.00000i 0.958315 + 0.285714i
\(50\) 0 0
\(51\) 8.47214 3.23607i 1.18634 0.453140i
\(52\) 0 0
\(53\) 0.472136i 0.0648529i −0.999474 0.0324264i \(-0.989677\pi\)
0.999474 0.0324264i \(-0.0103235\pi\)
\(54\) 0 0
\(55\) 4.47214i 0.603023i
\(56\) 0 0
\(57\) 5.23607 + 13.7082i 0.693534 + 1.81570i
\(58\) 0 0
\(59\) 4.47214 0.582223 0.291111 0.956689i \(-0.405975\pi\)
0.291111 + 0.956689i \(0.405975\pi\)
\(60\) 0 0
\(61\) 7.23607i 0.926484i 0.886232 + 0.463242i \(0.153314\pi\)
−0.886232 + 0.463242i \(0.846686\pi\)
\(62\) 0 0
\(63\) −6.61803 + 4.38197i −0.833794 + 0.552076i
\(64\) 0 0
\(65\) 1.23607i 0.153315i
\(66\) 0 0
\(67\) 12.0000 1.46603 0.733017 0.680211i \(-0.238112\pi\)
0.733017 + 0.680211i \(0.238112\pi\)
\(68\) 0 0
\(69\) 2.47214 + 6.47214i 0.297610 + 0.779154i
\(70\) 0 0
\(71\) 7.23607i 0.858763i −0.903123 0.429382i \(-0.858732\pi\)
0.903123 0.429382i \(-0.141268\pi\)
\(72\) 0 0
\(73\) 11.2361i 1.31508i −0.753419 0.657541i \(-0.771597\pi\)
0.753419 0.657541i \(-0.228403\pi\)
\(74\) 0 0
\(75\) −1.61803 + 0.618034i −0.186834 + 0.0713644i
\(76\) 0 0
\(77\) 1.70820 11.7082i 0.194668 1.33427i
\(78\) 0 0
\(79\) 8.94427 1.00631 0.503155 0.864196i \(-0.332173\pi\)
0.503155 + 0.864196i \(0.332173\pi\)
\(80\) 0 0
\(81\) 1.00000 8.94427i 0.111111 0.993808i
\(82\) 0 0
\(83\) 14.6525 1.60832 0.804159 0.594414i \(-0.202616\pi\)
0.804159 + 0.594414i \(0.202616\pi\)
\(84\) 0 0
\(85\) 5.23607 0.567931
\(86\) 0 0
\(87\) −4.76393 12.4721i −0.510747 1.33715i
\(88\) 0 0
\(89\) 5.52786 0.585952 0.292976 0.956120i \(-0.405354\pi\)
0.292976 + 0.956120i \(0.405354\pi\)
\(90\) 0 0
\(91\) −0.472136 + 3.23607i −0.0494933 + 0.339232i
\(92\) 0 0
\(93\) −1.70820 4.47214i −0.177132 0.463739i
\(94\) 0 0
\(95\) 8.47214i 0.869223i
\(96\) 0 0
\(97\) 0.763932i 0.0775655i 0.999248 + 0.0387828i \(0.0123480\pi\)
−0.999248 + 0.0387828i \(0.987652\pi\)
\(98\) 0 0
\(99\) 8.94427 + 10.0000i 0.898933 + 1.00504i
\(100\) 0 0
\(101\) 12.4721 1.24102 0.620512 0.784197i \(-0.286925\pi\)
0.620512 + 0.784197i \(0.286925\pi\)
\(102\) 0 0
\(103\) 14.6525i 1.44375i 0.692023 + 0.721876i \(0.256720\pi\)
−0.692023 + 0.721876i \(0.743280\pi\)
\(104\) 0 0
\(105\) −4.47214 + 1.00000i −0.436436 + 0.0975900i
\(106\) 0 0
\(107\) 11.4164i 1.10367i 0.833955 + 0.551833i \(0.186071\pi\)
−0.833955 + 0.551833i \(0.813929\pi\)
\(108\) 0 0
\(109\) 4.47214 0.428353 0.214176 0.976795i \(-0.431293\pi\)
0.214176 + 0.976795i \(0.431293\pi\)
\(110\) 0 0
\(111\) −1.23607 + 0.472136i −0.117322 + 0.0448132i
\(112\) 0 0
\(113\) 2.94427i 0.276974i 0.990364 + 0.138487i \(0.0442239\pi\)
−0.990364 + 0.138487i \(0.955776\pi\)
\(114\) 0 0
\(115\) 4.00000i 0.373002i
\(116\) 0 0
\(117\) −2.47214 2.76393i −0.228549 0.255526i
\(118\) 0 0
\(119\) 13.7082 + 2.00000i 1.25663 + 0.183340i
\(120\) 0 0
\(121\) −9.00000 −0.818182
\(122\) 0 0
\(123\) −4.00000 + 1.52786i −0.360668 + 0.137763i
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 0.291796 0.0258927 0.0129464 0.999916i \(-0.495879\pi\)
0.0129464 + 0.999916i \(0.495879\pi\)
\(128\) 0 0
\(129\) −8.00000 + 3.05573i −0.704361 + 0.269042i
\(130\) 0 0
\(131\) 5.41641 0.473234 0.236617 0.971603i \(-0.423961\pi\)
0.236617 + 0.971603i \(0.423961\pi\)
\(132\) 0 0
\(133\) −3.23607 + 22.1803i −0.280603 + 1.92328i
\(134\) 0 0
\(135\) 2.38197 4.61803i 0.205007 0.397457i
\(136\) 0 0
\(137\) 3.52786i 0.301406i −0.988579 0.150703i \(-0.951846\pi\)
