Properties

Label 882.2.f.s.295.1
Level $882$
Weight $2$
Character 882.295
Analytic conductor $7.043$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.f (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.04280545828\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 295.1
Root \(0.965926 - 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 882.295
Dual form 882.2.f.s.589.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-1.22474 - 1.22474i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.965926 - 1.67303i) q^{5} +(-1.67303 + 0.448288i) q^{6} -1.00000 q^{8} +3.00000i q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-1.22474 - 1.22474i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.965926 - 1.67303i) q^{5} +(-1.67303 + 0.448288i) q^{6} -1.00000 q^{8} +3.00000i q^{9} -1.93185 q^{10} +(-2.73205 + 4.73205i) q^{11} +(-0.448288 + 1.67303i) q^{12} +(1.22474 + 2.12132i) q^{13} +(-0.866025 + 3.23205i) q^{15} +(-0.500000 + 0.866025i) q^{16} -6.31319 q^{17} +(2.59808 + 1.50000i) q^{18} +1.93185 q^{19} +(-0.965926 + 1.67303i) q^{20} +(2.73205 + 4.73205i) q^{22} +(2.96410 + 5.13397i) q^{23} +(1.22474 + 1.22474i) q^{24} +(0.633975 - 1.09808i) q^{25} +2.44949 q^{26} +(3.67423 - 3.67423i) q^{27} +(0.366025 - 0.633975i) q^{29} +(2.36603 + 2.36603i) q^{30} +(-3.67423 - 6.36396i) q^{31} +(0.500000 + 0.866025i) q^{32} +(9.14162 - 2.44949i) q^{33} +(-3.15660 + 5.46739i) q^{34} +(2.59808 - 1.50000i) q^{36} -8.00000 q^{37} +(0.965926 - 1.67303i) q^{38} +(1.09808 - 4.09808i) q^{39} +(0.965926 + 1.67303i) q^{40} +(2.82843 + 4.89898i) q^{41} +(0.901924 - 1.56218i) q^{43} +5.46410 q^{44} +(5.01910 - 2.89778i) q^{45} +5.92820 q^{46} +(-4.76028 + 8.24504i) q^{47} +(1.67303 - 0.448288i) q^{48} +(-0.633975 - 1.09808i) q^{50} +(7.73205 + 7.73205i) q^{51} +(1.22474 - 2.12132i) q^{52} +3.26795 q^{53} +(-1.34486 - 5.01910i) q^{54} +10.5558 q^{55} +(-2.36603 - 2.36603i) q^{57} +(-0.366025 - 0.633975i) q^{58} +(2.50026 + 4.33057i) q^{59} +(3.23205 - 0.866025i) q^{60} +(-1.48356 + 2.56961i) q^{61} -7.34847 q^{62} +1.00000 q^{64} +(2.36603 - 4.09808i) q^{65} +(2.44949 - 9.14162i) q^{66} +(7.09808 + 12.2942i) q^{67} +(3.15660 + 5.46739i) q^{68} +(2.65754 - 9.91808i) q^{69} -11.1962 q^{71} -3.00000i q^{72} -9.52056 q^{73} +(-4.00000 + 6.92820i) q^{74} +(-2.12132 + 0.568406i) q^{75} +(-0.965926 - 1.67303i) q^{76} +(-3.00000 - 3.00000i) q^{78} +(5.06218 - 8.76795i) q^{79} +1.93185 q^{80} -9.00000 q^{81} +5.65685 q^{82} +(-4.94975 + 8.57321i) q^{83} +(6.09808 + 10.5622i) q^{85} +(-0.901924 - 1.56218i) q^{86} +(-1.22474 + 0.328169i) q^{87} +(2.73205 - 4.73205i) q^{88} -13.2827 q^{89} -5.79555i q^{90} +(2.96410 - 5.13397i) q^{92} +(-3.29423 + 12.2942i) q^{93} +(4.76028 + 8.24504i) q^{94} +(-1.86603 - 3.23205i) q^{95} +(0.448288 - 1.67303i) q^{96} +(1.93185 - 3.34607i) q^{97} +(-14.1962 - 8.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8} - 8 q^{11} - 4 q^{16} + 8 q^{22} - 4 q^{23} + 12 q^{25} - 4 q^{29} + 12 q^{30} + 4 q^{32} - 64 q^{37} - 12 q^{39} + 28 q^{43} + 16 q^{44} - 8 q^{46} - 12 q^{50} + 48 q^{51} + 40 q^{53} - 12 q^{57} + 4 q^{58} + 12 q^{60} + 8 q^{64} + 12 q^{65} + 36 q^{67} - 48 q^{71} - 32 q^{74} - 24 q^{78} - 8 q^{79} - 72 q^{81} + 28 q^{85} - 28 q^{86} + 8 q^{88} - 4 q^{92} + 36 q^{93} - 8 q^{95} - 72 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) −1.22474 1.22474i −0.707107 0.707107i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −0.965926 1.67303i −0.431975 0.748203i 0.565068 0.825044i \(-0.308850\pi\)
−0.997043 + 0.0768413i \(0.975517\pi\)
\(6\) −1.67303 + 0.448288i −0.683013 + 0.183013i
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) 3.00000i 1.00000i
\(10\) −1.93185 −0.610905
\(11\) −2.73205 + 4.73205i −0.823744 + 1.42677i 0.0791309 + 0.996864i \(0.474785\pi\)
−0.902875 + 0.429903i \(0.858548\pi\)
\(12\) −0.448288 + 1.67303i −0.129410 + 0.482963i
\(13\) 1.22474 + 2.12132i 0.339683 + 0.588348i 0.984373 0.176096i \(-0.0563468\pi\)
−0.644690 + 0.764444i \(0.723014\pi\)
\(14\) 0 0
\(15\) −0.866025 + 3.23205i −0.223607 + 0.834512i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −6.31319 −1.53117 −0.765587 0.643332i \(-0.777551\pi\)
−0.765587 + 0.643332i \(0.777551\pi\)
\(18\) 2.59808 + 1.50000i 0.612372 + 0.353553i
\(19\) 1.93185 0.443197 0.221599 0.975138i \(-0.428873\pi\)
0.221599 + 0.975138i \(0.428873\pi\)
\(20\) −0.965926 + 1.67303i −0.215988 + 0.374101i
\(21\) 0 0
\(22\) 2.73205 + 4.73205i 0.582475 + 1.00888i
\(23\) 2.96410 + 5.13397i 0.618058 + 1.07051i 0.989840 + 0.142188i \(0.0454136\pi\)
−0.371782 + 0.928320i \(0.621253\pi\)
\(24\) 1.22474 + 1.22474i 0.250000 + 0.250000i
\(25\) 0.633975 1.09808i 0.126795 0.219615i
\(26\) 2.44949 0.480384
\(27\) 3.67423 3.67423i 0.707107 0.707107i
\(28\) 0 0
\(29\) 0.366025 0.633975i 0.0679692 0.117726i −0.830038 0.557707i \(-0.811681\pi\)
0.898007 + 0.439981i \(0.145015\pi\)
\(30\) 2.36603 + 2.36603i 0.431975 + 0.431975i
\(31\) −3.67423 6.36396i −0.659912 1.14300i −0.980638 0.195829i \(-0.937260\pi\)
0.320726 0.947172i \(-0.396073\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 9.14162 2.44949i 1.59135 0.426401i
\(34\) −3.15660 + 5.46739i −0.541352 + 0.937649i
\(35\) 0 0
\(36\) 2.59808 1.50000i 0.433013 0.250000i
\(37\) −8.00000 −1.31519 −0.657596 0.753371i \(-0.728427\pi\)
−0.657596 + 0.753371i \(0.728427\pi\)
\(38\) 0.965926 1.67303i 0.156694 0.271402i
\(39\) 1.09808 4.09808i 0.175833 0.656217i
\(40\) 0.965926 + 1.67303i 0.152726 + 0.264530i
\(41\) 2.82843 + 4.89898i 0.441726 + 0.765092i 0.997818 0.0660290i \(-0.0210330\pi\)
−0.556092 + 0.831121i \(0.687700\pi\)
\(42\) 0 0
\(43\) 0.901924 1.56218i 0.137542 0.238230i −0.789024 0.614363i \(-0.789413\pi\)
0.926566 + 0.376133i \(0.122746\pi\)
\(44\) 5.46410 0.823744
\(45\) 5.01910 2.89778i 0.748203 0.431975i
\(46\) 5.92820 0.874066
\(47\) −4.76028 + 8.24504i −0.694358 + 1.20266i 0.276039 + 0.961147i \(0.410978\pi\)
−0.970397 + 0.241517i \(0.922355\pi\)
\(48\) 1.67303 0.448288i 0.241481 0.0647048i
\(49\) 0 0
\(50\) −0.633975 1.09808i −0.0896575 0.155291i
\(51\) 7.73205 + 7.73205i 1.08270 + 1.08270i
\(52\) 1.22474 2.12132i 0.169842 0.294174i
\(53\) 3.26795 0.448887 0.224444 0.974487i \(-0.427944\pi\)
0.224444 + 0.974487i \(0.427944\pi\)
\(54\) −1.34486 5.01910i −0.183013 0.683013i
\(55\) 10.5558 1.42335
\(56\) 0 0
\(57\) −2.36603 2.36603i −0.313388 0.313388i
\(58\) −0.366025 0.633975i −0.0480615 0.0832449i
\(59\) 2.50026 + 4.33057i 0.325506 + 0.563793i 0.981615 0.190874i \(-0.0611321\pi\)
−0.656109 + 0.754666i \(0.727799\pi\)
\(60\) 3.23205 0.866025i 0.417256 0.111803i
\(61\) −1.48356 + 2.56961i −0.189951 + 0.329005i −0.945234 0.326394i \(-0.894166\pi\)
0.755283 + 0.655399i \(0.227500\pi\)
\(62\) −7.34847 −0.933257
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 2.36603 4.09808i 0.293469 0.508304i
\(66\) 2.44949 9.14162i 0.301511 1.12526i
\(67\) 7.09808 + 12.2942i 0.867168 + 1.50198i 0.864878 + 0.501982i \(0.167396\pi\)
0.00228979 + 0.999997i \(0.499271\pi\)
\(68\) 3.15660 + 5.46739i 0.382794 + 0.663018i
\(69\) 2.65754 9.91808i 0.319930 1.19400i
\(70\) 0 0
\(71\) −11.1962 −1.32874 −0.664369 0.747404i \(-0.731300\pi\)
−0.664369 + 0.747404i \(0.731300\pi\)
\(72\) 3.00000i 0.353553i
\(73\) −9.52056 −1.11430 −0.557148 0.830413i \(-0.688105\pi\)
−0.557148 + 0.830413i \(0.688105\pi\)
\(74\) −4.00000 + 6.92820i −0.464991 + 0.805387i
\(75\) −2.12132 + 0.568406i −0.244949 + 0.0656339i
\(76\) −0.965926 1.67303i −0.110799 0.191910i
\(77\) 0 0
\(78\) −3.00000 3.00000i −0.339683 0.339683i
\(79\) 5.06218 8.76795i 0.569540 0.986471i −0.427072 0.904218i \(-0.640455\pi\)
0.996611 0.0822537i \(-0.0262118\pi\)
\(80\) 1.93185 0.215988
\(81\) −9.00000 −1.00000
\(82\) 5.65685 0.624695
\(83\) −4.94975 + 8.57321i −0.543305 + 0.941033i 0.455406 + 0.890284i \(0.349494\pi\)
−0.998711 + 0.0507487i \(0.983839\pi\)
\(84\) 0 0
\(85\) 6.09808 + 10.5622i 0.661429 + 1.14563i
\(86\) −0.901924 1.56218i −0.0972569 0.168454i
\(87\) −1.22474 + 0.328169i −0.131306 + 0.0351835i
\(88\) 2.73205 4.73205i 0.291238 0.504438i
\(89\) −13.2827 −1.40797 −0.703983 0.710217i \(-0.748597\pi\)
−0.703983 + 0.710217i \(0.748597\pi\)
\(90\) 5.79555i 0.610905i
\(91\) 0 0
\(92\) 2.96410 5.13397i 0.309029 0.535254i
\(93\) −3.29423 + 12.2942i −0.341596 + 1.27485i
\(94\) 4.76028 + 8.24504i 0.490985 + 0.850411i
\(95\) −1.86603 3.23205i −0.191450 0.331601i
\(96\) 0.448288 1.67303i 0.0457532 0.170753i
\(97\) 1.93185 3.34607i 0.196150 0.339741i −0.751127 0.660158i \(-0.770489\pi\)
0.947277 + 0.320416i \(0.103823\pi\)
\(98\) 0 0
\(99\) −14.1962 8.19615i −1.42677 0.823744i
\(100\) −1.26795 −0.126795
\(101\) −0.776457 + 1.34486i −0.0772604 + 0.133819i −0.902067 0.431596i \(-0.857951\pi\)
0.824807 + 0.565415i \(0.191284\pi\)
\(102\) 10.5622 2.83013i 1.04581 0.280224i
\(103\) 4.19187 + 7.26054i 0.413037 + 0.715402i 0.995220 0.0976561i \(-0.0311345\pi\)
−0.582183 + 0.813058i \(0.697801\pi\)
\(104\) −1.22474 2.12132i −0.120096 0.208013i
\(105\) 0 0
\(106\) 1.63397 2.83013i 0.158706 0.274886i
\(107\) 16.9282 1.63651 0.818256 0.574855i \(-0.194941\pi\)
0.818256 + 0.574855i \(0.194941\pi\)
\(108\) −5.01910 1.34486i −0.482963 0.129410i
\(109\) −20.5885 −1.97202 −0.986008 0.166696i \(-0.946690\pi\)
−0.986008 + 0.166696i \(0.946690\pi\)
\(110\) 5.27792 9.14162i 0.503230 0.871619i
\(111\) 9.79796 + 9.79796i 0.929981 + 0.929981i
\(112\) 0 0
\(113\) −1.33013 2.30385i −0.125128 0.216728i 0.796655 0.604434i \(-0.206601\pi\)
−0.921783 + 0.387706i \(0.873267\pi\)
\(114\) −3.23205 + 0.866025i −0.302709 + 0.0811107i
\(115\) 5.72620 9.91808i 0.533971 0.924865i
\(116\) −0.732051 −0.0679692
\(117\) −6.36396 + 3.67423i −0.588348 + 0.339683i
\(118\) 5.00052 0.460335
\(119\) 0 0
\(120\) 0.866025 3.23205i 0.0790569 0.295045i
\(121\) −9.42820 16.3301i −0.857109 1.48456i
\(122\) 1.48356 + 2.56961i 0.134316 + 0.232641i
\(123\) 2.53590 9.46410i 0.228654 0.853349i
\(124\) −3.67423 + 6.36396i −0.329956 + 0.571501i
\(125\) −12.1087 −1.08304
\(126\) 0 0
\(127\) 7.92820 0.703514 0.351757 0.936091i \(-0.385584\pi\)
0.351757 + 0.936091i \(0.385584\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) −3.01790 + 0.808643i −0.265711 + 0.0711970i
\(130\) −2.36603 4.09808i −0.207514 0.359425i
\(131\) 0.120118 + 0.208051i 0.0104948 + 0.0181775i 0.871225 0.490884i \(-0.163326\pi\)
−0.860730 + 0.509061i \(0.829993\pi\)
\(132\) −6.69213 6.69213i −0.582475 0.582475i
\(133\) 0 0
\(134\) 14.1962 1.22636
\(135\) −9.69615 2.59808i −0.834512 0.223607i
\(136\) 6.31319 0.541352
\(137\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(138\) −7.26054 7.26054i −0.618058 0.618058i
\(139\) 0.915158 + 1.58510i 0.0776227 + 0.134446i 0.902224 0.431268i \(-0.141934\pi\)
−0.824601 + 0.565715i \(0.808600\pi\)