0.988579 0.150703i \(-0.0481537\pi\)
\(138\) 0 0
\(139\) 11.5279i 0.977781i 0.872345 + 0.488890i \(0.162598\pi\)
−0.872345 + 0.488890i \(0.837402\pi\)
\(140\) 0 0
\(141\) 10.4721 4.00000i 0.881913 0.336861i
\(142\) 0 0
\(143\) 5.52786 0.462263
\(144\) 0 0
\(145\) 7.70820i 0.640131i
\(146\) 0 0
\(147\) −12.0902 + 0.909830i −0.997180 + 0.0750415i
\(148\) 0 0
\(149\) 4.29180i 0.351598i 0.984426 + 0.175799i \(0.0562508\pi\)
−0.984426 + 0.175799i \(0.943749\pi\)
\(150\) 0 0
\(151\) −20.9443 −1.70442 −0.852210 0.523199i \(-0.824738\pi\)
−0.852210 + 0.523199i \(0.824738\pi\)
\(152\) 0 0
\(153\) −11.7082 + 10.4721i −0.946552 + 0.846622i
\(154\) 0 0
\(155\) 2.76393i 0.222004i
\(156\) 0 0
\(157\) 9.23607i 0.737118i −0.929604 0.368559i \(-0.879851\pi\)
0.929604 0.368559i \(-0.120149\pi\)
\(158\) 0 0
\(159\) 0.291796 + 0.763932i 0.0231409 + 0.0605838i
\(160\) 0 0
\(161\) −1.52786 + 10.4721i −0.120413 + 0.825320i
\(162\) 0 0
\(163\) 10.4721 0.820241 0.410120 0.912031i \(-0.365487\pi\)
0.410120 + 0.912031i \(0.365487\pi\)
\(164\) 0 0
\(165\) 2.76393 + 7.23607i 0.215172 + 0.563327i
\(166\) 0 0
\(167\) −0.944272 −0.0730700 −0.0365350 0.999332i \(-0.511632\pi\)
−0.0365350 + 0.999332i \(0.511632\pi\)
\(168\) 0 0
\(169\) 11.4721 0.882472
\(170\) 0 0
\(171\) −16.9443 18.9443i −1.29576 1.44870i
\(172\) 0 0
\(173\) 9.41641 0.715916 0.357958 0.933738i \(-0.383473\pi\)
0.357958 + 0.933738i \(0.383473\pi\)
\(174\) 0 0
\(175\) −2.61803 0.381966i −0.197905 0.0288739i
\(176\) 0 0
\(177\) −7.23607 + 2.76393i −0.543896 + 0.207750i
\(178\) 0 0
\(179\) 14.9443i 1.11699i −0.829509 0.558494i \(-0.811380\pi\)
0.829509 0.558494i \(-0.188620\pi\)
\(180\) 0 0
\(181\) 16.1803i 1.20268i −0.798995 0.601338i \(-0.794635\pi\)
0.798995 0.601338i \(-0.205365\pi\)
\(182\) 0 0
\(183\) −4.47214 11.7082i −0.330590 0.865495i
\(184\) 0 0
\(185\) −0.763932 −0.0561654
\(186\) 0 0
\(187\) 23.4164i 1.71238i
\(188\) 0 0
\(189\) 8.00000 11.1803i 0.581914 0.813250i
\(190\) 0 0
\(191\) 7.23607i 0.523584i 0.965124 + 0.261792i \(0.0843134\pi\)
−0.965124 + 0.261792i \(0.915687\pi\)
\(192\) 0 0
\(193\) −6.00000 −0.431889 −0.215945 0.976406i \(-0.569283\pi\)
−0.215945 + 0.976406i \(0.569283\pi\)
\(194\) 0 0
\(195\) −0.763932 2.00000i −0.0547063 0.143223i
\(196\) 0 0
\(197\) 3.52786i 0.251350i −0.992071 0.125675i \(-0.959890\pi\)
0.992071 0.125675i \(-0.0401096\pi\)
\(198\) 0 0
\(199\) 22.1803i 1.57232i 0.618021 + 0.786161i \(0.287935\pi\)
−0.618021 + 0.786161i \(0.712065\pi\)
\(200\) 0 0
\(201\) −19.4164 + 7.41641i −1.36953 + 0.523113i
\(202\) 0 0
\(203\) 2.94427 20.1803i 0.206647 1.41638i
\(204\) 0 0
\(205\) −2.47214 −0.172661
\(206\) 0 0
\(207\) −8.00000 8.94427i −0.556038 0.621670i
\(208\) 0 0
\(209\) 37.8885 2.62081
\(210\) 0 0
\(211\) 8.00000 0.550743 0.275371 0.961338i \(-0.411199\pi\)
0.275371 + 0.961338i \(0.411199\pi\)
\(212\) 0 0
\(213\) 4.47214 + 11.7082i 0.306426 + 0.802233i
\(214\) 0 0
\(215\) −4.94427 −0.337197
\(216\) 0 0
\(217\) 1.05573 7.23607i 0.0716675 0.491216i
\(218\) 0 0
\(219\) 6.94427 + 18.1803i 0.469250 + 1.22851i
\(220\) 0 0
\(221\) 6.47214i 0.435363i
\(222\) 0 0
\(223\) 17.7082i 1.18583i −0.805265 0.592915i \(-0.797977\pi\)
0.805265 0.592915i \(-0.202023\pi\)
\(224\) 0 0
\(225\) 2.23607 2.00000i 0.149071 0.133333i
\(226\) 0 0
\(227\) 0.763932 0.0507039 0.0253520 0.999679i \(-0.491929\pi\)
0.0253520 + 0.999679i \(0.491929\pi\)
\(228\) 0 0