\(140\) 0 0
\(141\) 15.9282 4.26795i 1.34140 0.359426i
\(142\) −5.59808 + 9.69615i −0.469780 + 0.813683i
\(143\) −13.3843 −1.11925
\(144\) −2.59808 1.50000i −0.216506 0.125000i
\(145\) −1.41421 −0.117444
\(146\) −4.76028 + 8.24504i −0.393963 + 0.682365i
\(147\) 0 0
\(148\) 4.00000 + 6.92820i 0.328798 + 0.569495i
\(149\) −9.19615 15.9282i −0.753378 1.30489i −0.946177 0.323651i \(-0.895090\pi\)
0.192798 0.981238i \(-0.438244\pi\)
\(150\) −0.568406 + 2.12132i −0.0464102 + 0.173205i
\(151\) −1.69615 + 2.93782i −0.138031 + 0.239077i −0.926751 0.375676i \(-0.877411\pi\)
0.788720 + 0.614752i \(0.210744\pi\)
\(152\) −1.93185 −0.156694
\(153\) 18.9396i 1.53117i
\(154\) 0 0
\(155\) −7.09808 + 12.2942i −0.570131 + 0.987496i
\(156\) −4.09808 + 1.09808i −0.328109 + 0.0879165i
\(157\) 12.1781 + 21.0931i 0.971918 + 1.68341i 0.689752 + 0.724046i \(0.257720\pi\)
0.282166 + 0.959366i \(0.408947\pi\)
\(158\) −5.06218 8.76795i −0.402725 0.697541i
\(159\) −4.00240 4.00240i −0.317411 0.317411i
\(160\) 0.965926 1.67303i 0.0763631 0.132265i
\(161\) 0 0
\(162\) −4.50000 + 7.79423i −0.353553 + 0.612372i
\(163\) −20.9282 −1.63922 −0.819612 0.572919i \(-0.805811\pi\)
−0.819612 + 0.572919i \(0.805811\pi\)
\(164\) 2.82843 4.89898i 0.220863 0.382546i
\(165\) −12.9282 12.9282i −1.00646 1.00646i
\(166\) 4.94975 + 8.57321i 0.384175 + 0.665410i
\(167\) −8.05558 13.9527i −0.623359 1.07969i −0.988856 0.148877i \(-0.952434\pi\)
0.365497 0.930813i \(-0.380899\pi\)
\(168\) 0 0
\(169\) 3.50000 6.06218i 0.269231 0.466321i
\(170\) 12.1962 0.935402
\(171\) 5.79555i 0.443197i
\(172\) −1.80385 −0.137542
\(173\) −7.26054 + 12.5756i −0.552008 + 0.956107i 0.446121 + 0.894973i \(0.352805\pi\)
−0.998130 + 0.0611340i \(0.980528\pi\)
\(174\) −0.328169 + 1.22474i −0.0248785 + 0.0928477i
\(175\) 0 0
\(176\) −2.73205 4.73205i −0.205936 0.356692i
\(177\) 2.24167 8.36603i 0.168494 0.628829i
\(178\) −6.64136 + 11.5032i −0.497791 + 0.862200i
\(179\) 2.19615 0.164148 0.0820741 0.996626i \(-0.473846\pi\)
0.0820741 + 0.996626i \(0.473846\pi\)
\(180\) −5.01910 2.89778i −0.374101 0.215988i
\(181\) 8.72552 0.648563 0.324281 0.945961i \(-0.394878\pi\)
0.324281 + 0.945961i \(0.394878\pi\)
\(182\) 0 0
\(183\) 4.96410 1.33013i 0.366957 0.0983258i
\(184\) −2.96410 5.13397i −0.218516 0.378482i
\(185\) 7.72741 + 13.3843i 0.568130 + 0.984030i
\(186\) 9.00000 + 9.00000i 0.659912 + 0.659912i
\(187\) 17.2480 29.8744i 1.26130 2.18463i
\(188\) 9.52056 0.694358
\(189\) 0 0
\(190\) −3.73205 −0.270751
\(191\) −1.59808 + 2.76795i −0.115633 + 0.200282i −0.918033 0.396505i \(-0.870223\pi\)
0.802400 + 0.596787i \(0.203556\pi\)
\(192\) −1.22474 1.22474i −0.0883883 0.0883883i
\(193\) 10.1340 + 17.5526i 0.729459 + 1.26346i 0.957112 + 0.289718i \(0.0935617\pi\)
−0.227652 + 0.973742i \(0.573105\pi\)
\(194\) −1.93185 3.34607i −0.138699 0.240233i
\(195\) −7.91688 + 2.12132i −0.566939 + 0.151911i
\(196\) 0 0
\(197\) −7.66025 −0.545771 −0.272885 0.962047i \(-0.587978\pi\)
−0.272885 + 0.962047i \(0.587978\pi\)
\(198\) −14.1962 + 8.19615i −1.00888 + 0.582475i
\(199\) 3.10583 0.220166 0.110083 0.993922i \(-0.464888\pi\)
0.110083 + 0.993922i \(0.464888\pi\)
\(200\) −0.633975 + 1.09808i −0.0448288 + 0.0776457i
\(201\) 6.36396 23.7506i 0.448879 1.67524i
\(202\) 0.776457 + 1.34486i 0.0546313 + 0.0946242i
\(203\) 0 0
\(204\) 2.83013 10.5622i 0.198149 0.739500i
\(205\) 5.46410 9.46410i 0.381629 0.661002i
\(206\) 8.38375 0.584123
\(207\) −15.4019 + 8.89230i −1.07051 + 0.618058i
\(208\) −2.44949 −0.169842
\(209\) −5.27792 + 9.14162i −0.365081 + 0.632339i
\(210\) 0 0
\(211\) −2.36603 4.09808i −0.162884 0.282123i 0.773018 0.634384i \(-0.218746\pi\)
−0.935902 + 0.352261i \(0.885413\pi\)
\(212\) −1.63397 2.83013i −0.112222 0.194374i
\(213\) 13.7124 + 13.7124i 0.939560 + 0.939560i
\(214\) 8.46410 14.6603i 0.578594 1.00215i
\(215\) −3.48477 −0.237659
\(216\) −3.67423 + 3.67423i −0.250000 + 0.250000i
\(217\) 0 0
\(218\) −10.2942 + 17.8301i −0.697213 + 1.20761i
\(219\) 11.6603 + 11.6603i 0.787927 + 0.787927i
\(220\) −5.27792 9.14162i −0.355837 0.616328i
\(221\) −7.73205 13.3923i −0.520114 0.900864i
\(222\) 13.3843 3.58630i 0.898293 0.240697i
\(223\) −10.3664 + 17.9551i −0.694183 + 1.20236i 0.276272 + 0.961079i \(0.410901\pi\)
−0.970455 + 0.241281i \(0.922432\pi\)
\(224\) 0 0
\(225\) 3.29423 + 1.90192i 0.219615 + 0.126795i
\(226\) −2.66025 −0.176957
\(227\) 0.448288 0.776457i 0.0297539 0.0515353i −0.850765 0.525546i \(-0.823861\pi\)
0.880519 + 0.474011i \(0.157194\pi\)
\(228\) −0.866025 + 3.23205i −0.0573539 + 0.214048i
\(229\) −9.02150 15.6257i −0.596158 1.03258i −0.993382 0.114854i \(-0.963360\pi\)
0.397225 0.917721i \(-0.369973\pi\)
\(230\) −5.72620 9.91808i −0.377575 0.653979i
\(231\) 0 0
\(232\) −0.366025 + 0.633975i −0.0240307 + 0.0416225i
\(233\) −19.3923 −1.27043 −0.635216 0.772334i \(-0.719089\pi\)
−0.635216 + 0.772334i \(0.719089\pi\)
\(234\) 7.34847i 0.480384i
\(235\) 18.3923 1.19978
\(236\) 2.50026 4.33057i 0.162753 0.281896i
\(237\) −16.9384 + 4.53862i −1.10027 + 0.294815i
\(238\) 0 0
\(239\) 2.76795 + 4.79423i 0.179044 + 0.310113i 0.941553 0.336864i \(-0.109366\pi\)
−0.762510 + 0.646977i \(0.776033\pi\)
\(240\) −2.36603 2.36603i −0.152726 0.152726i
\(241\) 6.36396 11.0227i 0.409939 0.710035i −0.584944 0.811074i \(-0.698883\pi\)
0.994882 + 0.101039i \(0.0322167\pi\)
\(242\) −18.8564 −1.21214
\(243\) 11.0227 + 11.0227i 0.707107 + 0.707107i
\(244\) 2.96713 0.189951
\(245\) 0 0
\(246\) −6.92820 6.92820i −0.441726 0.441726i
\(247\) 2.36603 + 4.09808i 0.150547 + 0.260754i
\(248\) 3.67423 + 6.36396i 0.233314 + 0.404112i
\(249\) 16.5622 4.43782i 1.04959 0.281236i
\(250\) −6.05437 + 10.4865i −0.382912 + 0.663223i
\(251\) −1.93185 −0.121937 −0.0609687 0.998140i \(-0.519419\pi\)
−0.0609687 + 0.998140i \(0.519419\pi\)
\(252\) 0 0
\(253\) −32.3923 −2.03649
\(254\) 3.96410 6.86603i 0.248730 0.430813i
\(255\) 5.46739 20.4046i 0.342381 1.27778i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −10.3664 17.9551i −0.646636 1.12001i −0.983921 0.178604i \(-0.942842\pi\)
0.337285 0.941403i \(-0.390491\pi\)
\(258\) −0.808643 + 3.01790i −0.0503439 + 0.187886i
\(259\) 0 0
\(260\) −4.73205 −0.293469
\(261\) 1.90192 + 1.09808i 0.117726 + 0.0679692i
\(262\) 0.240237 0.0148419
\(263\) 7.33013 12.6962i 0.451995 0.782878i −0.546515 0.837449i \(-0.684046\pi\)
0.998510 + 0.0545711i \(0.0173792\pi\)
\(264\) −9.14162 + 2.44949i −0.562628 + 0.150756i
\(265\) −3.15660 5.46739i −0.193908 0.335859i
\(266\) 0 0
\(267\) 16.2679 + 16.2679i 0.995582 + 0.995582i
\(268\) 7.09808 12.2942i 0.433584 0.750990i
\(269\) 0.0371647 0.00226597 0.00113299 0.999999i \(-0.499639\pi\)
0.00113299 + 0.999999i \(0.499639\pi\)
\(270\) −7.09808 + 7.09808i −0.431975 + 0.431975i
\(271\) −5.00052 −0.303760 −0.151880 0.988399i \(-0.548533\pi\)
−0.151880 + 0.988399i \(0.548533\pi\)
\(272\) 3.15660 5.46739i 0.191397 0.331509i
\(273\) 0 0
\(274\) 0 0
\(275\) 3.46410 + 6.00000i 0.208893 + 0.361814i
\(276\) −9.91808 + 2.65754i −0.596998 + 0.159965i
\(277\) 2.90192 5.02628i 0.174360 0.302000i −0.765580 0.643341i \(-0.777548\pi\)
0.939940 + 0.341341i \(0.110881\pi\)
\(278\) 1.83032 0.109775
\(279\) 19.0919 11.0227i 1.14300 0.659912i
\(280\) 0 0
\(281\) −1.69615 + 2.93782i −0.101184 + 0.175256i −0.912173 0.409806i \(-0.865596\pi\)
0.810989 + 0.585062i \(0.198930\pi\)
\(282\) 4.26795 15.9282i 0.254153 0.948511i
\(283\) 8.55463 + 14.8171i 0.508520 + 0.880783i 0.999951 + 0.00986623i \(0.00314057\pi\)
−0.491431 + 0.870916i \(0.663526\pi\)
\(284\) 5.59808 + 9.69615i 0.332185 + 0.575361i
\(285\) −1.67303 + 6.24384i −0.0991019 + 0.369853i
\(286\) −6.69213 + 11.5911i −0.395714 + 0.685397i
\(287\) 0 0
\(288\) −2.59808 + 1.50000i −0.153093 + 0.0883883i
\(289\) 22.8564 1.34449
\(290\) −0.707107 + 1.22474i −0.0415227 + 0.0719195i
\(291\) −6.46410 + 1.73205i −0.378932 + 0.101535i
\(292\) 4.76028 + 8.24504i 0.278574 + 0.482505i
\(293\) 2.19067 + 3.79435i 0.127980 + 0.221668i 0.922894 0.385054i \(-0.125817\pi\)
−0.794914 + 0.606723i \(0.792484\pi\)
\(294\) 0 0
\(295\) 4.83013 8.36603i 0.281221 0.487089i
\(296\) 8.00000 0.464991
\(297\) 7.34847 + 27.4249i 0.426401 + 1.59135i
\(298\) −18.3923 −1.06544
\(299\) −7.26054 + 12.5756i −0.419888 + 0.727267i
\(300\) 1.55291 + 1.55291i 0.0896575 + 0.0896575i
\(301\) 0 0
\(302\) 1.69615 + 2.93782i 0.0976026 + 0.169053i
\(303\) 2.59808 0.696152i 0.149256 0.0399929i
\(304\) −0.965926 + 1.67303i −0.0553996 + 0.0959550i
\(305\) 5.73205 0.328216
\(306\) −16.4022 9.46979i −0.937649 0.541352i
\(307\) 29.0793 1.65964 0.829822 0.558028i \(-0.188442\pi\)
0.829822 + 0.558028i \(0.188442\pi\)
\(308\) 0 0
\(309\) 3.75833 14.0263i 0.213804 0.797927i
\(310\) 7.09808 + 12.2942i 0.403144 + 0.698265i
\(311\) −10.5051 18.1953i −0.595688 1.03176i −0.993449 0.114273i \(-0.963546\pi\)
0.397762 0.917489i \(-0.369787\pi\)
\(312\) −1.09808 + 4.09808i −0.0621663 + 0.232008i
\(313\) −0.896575 + 1.55291i −0.0506774 + 0.0877759i −0.890251 0.455470i \(-0.849471\pi\)
0.839574 + 0.543245i \(0.182805\pi\)
\(314\) 24.3562 1.37450
\(315\) 0 0
\(316\) −10.1244 −0.569540
\(317\) −0.705771 + 1.22243i −0.0396401 + 0.0686586i −0.885165 0.465278i \(-0.845954\pi\)
0.845525 + 0.533936i \(0.179288\pi\)
\(318\) −5.46739 + 1.46498i −0.306596 + 0.0821521i
\(319\) 2.00000 + 3.46410i 0.111979 + 0.193952i
\(320\) −0.965926 1.67303i −0.0539969 0.0935254i
\(321\) −20.7327 20.7327i −1.15719 1.15719i
\(322\) 0 0
\(323\) −12.1962 −0.678612
\(324\) 4.50000 + 7.79423i 0.250000 + 0.433013i
\(325\) 3.10583 0.172280
\(326\) −10.4641 + 18.1244i −0.579553 + 1.00382i
\(327\) 25.2156 + 25.2156i 1.39443 + 1.39443i
\(328\) −2.82843 4.89898i −0.156174 0.270501i
\(329\) 0 0
\(330\) −17.6603 + 4.73205i −0.972165 + 0.260491i
\(331\) −13.0263 + 22.5622i −0.715989 + 1.24013i 0.246588 + 0.969120i \(0.420691\pi\)
−0.962577 + 0.271009i \(0.912643\pi\)
\(332\) 9.89949 0.543305
\(333\) 24.0000i 1.31519i
\(334\) −16.1112 −0.881563
\(335\) 13.7124 23.7506i 0.749190 1.29764i
\(336\) 0 0
\(337\) −6.66025 11.5359i −0.362807 0.628400i 0.625615 0.780132i \(-0.284848\pi\)
−0.988422 + 0.151732i \(0.951515\pi\)
\(338\) −3.50000 6.06218i −0.190375 0.329739i
\(339\) −1.19256 + 4.45069i −0.0647709 + 0.241728i
\(340\) 6.09808 10.5622i 0.330715 0.572815i
\(341\) 40.1528 2.17440
\(342\) 5.01910 + 2.89778i 0.271402 + 0.156694i
\(343\) 0 0
\(344\) −0.901924 + 1.56218i −0.0486285 + 0.0842270i
\(345\) −19.1603 + 5.13397i −1.03155 + 0.276404i
\(346\) 7.26054 + 12.5756i 0.390329 + 0.676069i
\(347\) 16.8564 + 29.1962i 0.904899 + 1.56733i 0.821052 + 0.570853i \(0.193387\pi\)
0.0838470 + 0.996479i \(0.473279\pi\)
\(348\) 0.896575 + 0.896575i 0.0480615 + 0.0480615i
\(349\) −12.3998 + 21.4770i −0.663744 + 1.14964i 0.315881 + 0.948799i \(0.397700\pi\)