\(229\) 8.76393i 0.579137i −0.957157 0.289568i \(-0.906488\pi\)
0.957157 0.289568i \(-0.0935118\pi\)
\(230\) 0 0
\(231\) 4.47214 + 20.0000i 0.294245 + 1.31590i
\(232\) 0 0
\(233\) 11.5279i 0.755215i −0.925966 0.377608i \(-0.876747\pi\)
0.925966 0.377608i \(-0.123253\pi\)
\(234\) 0 0
\(235\) 6.47214 0.422196
\(236\) 0 0
\(237\) −14.4721 + 5.52786i −0.940066 + 0.359073i
\(238\) 0 0
\(239\) 0.180340i 0.0116652i 0.999983 + 0.00583261i \(0.00185659\pi\)
−0.999983 + 0.00583261i \(0.998143\pi\)
\(240\) 0 0
\(241\) 17.8885i 1.15230i 0.817343 + 0.576151i \(0.195446\pi\)
−0.817343 + 0.576151i \(0.804554\pi\)
\(242\) 0 0
\(243\) 3.90983 + 15.0902i 0.250816 + 0.968035i
\(244\) 0 0
\(245\) −6.70820 2.00000i −0.428571 0.127775i
\(246\) 0 0
\(247\) −10.4721 −0.666326
\(248\) 0 0
\(249\) −23.7082 + 9.05573i −1.50245 + 0.573883i
\(250\) 0 0
\(251\) −12.4721 −0.787234 −0.393617 0.919274i \(-0.628776\pi\)
−0.393617 + 0.919274i \(0.628776\pi\)
\(252\) 0 0
\(253\) 17.8885 1.12464
\(254\) 0 0
\(255\) −8.47214 + 3.23607i −0.530546 + 0.202650i
\(256\) 0 0
\(257\) −14.1803 −0.884545 −0.442273 0.896881i \(-0.645828\pi\)
−0.442273 + 0.896881i \(0.645828\pi\)
\(258\) 0 0
\(259\) −2.00000 0.291796i −0.124274 0.0181313i
\(260\) 0 0
\(261\) 15.4164 + 17.2361i 0.954252 + 1.06689i
\(262\) 0 0
\(263\) 12.9443i 0.798178i −0.916912 0.399089i \(-0.869326\pi\)
0.916912 0.399089i \(-0.130674\pi\)
\(264\) 0 0
\(265\) 0.472136i 0.0290031i
\(266\) 0 0
\(267\) −8.94427 + 3.41641i −0.547381 + 0.209081i
\(268\) 0 0
\(269\) −4.47214 −0.272671 −0.136335 0.990663i \(-0.543533\pi\)
−0.136335 + 0.990663i \(0.543533\pi\)
\(270\) 0 0
\(271\) 31.7082i 1.92614i −0.269258 0.963068i \(-0.586778\pi\)
0.269258 0.963068i \(-0.413222\pi\)
\(272\) 0 0
\(273\) −1.23607 5.52786i −0.0748102 0.334562i
\(274\) 0 0
\(275\) 4.47214i 0.269680i
\(276\) 0 0
\(277\) −17.1246 −1.02892 −0.514459 0.857515i \(-0.672007\pi\)
−0.514459 + 0.857515i \(0.672007\pi\)
\(278\) 0 0
\(279\) 5.52786 + 6.18034i 0.330945 + 0.370007i
\(280\) 0 0
\(281\) 20.0000i 1.19310i −0.802576 0.596550i \(-0.796538\pi\)
0.802576 0.596550i \(-0.203462\pi\)
\(282\) 0 0
\(283\) 13.2361i 0.786803i −0.919367 0.393401i \(-0.871298\pi\)
0.919367 0.393401i \(-0.128702\pi\)
\(284\) 0 0
\(285\) −5.23607 13.7082i −0.310158 0.812004i
\(286\) 0 0
\(287\) −6.47214 0.944272i −0.382038 0.0557386i
\(288\) 0 0
\(289\) 10.4164 0.612730
\(290\) 0 0
\(291\) −0.472136 1.23607i −0.0276771 0.0724596i
\(292\) 0 0
\(293\) 2.58359 0.150935 0.0754675 0.997148i \(-0.475955\pi\)
0.0754675 + 0.997148i \(0.475955\pi\)
\(294\) 0 0
\(295\) −4.47214 −0.260378
\(296\) 0 0
\(297\) −20.6525 10.6525i −1.19838 0.618119i
\(298\) 0 0
\(299\) −4.94427 −0.285935
\(300\) 0 0
\(301\) −12.9443 1.88854i −0.746095 0.108854i
\(302\) 0 0
\(303\) −20.1803 + 7.70820i −1.15933 + 0.442825i
\(304\) 0 0
\(305\) 7.23607i 0.414336i
\(306\) 0 0
\(307\) 18.1803i 1.03761i 0.854894 + 0.518803i \(0.173622\pi\)
−0.854894 + 0.518803i \(0.826378\pi\)
\(308\) 0 0
\(309\) −9.05573 23.7082i −0.515162 1.34871i
\(310\) 0 0
\(311\) 17.5279 0.993914 0.496957 0.867775i \(-0.334451\pi\)
0.496957 + 0.867775i \(0.334451\pi\)
\(312\) 0 0
\(313\) 5.70820i 0.322647i −0.986902 0.161323i \(-0.948424\pi\)
0.986902 0.161323i \(-0.0515762\pi\)
\(314\) 0 0
\(315\) 6.61803 4.38197i 0.372884 0.246896i
\(316\) 0 0
\(317\) 10.9443i 0.614692i 0.951598 + 0.307346i \(0.0994408\pi\)
−0.951598 + 0.307346i \(0.900559\pi\)
\(318\) 0 0
\(319\) −34.4721 −1.93007
\(320\) 0 0
\(321\) −7.05573 18.4721i −0.393812 1.03101i
\(322\) 0 0
\(323\) 44.3607i 2.46829i
\(324\) 0 0
\(325\) 1.23607i 0.0685647i
\(326\) 0 0
\(327\) −7.23607 + 2.76393i −0.400155 + 0.152846i
\(328\) 0 0
\(329\) 16.9443 + 2.47214i 0.934168 + 0.136293i
\(330\) 0 0
\(331\) −3.05573 −0.167958 −0.0839790 0.996468i \(-0.526763\pi\)
−0.0839790 + 0.996468i \(0.526763\pi\)
\(332\) 0 0
\(333\) 1.70820 1.52786i 0.0936090 0.0837264i
\(334\) 0 0
\(335\) −12.0000 −0.655630
\(336\) 0 0
\(337\) 21.4164 1.16663 0.583313 0.812247i \(-0.301756\pi\)
0.583313 + 0.812247i \(0.301756\pi\)
\(338\) 0 0
\(339\) −1.81966 4.76393i −0.0988304 0.258741i
\(340\) 0 0
\(341\) −12.3607 −0.669368
\(342\) 0 0
\(343\) −16.7984 7.79837i −0.907027 0.421073i
\(344\) 0 0
\(345\) −2.47214 6.47214i −0.133095 0.348448i
\(346\) 0 0
\(347\) 2.47214i 0.132711i 0.997796 + 0.0663556i \(0.0211372\pi\)
−0.997796 + 0.0663556i \(0.978863\pi\)
\(348\) 0 0
\(349\) 20.1803i 1.08023i 0.841592 + 0.540114i \(0.181619\pi\)
−0.841592 + 0.540114i \(0.818381\pi\)
\(350\) 0 0
\(351\) 5.70820 + 2.94427i 0.304681 + 0.157154i
\(352\) 0 0
\(353\) 27.7082 1.47476 0.737379 0.675479i \(-0.236063\pi\)
0.737379 + 0.675479i \(0.236063\pi\)
\(354\) 0 0
\(355\) 7.23607i 0.384051i
\(356\) 0 0
\(357\) −23.4164 + 5.23607i −1.23933 + 0.277122i
\(358\) 0 0
\(359\) 12.1803i 0.642854i −0.946934 0.321427i \(-0.895838\pi\)
0.946934 0.321427i \(-0.104162\pi\)
\(360\) 0 0
\(361\) −52.7771 −2.77774
\(362\) 0 0
\(363\) 14.5623 5.56231i 0.764323 0.291945i
\(364\) 0 0
\(365\) 11.2361i 0.588123i
\(366\) 0 0
\(367\) 8.18034i 0.427010i 0.976942 + 0.213505i \(0.0684880\pi\)
−0.976942 + 0.213505i \(0.931512\pi\)
\(368\) 0 0
\(369\) 5.52786 4.94427i 0.287769 0.257389i
\(370\) 0 0
\(371\) −0.180340 + 1.23607i −0.00936278 + 0.0641735i
\(372\) 0 0
\(373\) −32.1803 −1.66623 −0.833117 0.553096i \(-0.813446\pi\)
−0.833117 + 0.553096i \(0.813446\pi\)
\(374\) 0 0
\(375\) 1.61803 0.618034i 0.0835549 0.0319151i
\(376\) 0 0
\(377\) 9.52786 0.490710
\(378\) 0 0
\(379\) 17.8885 0.918873 0.459436 0.888211i \(-0.348051\pi\)
0.459436 + 0.888211i \(0.348051\pi\)
\(380\) 0 0
\(381\) −0.472136 + 0.180340i −0.0241883 + 0.00923909i
\(382\) 0 0
\(383\) −13.8885 −0.709671 −0.354836 0.934929i \(-0.615463\pi\)
−0.354836 + 0.934929i \(0.615463\pi\)
\(384\) 0 0
\(385\) −1.70820 + 11.7082i −0.0870581 + 0.596705i
\(386\) 0 0
\(387\) 11.0557 9.88854i 0.561994 0.502663i
\(388\) 0 0
\(389\) 30.1803i 1.53020i −0.643909 0.765102i \(-0.722689\pi\)
0.643909 0.765102i \(-0.277311\pi\)
\(390\) 0 0
\(391\) 20.9443i 1.05920i
\(392\) 0 0
\(393\) −8.76393 + 3.34752i −0.442082 + 0.168860i
\(394\) 0 0
\(395\) −8.94427 −0.450035
\(396\) 0 0
\(397\) 23.1246i 1.16059i 0.814406 + 0.580295i \(0.197063\pi\)
−0.814406 + 0.580295i \(0.802937\pi\)
\(398\) 0 0
\(399\) −8.47214 37.8885i −0.424137 1.89680i
\(400\) 0 0
\(401\) 14.4721i 0.722704i −0.932429 0.361352i \(-0.882315\pi\)
0.932429 0.361352i \(-0.117685\pi\)
\(402\) 0 0
\(403\) 3.41641 0.170183
\(404\) 0 0
\(405\) −1.00000 + 8.94427i −0.0496904 + 0.444444i
\(406\) 0 0
\(407\) 3.41641i 0.169345i
\(408\) 0 0
\(409\) 7.41641i 0.366718i 0.983046 + 0.183359i \(0.0586970\pi\)
−0.983046 + 0.183359i \(0.941303\pi\)
\(410\) 0 0
\(411\) 2.18034 + 5.70820i 0.107548 + 0.281565i
\(412\) 0 0
\(413\) −11.7082 1.70820i −0.576123 0.0840552i