−0.979624 + 0.200839i \(0.935633\pi\)
\(350\) 0 0
\(351\) 12.2942 + 3.29423i 0.656217 + 0.175833i
\(352\) −5.46410 −0.291238
\(353\) 9.84873 17.0585i 0.524195 0.907932i −0.475408 0.879765i \(-0.657700\pi\)
0.999603 0.0281669i \(-0.00896698\pi\)
\(354\) −6.12436 6.12436i −0.325506 0.325506i
\(355\) 10.8147 + 18.7315i 0.573982 + 0.994166i
\(356\) 6.64136 + 11.5032i 0.351992 + 0.609667i
\(357\) 0 0
\(358\) 1.09808 1.90192i 0.0580351 0.100520i
\(359\) −0.0717968 −0.00378929 −0.00189464 0.999998i \(-0.500603\pi\)
−0.00189464 + 0.999998i \(0.500603\pi\)
\(360\) −5.01910 + 2.89778i −0.264530 + 0.152726i
\(361\) −15.2679 −0.803576
\(362\) 4.36276 7.55652i 0.229302 0.397162i
\(363\) −8.45310 + 31.5474i −0.443672 + 1.65581i
\(364\) 0 0
\(365\) 9.19615 + 15.9282i 0.481349 + 0.833720i
\(366\) 1.33013 4.96410i 0.0695269 0.259478i
\(367\) 7.20977 12.4877i 0.376347 0.651852i −0.614181 0.789165i \(-0.710513\pi\)
0.990528 + 0.137313i \(0.0438468\pi\)
\(368\) −5.92820 −0.309029
\(369\) −14.6969 + 8.48528i −0.765092 + 0.441726i
\(370\) 15.4548 0.803457
\(371\) 0 0
\(372\) 12.2942 3.29423i 0.637426 0.170798i
\(373\) 2.56218 + 4.43782i 0.132665 + 0.229782i 0.924703 0.380690i \(-0.124313\pi\)
−0.792038 + 0.610471i \(0.790980\pi\)
\(374\) −17.2480 29.8744i −0.891871 1.54477i
\(375\) 14.8301 + 14.8301i 0.765824 + 0.765824i
\(376\) 4.76028 8.24504i 0.245493 0.425206i
\(377\) 1.79315 0.0923520
\(378\) 0 0
\(379\) 17.5167 0.899770 0.449885 0.893086i \(-0.351465\pi\)
0.449885 + 0.893086i \(0.351465\pi\)
\(380\) −1.86603 + 3.23205i −0.0957251 + 0.165801i
\(381\) −9.71003 9.71003i −0.497460 0.497460i
\(382\) 1.59808 + 2.76795i 0.0817647 + 0.141621i
\(383\) −9.76079 16.9062i −0.498753 0.863866i 0.501246 0.865305i \(-0.332875\pi\)
−0.999999 + 0.00143898i \(0.999542\pi\)
\(384\) −1.67303 + 0.448288i −0.0853766 + 0.0228766i
\(385\) 0 0
\(386\) 20.2679 1.03161
\(387\) 4.68653 + 2.70577i 0.238230 + 0.137542i
\(388\) −3.86370 −0.196150
\(389\) 14.5622 25.2224i 0.738332 1.27883i −0.214914 0.976633i \(-0.568947\pi\)
0.953246 0.302195i \(-0.0977194\pi\)
\(390\) −2.12132 + 7.91688i −0.107417 + 0.400887i
\(391\) −18.7129 32.4118i −0.946354 1.63913i
\(392\) 0 0
\(393\) 0.107695 0.401924i 0.00543250 0.0202744i
\(394\) −3.83013 + 6.63397i −0.192959 + 0.334215i
\(395\) −19.5588 −0.984108
\(396\) 16.3923i 0.823744i
\(397\) −1.89469 −0.0950916 −0.0475458 0.998869i \(-0.515140\pi\)
−0.0475458 + 0.998869i \(0.515140\pi\)
\(398\) 1.55291 2.68973i 0.0778406 0.134824i
\(399\) 0 0
\(400\) 0.633975 + 1.09808i 0.0316987 + 0.0549038i
\(401\) −6.52628 11.3038i −0.325907 0.564487i 0.655789 0.754945i \(-0.272336\pi\)
−0.981695 + 0.190457i \(0.939003\pi\)
\(402\) −17.3867 17.3867i −0.867168 0.867168i
\(403\) 9.00000 15.5885i 0.448322 0.776516i
\(404\) 1.55291 0.0772604
\(405\) 8.69333 + 15.0573i 0.431975 + 0.748203i
\(406\) 0 0
\(407\) 21.8564 37.8564i 1.08338 1.87647i
\(408\) −7.73205 7.73205i −0.382794 0.382794i
\(409\) −13.1440 22.7661i −0.649930 1.12571i −0.983139 0.182859i \(-0.941465\pi\)
0.333209 0.942853i \(-0.391869\pi\)
\(410\) −5.46410 9.46410i −0.269853 0.467399i
\(411\) 0 0
\(412\) 4.19187 7.26054i 0.206519 0.357701i
\(413\) 0 0
\(414\) 17.7846i 0.874066i
\(415\) 19.1244 0.938778
\(416\) −1.22474 + 2.12132i −0.0600481 + 0.104006i
\(417\) 0.820508 3.06218i 0.0401805 0.149955i
\(418\) 5.27792 + 9.14162i 0.258151 + 0.447131i
\(419\) 2.13990 + 3.70642i 0.104541 + 0.181070i 0.913551 0.406725i \(-0.133329\pi\)
−0.809010 + 0.587796i \(0.799996\pi\)
\(420\) 0 0
\(421\) 5.02628 8.70577i 0.244966 0.424293i −0.717156 0.696913i \(-0.754557\pi\)
0.962122 + 0.272619i \(0.0878899\pi\)
\(422\) −4.73205 −0.230353
\(423\) −24.7351 14.2808i −1.20266 0.694358i
\(424\) −3.26795 −0.158706
\(425\) −4.00240 + 6.93237i −0.194145 + 0.336269i
\(426\) 18.7315 5.01910i 0.907546 0.243176i
\(427\) 0 0
\(428\) −8.46410 14.6603i −0.409128 0.708630i
\(429\) 16.3923 + 16.3923i 0.791428 + 0.791428i
\(430\) −1.74238 + 3.01790i −0.0840252 + 0.145536i
\(431\) 14.7846 0.712150 0.356075 0.934457i \(-0.384115\pi\)
0.356075 + 0.934457i \(0.384115\pi\)
\(432\) 1.34486 + 5.01910i 0.0647048 + 0.241481i
\(433\) −28.7375 −1.38104 −0.690519 0.723314i \(-0.742618\pi\)
−0.690519 + 0.723314i \(0.742618\pi\)
\(434\) 0 0
\(435\) 1.73205 + 1.73205i 0.0830455 + 0.0830455i
\(436\) 10.2942 + 17.8301i 0.493004 + 0.853908i
\(437\) 5.72620 + 9.91808i 0.273922 + 0.474446i
\(438\) 15.9282 4.26795i 0.761079 0.203931i
\(439\) −0.656339 + 1.13681i −0.0313253 + 0.0542571i −0.881263 0.472626i \(-0.843306\pi\)
0.849938 + 0.526883i \(0.176639\pi\)
\(440\) −10.5558 −0.503230
\(441\) 0 0
\(442\) −15.4641 −0.735552
\(443\) −7.49038 + 12.9737i −0.355879 + 0.616400i −0.987268 0.159066i \(-0.949152\pi\)
0.631389 + 0.775466i \(0.282485\pi\)
\(444\) 3.58630 13.3843i 0.170198 0.635189i
\(445\) 12.8301 + 22.2224i 0.608206 + 1.05344i
\(446\) 10.3664 + 17.9551i 0.490862 + 0.850197i
\(447\) −8.24504 + 30.7709i −0.389977 + 1.45541i
\(448\) 0 0
\(449\) 17.7846 0.839308 0.419654 0.907684i \(-0.362151\pi\)
0.419654 + 0.907684i \(0.362151\pi\)
\(450\) 3.29423 1.90192i 0.155291 0.0896575i
\(451\) −30.9096 −1.45548
\(452\) −1.33013 + 2.30385i −0.0625639 + 0.108364i
\(453\) 5.67544 1.52073i 0.266655 0.0714501i
\(454\) −0.448288 0.776457i −0.0210392 0.0364409i
\(455\) 0 0
\(456\) 2.36603 + 2.36603i 0.110799 + 0.110799i