\(414\) 0 0
\(415\) −14.6525 −0.719262
\(416\) 0 0
\(417\) −7.12461 18.6525i −0.348894 0.913416i
\(418\) 0 0
\(419\) 36.8328 1.79940 0.899700 0.436508i \(-0.143785\pi\)
0.899700 + 0.436508i \(0.143785\pi\)
\(420\) 0 0
\(421\) −3.52786 −0.171938 −0.0859688 0.996298i \(-0.527399\pi\)
−0.0859688 + 0.996298i \(0.527399\pi\)
\(422\) 0 0
\(423\) −14.4721 + 12.9443i −0.703659 + 0.629372i
\(424\) 0 0
\(425\) −5.23607 −0.253987
\(426\) 0 0
\(427\) 2.76393 18.9443i 0.133756 0.916778i
\(428\) 0 0
\(429\) −8.94427 + 3.41641i −0.431834 + 0.164946i
\(430\) 0 0
\(431\) 39.5967i 1.90731i −0.300905 0.953654i \(-0.597289\pi\)
0.300905 0.953654i \(-0.402711\pi\)
\(432\) 0 0
\(433\) 26.6525i 1.28084i 0.768026 + 0.640418i \(0.221239\pi\)
−0.768026 + 0.640418i \(0.778761\pi\)
\(434\) 0 0
\(435\) 4.76393 + 12.4721i 0.228413 + 0.597993i
\(436\) 0 0
\(437\) −33.8885 −1.62111
\(438\) 0 0
\(439\) 10.1803i 0.485881i −0.970041 0.242941i \(-0.921888\pi\)
0.970041 0.242941i \(-0.0781120\pi\)
\(440\) 0 0
\(441\) 19.0000 8.94427i 0.904762 0.425918i
\(442\) 0 0
\(443\) 18.4721i 0.877638i −0.898576 0.438819i \(-0.855397\pi\)
0.898576 0.438819i \(-0.144603\pi\)
\(444\) 0 0
\(445\) −5.52786 −0.262046
\(446\) 0 0
\(447\) −2.65248 6.94427i −0.125458 0.328453i
\(448\) 0 0
\(449\) 10.4721i 0.494211i 0.968989 + 0.247105i \(0.0794794\pi\)
−0.968989 + 0.247105i \(0.920521\pi\)
\(450\) 0 0
\(451\) 11.0557i 0.520594i
\(452\) 0 0
\(453\) 33.8885 12.9443i 1.59222 0.608175i
\(454\) 0 0
\(455\) 0.472136 3.23607i 0.0221341 0.151709i
\(456\) 0 0
\(457\) 26.9443 1.26040 0.630200 0.776433i \(-0.282973\pi\)
0.630200 + 0.776433i \(0.282973\pi\)
\(458\) 0 0
\(459\) 12.4721 24.1803i 0.582149 1.12864i
\(460\) 0 0
\(461\) 6.94427 0.323427 0.161713 0.986838i \(-0.448298\pi\)
0.161713 + 0.986838i \(0.448298\pi\)
\(462\) 0 0
\(463\) 22.1803 1.03081 0.515404 0.856947i \(-0.327642\pi\)
0.515404 + 0.856947i \(0.327642\pi\)
\(464\) 0 0
\(465\) 1.70820 + 4.47214i 0.0792161 + 0.207390i
\(466\) 0 0
\(467\) −33.7082 −1.55983 −0.779915 0.625886i \(-0.784738\pi\)
−0.779915 + 0.625886i \(0.784738\pi\)
\(468\) 0 0
\(469\) −31.4164 4.58359i −1.45067 0.211651i
\(470\) 0 0
\(471\) 5.70820 + 14.9443i 0.263020 + 0.688596i
\(472\) 0 0
\(473\) 22.1115i 1.01669i
\(474\) 0 0
\(475\) 8.47214i 0.388728i
\(476\) 0 0
\(477\) −0.944272 1.05573i −0.0432352 0.0483385i
\(478\) 0 0
\(479\) 37.8885 1.73117 0.865586 0.500761i \(-0.166946\pi\)
0.865586 + 0.500761i \(0.166946\pi\)
\(480\) 0 0
\(481\) 0.944272i 0.0430551i
\(482\) 0 0
\(483\) −4.00000 17.8885i −0.182006 0.813957i
\(484\) 0 0
\(485\) 0.763932i 0.0346884i
\(486\) 0 0
\(487\) −17.5967 −0.797385 −0.398692 0.917085i \(-0.630536\pi\)
−0.398692 + 0.917085i \(0.630536\pi\)
\(488\) 0 0
\(489\) −16.9443 + 6.47214i −0.766246 + 0.292680i
\(490\) 0 0
\(491\) 13.4164i 0.605474i 0.953074 + 0.302737i \(0.0979004\pi\)
−0.953074 + 0.302737i \(0.902100\pi\)
\(492\) 0 0
\(493\) 40.3607i 1.81775i
\(494\) 0 0
\(495\) −8.94427 10.0000i −0.402015 0.449467i
\(496\) 0 0
\(497\) −2.76393 + 18.9443i −0.123979 + 0.849767i
\(498\) 0 0
\(499\) −17.8885 −0.800801 −0.400401 0.916340i \(-0.631129\pi\)
−0.400401 + 0.916340i \(0.631129\pi\)
\(500\) 0 0
\(501\) 1.52786 0.583592i 0.0682599 0.0260730i
\(502\) 0 0
\(503\) −28.3607 −1.26454 −0.632270 0.774748i \(-0.717877\pi\)
−0.632270 + 0.774748i \(0.717877\pi\)
\(504\) 0 0
\(505\) −12.4721 −0.555003