\(457\) 12.8660 22.2846i 0.601847 1.04243i −0.390694 0.920521i \(-0.627765\pi\)
0.992541 0.121909i \(-0.0389017\pi\)
\(458\) −18.0430 −0.843094
\(459\) −23.1962 + 23.1962i −1.08270 + 1.08270i
\(460\) −11.4524 −0.533971
\(461\) 10.9162 18.9074i 0.508418 0.880605i −0.491535 0.870858i \(-0.663564\pi\)
0.999952 0.00974723i \(-0.00310269\pi\)
\(462\) 0 0
\(463\) 5.33013 + 9.23205i 0.247712 + 0.429050i 0.962891 0.269892i \(-0.0869880\pi\)
−0.715179 + 0.698942i \(0.753655\pi\)
\(464\) 0.366025 + 0.633975i 0.0169923 + 0.0294315i
\(465\) 23.7506 6.36396i 1.10141 0.295122i
\(466\) −9.69615 + 16.7942i −0.449166 + 0.777978i
\(467\) 4.79744 0.221999 0.111000 0.993820i \(-0.464595\pi\)
0.111000 + 0.993820i \(0.464595\pi\)
\(468\) 6.36396 + 3.67423i 0.294174 + 0.169842i
\(469\) 0 0
\(470\) 9.19615 15.9282i 0.424187 0.734713i
\(471\) 10.9186 40.7487i 0.503102 1.87760i
\(472\) −2.50026 4.33057i −0.115084 0.199331i
\(473\) 4.92820 + 8.53590i 0.226599 + 0.392481i
\(474\) −4.53862 + 16.9384i −0.208466 + 0.778005i
\(475\) 1.22474 2.12132i 0.0561951 0.0973329i
\(476\) 0 0
\(477\) 9.80385i 0.448887i
\(478\) 5.53590 0.253206
\(479\) 8.05558 13.9527i 0.368069 0.637514i −0.621195 0.783656i \(-0.713352\pi\)
0.989264 + 0.146142i \(0.0466858\pi\)
\(480\) −3.23205 + 0.866025i −0.147522 + 0.0395285i
\(481\) −9.79796 16.9706i −0.446748 0.773791i
\(482\) −6.36396 11.0227i −0.289870 0.502070i
\(483\) 0 0
\(484\) −9.42820 + 16.3301i −0.428555 + 0.742279i
\(485\) −7.46410 −0.338927
\(486\) 15.0573 4.03459i 0.683013 0.183013i
\(487\) 2.32051 0.105152 0.0525761 0.998617i \(-0.483257\pi\)
0.0525761 + 0.998617i \(0.483257\pi\)
\(488\) 1.48356 2.56961i 0.0671578 0.116321i
\(489\) 25.6317 + 25.6317i 1.15911 + 1.15911i
\(490\) 0 0
\(491\) 9.46410 + 16.3923i 0.427109 + 0.739774i 0.996615 0.0822129i \(-0.0261988\pi\)
−0.569506 + 0.821987i \(0.692865\pi\)
\(492\) −9.46410 + 2.53590i −0.426675 + 0.114327i
\(493\) −2.31079 + 4.00240i −0.104073 + 0.180259i
\(494\) 4.73205 0.212905
\(495\) 31.6675i 1.42335i
\(496\) 7.34847 0.329956
\(497\) 0 0
\(498\) 4.43782 16.5622i 0.198864 0.742169i
\(499\) 13.6603 + 23.6603i 0.611517 + 1.05918i 0.990985 + 0.133974i \(0.0427737\pi\)
−0.379468 + 0.925205i \(0.623893\pi\)
\(500\) 6.05437 + 10.4865i 0.270760 + 0.468970i
\(501\) −7.22243 + 26.9545i −0.322674 + 1.20424i
\(502\) −0.965926 + 1.67303i −0.0431114 + 0.0746711i
\(503\) −19.1427 −0.853529 −0.426764 0.904363i \(-0.640347\pi\)
−0.426764 + 0.904363i \(0.640347\pi\)
\(504\) 0 0
\(505\) 3.00000 0.133498
\(506\) −16.1962 + 28.0526i −0.720007 + 1.24709i
\(507\) −11.7112 + 3.13801i −0.520114 + 0.139364i
\(508\) −3.96410 6.86603i −0.175879 0.304631i
\(509\) 10.8840 + 18.8516i 0.482425 + 0.835585i 0.999796 0.0201764i \(-0.00642278\pi\)
−0.517371 + 0.855761i \(0.673089\pi\)
\(510\) −14.9372 14.9372i −0.661429 0.661429i
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 7.09808 7.09808i 0.313388 0.313388i
\(514\) −20.7327 −0.914482
\(515\) 8.09808 14.0263i 0.356844 0.618072i
\(516\) 2.20925 + 2.20925i 0.0972569 + 0.0972569i
\(517\) −26.0106 45.0518i −1.14395 1.98137i
\(518\) 0 0
\(519\) 24.2942 6.50962i 1.06640 0.285741i
\(520\) −2.36603 + 4.09808i −0.103757 + 0.179713i
\(521\) 32.5269 1.42503 0.712515 0.701657i \(-0.247556\pi\)
0.712515 + 0.701657i \(0.247556\pi\)
\(522\) 1.90192 1.09808i 0.0832449 0.0480615i
\(523\) −7.41284 −0.324141 −0.162070 0.986779i \(-0.551817\pi\)
−0.162070 + 0.986779i \(0.551817\pi\)
\(524\) 0.120118 0.208051i 0.00524739 0.00908875i
\(525\) 0 0
\(526\) −7.33013 12.6962i −0.319609 0.553579i
\(527\) 23.1962 + 40.1769i 1.01044 + 1.75013i
\(528\) −2.44949 + 9.14162i −0.106600 + 0.397838i
\(529\) −6.07180 + 10.5167i −0.263991 + 0.457246i
\(530\) −6.31319 −0.274228
\(531\) −12.9917 + 7.50077i −0.563793 + 0.325506i
\(532\) 0 0
\(533\) −6.92820 + 12.0000i −0.300094 + 0.519778i
\(534\) 22.2224 5.95448i 0.961659 0.257676i
\(535\) −16.3514 28.3214i −0.706932 1.22444i
\(536\) −7.09808 12.2942i −0.306590 0.531030i
\(537\) −2.68973 2.68973i −0.116070 0.116070i
\(538\) 0.0185824 0.0321856i 0.000801143 0.00138762i
\(539\) 0 0
\(540\) 2.59808 + 9.69615i 0.111803 + 0.417256i
\(541\) 17.2679 0.742407 0.371204 0.928552i \(-0.378945\pi\)
0.371204 + 0.928552i \(0.378945\pi\)
\(542\) −2.50026 + 4.33057i −0.107395 + 0.186014i
\(543\) −10.6865 10.6865i −0.458603 0.458603i
\(544\) −3.15660 5.46739i −0.135338 0.234412i
\(545\) 19.8869 + 34.4452i 0.851862 + 1.47547i
\(546\) 0 0
\(547\) 2.26795 3.92820i 0.0969705 0.167958i −0.813459 0.581623i \(-0.802418\pi\)
0.910429 + 0.413665i \(0.135751\pi\)
\(548\) 0 0
\(549\) −7.70882 4.45069i −0.329005 0.189951i
\(550\) 6.92820 0.295420
\(551\) 0.707107 1.22474i 0.0301238 0.0521759i
\(552\) −2.65754 + 9.91808i −0.113112 + 0.422141i
\(553\) 0 0
\(554\) −2.90192 5.02628i −0.123291 0.213546i
\(555\) 6.92820 25.8564i 0.294086 1.09754i
\(556\) 0.915158 1.58510i 0.0388113 0.0672232i
\(557\) 27.1244 1.14930 0.574648 0.818401i \(-0.305139\pi\)
0.574648 + 0.818401i \(0.305139\pi\)
\(558\) 22.0454i 0.933257i
\(559\) 4.41851 0.186883
\(560\) 0 0
\(561\) −57.7128 + 15.4641i −2.43664 + 0.652895i
\(562\) 1.69615 + 2.93782i 0.0715479 + 0.123925i
\(563\) −4.31199 7.46859i −0.181729 0.314763i 0.760741 0.649056i \(-0.224836\pi\)
−0.942469 + 0.334293i \(0.891503\pi\)
\(564\) −11.6603 11.6603i −0.490985 0.490985i
\(565\) −2.56961 + 4.45069i −0.108104 + 0.187242i