\(506\) 0 0
\(507\) −18.5623 + 7.09017i −0.824381 + 0.314886i
\(508\) 0 0
\(509\) −15.5279 −0.688260 −0.344130 0.938922i \(-0.611826\pi\)
−0.344130 + 0.938922i \(0.611826\pi\)
\(510\) 0 0
\(511\) −4.29180 + 29.4164i −0.189858 + 1.30131i
\(512\) 0 0
\(513\) 39.1246 + 20.1803i 1.72739 + 0.890984i
\(514\) 0 0
\(515\) 14.6525i 0.645665i
\(516\) 0 0
\(517\) 28.9443i 1.27297i
\(518\) 0 0
\(519\) −15.2361 + 5.81966i −0.668789 + 0.255455i
\(520\) 0 0
\(521\) 36.9443 1.61856 0.809279 0.587425i \(-0.199858\pi\)
0.809279 + 0.587425i \(0.199858\pi\)
\(522\) 0 0
\(523\) 42.5410i 1.86019i 0.367320 + 0.930094i \(0.380275\pi\)
−0.367320 + 0.930094i \(0.619725\pi\)
\(524\) 0 0
\(525\) 4.47214 1.00000i 0.195180 0.0436436i
\(526\) 0 0
\(527\) 14.4721i 0.630416i
\(528\) 0 0
\(529\) 7.00000 0.304348
\(530\) 0 0
\(531\) 10.0000 8.94427i 0.433963 0.388148i
\(532\) 0 0
\(533\) 3.05573i 0.132358i
\(534\) 0 0
\(535\) 11.4164i 0.493574i
\(536\) 0 0
\(537\) 9.23607 + 24.1803i 0.398566 + 1.04346i
\(538\) 0 0
\(539\) −8.94427 + 30.0000i −0.385257 + 1.29219i
\(540\) 0 0
\(541\) 30.9443 1.33040 0.665199 0.746666i \(-0.268347\pi\)
0.665199 + 0.746666i \(0.268347\pi\)
\(542\) 0 0
\(543\) 10.0000 + 26.1803i 0.429141 + 1.12351i
\(544\) 0 0
\(545\) −4.47214 −0.191565
\(546\) 0 0
\(547\) 35.4164 1.51430 0.757148 0.653243i \(-0.226592\pi\)
0.757148 + 0.653243i \(0.226592\pi\)
\(548\) 0 0
\(549\) 14.4721 + 16.1803i 0.617656 + 0.690560i
\(550\) 0 0
\(551\) 65.3050 2.78208
\(552\) 0 0
\(553\) −23.4164 3.41641i −0.995767 0.145280i
\(554\) 0 0
\(555\) 1.23607 0.472136i 0.0524682 0.0200411i
\(556\) 0 0
\(557\) 7.52786i 0.318966i 0.987201 + 0.159483i \(0.0509827\pi\)
−0.987201 + 0.159483i \(0.949017\pi\)
\(558\) 0 0
\(559\) 6.11146i 0.258487i
\(560\) 0 0
\(561\) 14.4721 + 37.8885i 0.611014 + 1.59966i
\(562\) 0 0
\(563\) 40.1803 1.69340 0.846700 0.532071i \(-0.178586\pi\)
0.846700 + 0.532071i \(0.178586\pi\)
\(564\) 0 0
\(565\) 2.94427i 0.123866i
\(566\) 0 0
\(567\) −6.03444 + 23.0344i −0.253423 + 0.967356i
\(568\) 0 0
\(569\) 9.52786i 0.399429i −0.979854 0.199714i \(-0.935999\pi\)
0.979854 0.199714i \(-0.0640014\pi\)
\(570\) 0 0
\(571\) −18.8328 −0.788129 −0.394064 0.919083i \(-0.628931\pi\)
−0.394064 + 0.919083i \(0.628931\pi\)
\(572\) 0 0
\(573\) −4.47214 11.7082i −0.186826 0.489117i
\(574\) 0 0
\(575\) 4.00000i 0.166812i
\(576\) 0 0
\(577\) 8.18034i 0.340552i −0.985396 0.170276i \(-0.945534\pi\)
0.985396 0.170276i \(-0.0544659\pi\)
\(578\) 0 0
\(579\) 9.70820 3.70820i 0.403459 0.154108i
\(580\) 0 0
\(581\) −38.3607 5.59675i −1.59147 0.232192i
\(582\) 0 0
\(583\) 2.11146 0.0874476
\(584\) 0 0
\(585\) 2.47214 + 2.76393i 0.102210 + 0.114275i
\(586\) 0 0
\(587\) −10.2918 −0.424788 −0.212394 0.977184i \(-0.568126\pi\)
−0.212394 + 0.977184i \(0.568126\pi\)
\(588\) 0 0
\(589\) 23.4164 0.964856
\(590\) 0 0
\(591\) 2.18034 + 5.70820i 0.0896872 + 0.234804i
\(592\) 0 0
\(593\) 29.0132 1.19143 0.595714 0.803197i \(-0.296869\pi\)
0.595714 + 0.803197i \(0.296869\pi\)
\(594\) 0 0
\(595\) −13.7082 2.00000i −0.561982 0.0819920i
\(596\) 0 0
\(597\) −13.7082 35.8885i −0.561039 1.46882i
\(598\) 0 0
\(599\) 36.7639i 1.50213i 0.660226 + 0.751067i \(0.270460\pi\)
−0.660226 + 0.751067i \(0.729540\pi\)
\(600\) 0 0
\(601\) 5.52786i 0.225486i 0.993624 + 0.112743i \(0.0359637\pi\)
−0.993624 + 0.112743i \(0.964036\pi\)
\(602\) 0 0
\(603\) 26.8328 24.0000i 1.09272 0.977356i