\(566\) 17.1093 0.719156
\(567\) 0 0
\(568\) 11.1962 0.469780
\(569\) −6.53590 + 11.3205i −0.273999 + 0.474580i −0.969882 0.243575i \(-0.921680\pi\)
0.695883 + 0.718155i \(0.255013\pi\)
\(570\) 4.57081 + 4.57081i 0.191450 + 0.191450i
\(571\) −2.00000 3.46410i −0.0836974 0.144968i 0.821138 0.570730i \(-0.193340\pi\)
−0.904835 + 0.425762i \(0.860006\pi\)
\(572\) 6.69213 + 11.5911i 0.279812 + 0.484649i
\(573\) 5.34727 1.43280i 0.223385 0.0598559i
\(574\) 0 0
\(575\) 7.51666 0.313466
\(576\) 3.00000i 0.125000i
\(577\) 17.8028 0.741139 0.370569 0.928805i \(-0.379163\pi\)
0.370569 + 0.928805i \(0.379163\pi\)
\(578\) 11.4282 19.7942i 0.475351 0.823331i
\(579\) 9.08587 33.9089i 0.377596 1.40921i
\(580\) 0.707107 + 1.22474i 0.0293610 + 0.0508548i
\(581\) 0 0
\(582\) −1.73205 + 6.46410i −0.0717958 + 0.267946i
\(583\) −8.92820 + 15.4641i −0.369768 + 0.640458i
\(584\) 9.52056 0.393963
\(585\) 12.2942 + 7.09808i 0.508304 + 0.293469i
\(586\) 4.38134 0.180992
\(587\) −16.6102 + 28.7697i −0.685577 + 1.18745i 0.287679 + 0.957727i \(0.407117\pi\)
−0.973255 + 0.229727i \(0.926217\pi\)
\(588\) 0 0
\(589\) −7.09808 12.2942i −0.292471 0.506575i
\(590\) −4.83013 8.36603i −0.198853 0.344424i
\(591\) 9.38186 + 9.38186i 0.385918 + 0.385918i
\(592\) 4.00000 6.92820i 0.164399 0.284747i
\(593\) 21.4906 0.882513 0.441257 0.897381i \(-0.354533\pi\)
0.441257 + 0.897381i \(0.354533\pi\)
\(594\) 27.4249 + 7.34847i 1.12526 + 0.301511i
\(595\) 0 0
\(596\) −9.19615 + 15.9282i −0.376689 + 0.652445i
\(597\) −3.80385 3.80385i −0.155681 0.155681i
\(598\) 7.26054 + 12.5756i 0.296905 + 0.514255i
\(599\) −4.19615 7.26795i −0.171450 0.296960i 0.767477 0.641077i \(-0.221512\pi\)
−0.938927 + 0.344116i \(0.888179\pi\)
\(600\) 2.12132 0.568406i 0.0866025 0.0232051i
\(601\) −8.72552 + 15.1130i −0.355921 + 0.616474i −0.987275 0.159021i \(-0.949166\pi\)
0.631354 + 0.775495i \(0.282500\pi\)
\(602\) 0 0
\(603\) −36.8827 + 21.2942i −1.50198 + 0.867168i
\(604\) 3.39230 0.138031
\(605\) −18.2139 + 31.5474i −0.740500 + 1.28258i
\(606\) 0.696152 2.59808i 0.0282793 0.105540i
\(607\) 6.45189 + 11.1750i 0.261874 + 0.453580i 0.966740 0.255761i \(-0.0823261\pi\)
−0.704866 + 0.709341i \(0.748993\pi\)
\(608\) 0.965926 + 1.67303i 0.0391735 + 0.0678504i
\(609\) 0 0
\(610\) 2.86603 4.96410i 0.116042 0.200991i
\(611\) −23.3205 −0.943447
\(612\) −16.4022 + 9.46979i −0.663018 + 0.382794i
\(613\) −38.4449 −1.55277 −0.776387 0.630257i \(-0.782950\pi\)
−0.776387 + 0.630257i \(0.782950\pi\)
\(614\) 14.5397 25.1834i 0.586773 1.01632i
\(615\) −18.2832 + 4.89898i −0.737251 + 0.197546i
\(616\) 0 0
\(617\) −10.8038 18.7128i −0.434947 0.753349i 0.562345 0.826903i \(-0.309899\pi\)
−0.997291 + 0.0735534i \(0.976566\pi\)
\(618\) −10.2679 10.2679i −0.413037 0.413037i
\(619\) 7.27912 12.6078i 0.292572 0.506750i −0.681845 0.731497i \(-0.738822\pi\)
0.974417 + 0.224746i \(0.0721554\pi\)
\(620\) 14.1962 0.570131
\(621\) 29.7542 + 7.97262i 1.19400 + 0.319930i
\(622\) −21.0101 −0.842430
\(623\) 0 0
\(624\) 3.00000 + 3.00000i 0.120096 + 0.120096i
\(625\) 8.52628 + 14.7679i 0.341051 + 0.590718i
\(626\) 0.896575 + 1.55291i 0.0358344 + 0.0620669i
\(627\) 17.6603 4.73205i 0.705283 0.188980i
\(628\) 12.1781 21.0931i 0.485959 0.841706i
\(629\) 50.5055 2.01379
\(630\) 0 0
\(631\) −28.1244 −1.11961 −0.559806 0.828623i \(-0.689125\pi\)
−0.559806 + 0.828623i \(0.689125\pi\)
\(632\) −5.06218 + 8.76795i −0.201363 + 0.348770i
\(633\) −2.12132 + 7.91688i −0.0843149 + 0.314668i
\(634\) 0.705771 + 1.22243i 0.0280298 + 0.0485490i
\(635\) −7.65806 13.2641i −0.303901 0.526371i
\(636\) −1.46498 + 5.46739i −0.0580903 + 0.216796i
\(637\) 0 0
\(638\) 4.00000 0.158362
\(639\) 33.5885i 1.32874i
\(640\) −1.93185 −0.0763631
\(641\) −17.5263 + 30.3564i −0.692246 + 1.19901i 0.278854 + 0.960334i \(0.410046\pi\)
−0.971100 + 0.238672i \(0.923288\pi\)
\(642\) −28.3214 + 7.58871i −1.11776 + 0.299502i
\(643\) 6.50266 + 11.2629i 0.256440 + 0.444167i 0.965286 0.261197i \(-0.0841171\pi\)
−0.708846 + 0.705364i \(0.750784\pi\)
\(644\) 0 0
\(645\) 4.26795 + 4.26795i 0.168050 + 0.168050i
\(646\) −6.09808 + 10.5622i −0.239926 + 0.415563i
\(647\) 1.13681 0.0446927 0.0223463 0.999750i \(-0.492886\pi\)
0.0223463 + 0.999750i \(0.492886\pi\)
\(648\) 9.00000 0.353553
\(649\) −27.3233 −1.07253
\(650\) 1.55291 2.68973i 0.0609103 0.105500i
\(651\) 0 0
\(652\) 10.4641 + 18.1244i 0.409806 + 0.709805i
\(653\) 3.33975 + 5.78461i 0.130694 + 0.226369i 0.923944 0.382527i \(-0.124946\pi\)
−0.793250 + 0.608896i \(0.791613\pi\)
\(654\) 34.4452 9.22955i 1.34691 0.360904i
\(655\) 0.232051 0.401924i 0.00906698 0.0157045i
\(656\) −5.65685 −0.220863
\(657\) 28.5617i 1.11430i
\(658\) 0 0
\(659\) 7.43782 12.8827i 0.289736 0.501838i −0.684010 0.729472i \(-0.739766\pi\)
0.973747 + 0.227634i \(0.0730990\pi\)
\(660\) −4.73205 + 17.6603i −0.184195 + 0.687424i
\(661\) 16.8504 + 29.1858i 0.655406 + 1.13520i 0.981792 + 0.189960i \(0.0608359\pi\)
−0.326385 + 0.945237i \(0.605831\pi\)
\(662\) 13.0263 + 22.5622i 0.506281 + 0.876904i
\(663\) −6.93237 + 25.8719i −0.269231 + 1.00478i
\(664\) 4.94975 8.57321i 0.192087 0.332705i
\(665\) 0 0
\(666\) −20.7846 12.0000i −0.805387 0.464991i
\(667\) 4.33975 0.168036
\(668\) −8.05558 + 13.9527i −0.311680 + 0.539845i
\(669\) 34.6865 9.29423i 1.34106 0.359336i
\(670\) −13.7124 23.7506i −0.529757 0.917567i
\(671\) −8.10634 14.0406i −0.312942 0.542031i