\(604\) 0 0
\(605\) 9.00000 0.365902
\(606\) 0 0
\(607\) 19.2361i 0.780768i 0.920652 + 0.390384i \(0.127658\pi\)
−0.920652 + 0.390384i \(0.872342\pi\)
\(608\) 0 0
\(609\) 7.70820 + 34.4721i 0.312352 + 1.39688i
\(610\) 0 0
\(611\) 8.00000i 0.323645i
\(612\) 0 0
\(613\) 38.0689 1.53759 0.768794 0.639497i \(-0.220857\pi\)
0.768794 + 0.639497i \(0.220857\pi\)
\(614\) 0 0
\(615\) 4.00000 1.52786i 0.161296 0.0616094i
\(616\) 0 0
\(617\) 2.00000i 0.0805170i 0.999189 + 0.0402585i \(0.0128181\pi\)
−0.999189 + 0.0402585i \(0.987182\pi\)
\(618\) 0 0
\(619\) 14.0000i 0.562708i −0.959604 0.281354i \(-0.909217\pi\)
0.959604 0.281354i \(-0.0907834\pi\)
\(620\) 0 0
\(621\) 18.4721 + 9.52786i 0.741261 + 0.382340i
\(622\) 0 0
\(623\) −14.4721 2.11146i −0.579814 0.0845937i
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −61.3050 + 23.4164i −2.44828 + 0.935161i
\(628\) 0 0
\(629\) −4.00000 −0.159490
\(630\) 0 0
\(631\) 5.88854 0.234419 0.117210 0.993107i \(-0.462605\pi\)
0.117210 + 0.993107i \(0.462605\pi\)
\(632\) 0 0
\(633\) −12.9443 + 4.94427i −0.514489 + 0.196517i
\(634\) 0 0
\(635\) −0.291796 −0.0115796
\(636\) 0 0
\(637\) 2.47214 8.29180i 0.0979496 0.328533i
\(638\) 0 0
\(639\) −14.4721 16.1803i −0.572509 0.640084i
\(640\) 0 0
\(641\) 23.4164i 0.924893i −0.886647 0.462446i \(-0.846972\pi\)
0.886647 0.462446i \(-0.153028\pi\)
\(642\) 0 0
\(643\) 12.2918i 0.484741i 0.970184 + 0.242371i \(0.0779250\pi\)
−0.970184 + 0.242371i \(0.922075\pi\)
\(644\) 0 0
\(645\) 8.00000 3.05573i 0.315000 0.120319i
\(646\) 0 0
\(647\) 34.8328 1.36942 0.684710 0.728816i \(-0.259929\pi\)
0.684710 + 0.728816i \(0.259929\pi\)
\(648\) 0 0
\(649\) 20.0000i 0.785069i
\(650\) 0 0
\(651\) 2.76393 + 12.3607i 0.108327 + 0.484453i
\(652\) 0 0
\(653\) 23.8885i 0.934831i −0.884038 0.467415i \(-0.845185\pi\)
0.884038 0.467415i \(-0.154815\pi\)
\(654\) 0 0
\(655\) −5.41641 −0.211637
\(656\) 0 0
\(657\) −22.4721 25.1246i −0.876722 0.980204i
\(658\) 0 0
\(659\) 31.5279i 1.22815i −0.789247 0.614076i \(-0.789529\pi\)
0.789247 0.614076i \(-0.210471\pi\)
\(660\) 0 0
\(661\) 18.2918i 0.711468i 0.934587 + 0.355734i \(0.115769\pi\)
−0.934587 + 0.355734i \(0.884231\pi\)
\(662\) 0 0
\(663\) −4.00000 10.4721i −0.155347 0.406704i
\(664\) 0 0
\(665\) 3.23607 22.1803i 0.125489 0.860117i
\(666\) 0 0
\(667\) 30.8328 1.19385
\(668\) 0 0
\(669\) 10.9443 + 28.6525i 0.423130 + 1.10777i
\(670\) 0 0
\(671\) −32.3607 −1.24927
\(672\) 0 0
\(673\) 19.5279 0.752744 0.376372 0.926469i \(-0.377171\pi\)
0.376372 + 0.926469i \(0.377171\pi\)
\(674\) 0 0
\(675\) −2.38197 + 4.61803i −0.0916819 + 0.177748i
\(676\) 0 0
\(677\) −18.0000 −0.691796 −0.345898 0.938272i \(-0.612426\pi\)
−0.345898 + 0.938272i \(0.612426\pi\)
\(678\) 0 0
\(679\) 0.291796 2.00000i 0.0111981 0.0767530i
\(680\) 0 0
\(681\) −1.23607 + 0.472136i −0.0473662 + 0.0180923i
\(682\) 0 0
\(683\) 36.0000i 1.37750i 0.724998 + 0.688751i \(0.241841\pi\)
−0.724998 + 0.688751i \(0.758159\pi\)
\(684\) 0 0
\(685\) 3.52786i 0.134793i
\(686\) 0 0
\(687\) 5.41641 + 14.1803i 0.206649 + 0.541014i
\(688\) 0 0
\(689\) −0.583592 −0.0222331
\(690\) 0 0
\(691\) 21.0557i 0.800998i 0.916297 + 0.400499i \(0.131163\pi\)
−0.916297 + 0.400499i \(0.868837\pi\)
\(692\) 0 0
\(693\) −19.5967 29.5967i −0.744419 1.12429i
\(694\) 0 0
\(695\) 11.5279i 0.437277i
\(696\) 0 0
\(697\) −12.9443 −0.490299
\(698\) 0 0
\(699\) 7.12461 + 18.6525i 0.269478 + 0.705501i