\(672\) 0 0
\(673\) −11.0885 + 19.2058i −0.427429 + 0.740328i −0.996644 0.0818605i \(-0.973914\pi\)
0.569215 + 0.822189i \(0.307247\pi\)
\(674\) −13.3205 −0.513087
\(675\) −1.70522 6.36396i −0.0656339 0.244949i
\(676\) −7.00000 −0.269231
\(677\) 7.91688 13.7124i 0.304270 0.527012i −0.672828 0.739799i \(-0.734921\pi\)
0.977099 + 0.212787i \(0.0682541\pi\)
\(678\) 3.25813 + 3.25813i 0.125128 + 0.125128i
\(679\) 0 0
\(680\) −6.09808 10.5622i −0.233851 0.405041i
\(681\) −1.50000 + 0.401924i −0.0574801 + 0.0154018i
\(682\) 20.0764 34.7733i 0.768765 1.33154i
\(683\) −34.3923 −1.31598 −0.657992 0.753024i \(-0.728594\pi\)
−0.657992 + 0.753024i \(0.728594\pi\)
\(684\) 5.01910 2.89778i 0.191910 0.110799i
\(685\) 0 0
\(686\) 0 0
\(687\) −8.08846 + 30.1865i −0.308594 + 1.15169i
\(688\) 0.901924 + 1.56218i 0.0343855 + 0.0595575i
\(689\) 4.00240 + 6.93237i 0.152479 + 0.264102i
\(690\) −5.13397 + 19.1603i −0.195447 + 0.729418i
\(691\) 12.1273 21.0052i 0.461345 0.799074i −0.537683 0.843147i \(-0.680700\pi\)
0.999028 + 0.0440735i \(0.0140336\pi\)
\(692\) 14.5211 0.552008
\(693\) 0 0
\(694\) 33.7128 1.27972
\(695\) 1.76795 3.06218i 0.0670621 0.116155i
\(696\) 1.22474 0.328169i 0.0464238 0.0124392i
\(697\) −17.8564 30.9282i −0.676360 1.17149i
\(698\) 12.3998 + 21.4770i 0.469338 + 0.812916i
\(699\) 23.7506 + 23.7506i 0.898331 + 0.898331i
\(700\) 0 0
\(701\) 27.4641 1.03730 0.518652 0.854985i \(-0.326434\pi\)
0.518652 + 0.854985i \(0.326434\pi\)
\(702\) 9.00000 9.00000i 0.339683 0.339683i
\(703\) −15.4548 −0.582889
\(704\) −2.73205 + 4.73205i −0.102968 + 0.178346i
\(705\) −22.5259 22.5259i −0.848374 0.848374i
\(706\) −9.84873 17.0585i −0.370662 0.642005i
\(707\) 0 0
\(708\) −8.36603 + 2.24167i −0.314414 + 0.0842471i
\(709\) 14.7321 25.5167i 0.553274 0.958298i −0.444762 0.895649i \(-0.646712\pi\)
0.998036 0.0626494i \(-0.0199550\pi\)
\(710\) 21.6293 0.811733
\(711\) 26.3038 + 15.1865i 0.986471 + 0.569540i
\(712\) 13.2827 0.497791
\(713\) 21.7816 37.7269i 0.815728 1.41288i
\(714\) 0 0
\(715\) 12.9282 + 22.3923i 0.483487 + 0.837425i
\(716\) −1.09808 1.90192i −0.0410370 0.0710782i
\(717\) 2.48168 9.26174i 0.0926799 0.345886i
\(718\) −0.0358984 + 0.0621778i −0.00133972 + 0.00232046i
\(719\) −19.8733 −0.741150 −0.370575 0.928803i \(-0.620839\pi\)
−0.370575 + 0.928803i \(0.620839\pi\)
\(720\) 5.79555i 0.215988i
\(721\) 0 0
\(722\) −7.63397 + 13.2224i −0.284107 + 0.492088i
\(723\) −21.2942 + 5.70577i −0.791941 + 0.212200i
\(724\) −4.36276 7.55652i −0.162141 0.280836i
\(725\) −0.464102 0.803848i −0.0172363 0.0298541i
\(726\) 23.0943 + 23.0943i 0.857109 + 0.857109i
\(727\) 12.0580 20.8850i 0.447206 0.774583i −0.550997 0.834507i \(-0.685753\pi\)
0.998203 + 0.0599240i \(0.0190858\pi\)
\(728\) 0 0
\(729\) 27.0000i 1.00000i
\(730\) 18.3923 0.680730
\(731\) −5.69402 + 9.86233i −0.210601 + 0.364771i
\(732\) −3.63397 3.63397i −0.134316 0.134316i
\(733\) 4.03459 + 6.98811i 0.149021 + 0.258112i 0.930866 0.365361i \(-0.119054\pi\)
−0.781845 + 0.623473i \(0.785721\pi\)
\(734\) −7.20977 12.4877i −0.266117 0.460929i
\(735\) 0 0
\(736\) −2.96410 + 5.13397i −0.109258 + 0.189241i
\(737\) −77.5692 −2.85730
\(738\) 16.9706i 0.624695i
\(739\) −43.8564 −1.61328 −0.806642 0.591040i \(-0.798717\pi\)
−0.806642 + 0.591040i \(0.798717\pi\)
\(740\) 7.72741 13.3843i 0.284065 0.492015i
\(741\) 2.12132 7.91688i 0.0779287 0.290834i
\(742\) 0 0
\(743\) −10.1244 17.5359i −0.371427 0.643330i 0.618359 0.785896i \(-0.287798\pi\)
−0.989785 + 0.142566i \(0.954465\pi\)
\(744\) 3.29423 12.2942i 0.120772 0.450728i
\(745\) −17.7656 + 30.7709i −0.650881 + 1.12736i
\(746\) 5.12436 0.187616
\(747\) −25.7196 14.8492i −0.941033 0.543305i
\(748\) −34.4959 −1.26130
\(749\) 0 0
\(750\) 20.2583 5.42820i 0.739730 0.198210i
\(751\) −6.08846 10.5455i −0.222171 0.384811i 0.733296 0.679910i \(-0.237981\pi\)
−0.955467 + 0.295098i \(0.904648\pi\)
\(752\) −4.76028 8.24504i −0.173590 0.300666i
\(753\) 2.36603 + 2.36603i 0.0862228 + 0.0862228i
\(754\) 0.896575 1.55291i 0.0326514 0.0565538i
\(755\) 6.55343 0.238504
\(756\) 0 0
\(757\) −28.2487 −1.02672 −0.513358 0.858174i \(-0.671599\pi\)
−0.513358 + 0.858174i \(0.671599\pi\)
\(758\) 8.75833 15.1699i 0.318117 0.550995i
\(759\) 39.6723 + 39.6723i 1.44001 + 1.44001i
\(760\) 1.86603 + 3.23205i 0.0676879 + 0.117239i
\(761\) −2.74049 4.74668i −0.0993428 0.172067i 0.812070 0.583560i \(-0.198341\pi\)
−0.911413 + 0.411493i \(0.865007\pi\)
\(762\) −13.2641 + 3.55412i −0.480509 + 0.128752i
\(763\) 0 0
\(764\) 3.19615 0.115633
\(765\) −31.6865 + 18.2942i −1.14563 + 0.661429i
\(766\) −19.5216 −0.705344
\(767\) −6.12436 + 10.6077i −0.221138 + 0.383022i
\(768\) −0.448288 + 1.67303i −0.0161762 + 0.0603704i
\(769\) −2.20925 3.82654i −0.0796677 0.137989i 0.823439 0.567405i \(-0.192053\pi\)
−0.903107 + 0.429416i \(0.858719\pi\)
\(770\) 0 0
\(771\) −9.29423 + 34.6865i −0.334723 + 1.24920i
\(772\) 10.1340 17.5526i 0.364730 0.631730i
\(773\) 3.62347 0.130327 0.0651635 0.997875i \(-0.479243\pi\)
0.0651635 + 0.997875i \(0.479243\pi\)
\(774\) 4.68653 2.70577i 0.168454 0.0972569i
\(775\) −9.31749 −0.334694
\(776\) −1.93185 + 3.34607i −0.0693494 + 0.120117i
\(777\) 0 0
\(778\) −14.5622 25.2224i −0.522079 0.904268i
\(779\) 5.46410 + 9.46410i 0.195772 + 0.339087i
\(780\) 5.79555 + 5.79555i 0.207514 + 0.207514i
\(781\) 30.5885 52.9808i 1.09454 1.89580i