\(700\) 0 0
\(701\) 44.0689i 1.66446i 0.554431 + 0.832229i \(0.312936\pi\)
−0.554431 + 0.832229i \(0.687064\pi\)
\(702\) 0 0
\(703\) 6.47214i 0.244101i
\(704\) 0 0
\(705\) −10.4721 + 4.00000i −0.394403 + 0.150649i
\(706\) 0 0
\(707\) −32.6525 4.76393i −1.22802 0.179166i
\(708\) 0 0
\(709\) −15.5279 −0.583161 −0.291581 0.956546i \(-0.594181\pi\)
−0.291581 + 0.956546i \(0.594181\pi\)
\(710\) 0 0
\(711\) 20.0000 17.8885i 0.750059 0.670873i
\(712\) 0 0
\(713\) 11.0557 0.414040
\(714\) 0 0
\(715\) −5.52786 −0.206730
\(716\) 0 0
\(717\) −0.111456 0.291796i −0.00416241 0.0108973i
\(718\) 0 0
\(719\) −34.4721 −1.28559 −0.642797 0.766037i \(-0.722226\pi\)
−0.642797 + 0.766037i \(0.722226\pi\)
\(720\) 0 0
\(721\) 5.59675 38.3607i 0.208434 1.42863i
\(722\) 0 0
\(723\) −11.0557 28.9443i −0.411167 1.07645i
\(724\) 0 0
\(725\) 7.70820i 0.286276i
\(726\) 0 0
\(727\) 26.2918i 0.975109i −0.873093 0.487554i \(-0.837889\pi\)
0.873093 0.487554i \(-0.162111\pi\)
\(728\) 0 0
\(729\) −15.6525 22.0000i −0.579721 0.814815i
\(730\) 0 0
\(731\) −25.8885 −0.957522
\(732\) 0 0
\(733\) 20.0689i 0.741261i 0.928780 + 0.370631i \(0.120858\pi\)
−0.928780 + 0.370631i \(0.879142\pi\)
\(734\) 0 0
\(735\) 12.0902 0.909830i 0.445953 0.0335596i
\(736\) 0 0
\(737\) 53.6656i 1.97680i
\(738\) 0 0
\(739\) −8.94427 −0.329020 −0.164510 0.986375i \(-0.552604\pi\)
−0.164510 + 0.986375i \(0.552604\pi\)
\(740\) 0 0
\(741\) 16.9443 6.47214i 0.622463 0.237760i
\(742\) 0 0
\(743\) 10.4721i 0.384185i 0.981377 + 0.192093i \(0.0615274\pi\)
−0.981377 + 0.192093i \(0.938473\pi\)
\(744\) 0 0
\(745\) 4.29180i 0.157239i
\(746\) 0 0
\(747\) 32.7639 29.3050i 1.19877 1.07221i
\(748\) 0 0
\(749\) 4.36068 29.8885i 0.159336 1.09210i
\(750\) 0 0
\(751\) −8.58359 −0.313220 −0.156610 0.987661i \(-0.550057\pi\)
−0.156610 + 0.987661i \(0.550057\pi\)
\(752\) 0 0
\(753\) 20.1803 7.70820i 0.735412 0.280903i
\(754\) 0 0
\(755\) 20.9443 0.762240
\(756\) 0 0
\(757\) −2.65248 −0.0964059 −0.0482029 0.998838i \(-0.515349\pi\)
−0.0482029 + 0.998838i \(0.515349\pi\)
\(758\) 0 0
\(759\) −28.9443 + 11.0557i −1.05061 + 0.401298i
\(760\) 0 0
\(761\) 5.88854 0.213460 0.106730 0.994288i \(-0.465962\pi\)
0.106730 + 0.994288i \(0.465962\pi\)
\(762\) 0 0
\(763\) −11.7082 1.70820i −0.423865 0.0618411i
\(764\) 0 0
\(765\) 11.7082 10.4721i 0.423311 0.378621i
\(766\) 0 0
\(767\) 5.52786i 0.199600i
\(768\) 0 0
\(769\) 36.0000i 1.29819i −0.760706 0.649097i \(-0.775147\pi\)
0.760706 0.649097i \(-0.224853\pi\)
\(770\) 0 0
\(771\) 22.9443 8.76393i 0.826318 0.315625i
\(772\) 0 0
\(773\) −10.5836 −0.380665 −0.190333 0.981720i \(-0.560957\pi\)
−0.190333 + 0.981720i \(0.560957\pi\)
\(774\) 0 0
\(775\) 2.76393i 0.0992834i
\(776\) 0 0
\(777\) 3.41641 0.763932i 0.122563 0.0274059i
\(778\) 0 0
\(779\) 20.9443i 0.750406i
\(780\) 0 0
\(781\) 32.3607 1.15796
\(782\) 0 0
\(783\) −35.5967 18.3607i −1.27212 0.656157i
\(784\) 0 0
\(785\) 9.23607i 0.329649i
\(786\) 0 0
\(787\) 36.2918i 1.29366i −0.762633 0.646831i \(-0.776094\pi\)
0.762633 0.646831i \(-0.223906\pi\)
\(788\) 0 0
\(789\) 8.00000 + 20.9443i 0.284808 + 0.745636i
\(790\) 0 0
\(791\) 1.12461 7.70820i 0.0399866 0.274072i
\(792\) 0 0
\(793\) 8.94427 0.317620
\(794\) 0 0
\(795\) −0.291796 0.763932i −0.0103489 0.0270939i
\(796\) 0 0
\(797\) −21.4164 −0.758608 −0.379304 0.925272i \(-0.623837\pi\)
−0.379304 + 0.925272i \(0.623837\pi\)
\(798\) 0 0