Properties

Label 1078.2.e.s.67.2
Level $1078$
Weight $2$
Character 1078.67
Analytic conductor $8.608$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1078.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.60787333789\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.2
Root \(0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 1078.67
Dual form 1078.2.e.s.177.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(0.707107 - 1.22474i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.707107 - 1.22474i) q^{5} +1.41421 q^{6} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(0.707107 - 1.22474i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.707107 - 1.22474i) q^{5} +1.41421 q^{6} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(0.707107 - 1.22474i) q^{10} +(0.500000 - 0.866025i) q^{11} +(0.707107 + 1.22474i) q^{12} +2.82843 q^{13} -2.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.82843 - 4.89898i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-1.41421 - 2.44949i) q^{19} +1.41421 q^{20} +1.00000 q^{22} +(1.00000 + 1.73205i) q^{23} +(-0.707107 + 1.22474i) q^{24} +(1.50000 - 2.59808i) q^{25} +(1.41421 + 2.44949i) q^{26} +5.65685 q^{27} -6.00000 q^{29} +(-1.00000 - 1.73205i) q^{30} +(0.707107 - 1.22474i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.707107 - 1.22474i) q^{33} +5.65685 q^{34} -1.00000 q^{36} +(1.00000 + 1.73205i) q^{37} +(1.41421 - 2.44949i) q^{38} +(2.00000 - 3.46410i) q^{39} +(0.707107 + 1.22474i) q^{40} +5.65685 q^{41} +4.00000 q^{43} +(0.500000 + 0.866025i) q^{44} +(0.707107 - 1.22474i) q^{45} +(-1.00000 + 1.73205i) q^{46} +(-2.12132 - 3.67423i) q^{47} -1.41421 q^{48} +3.00000 q^{50} +(-4.00000 - 6.92820i) q^{51} +(-1.41421 + 2.44949i) q^{52} +(6.00000 - 10.3923i) q^{53} +(2.82843 + 4.89898i) q^{54} -1.41421 q^{55} -4.00000 q^{57} +(-3.00000 - 5.19615i) q^{58} +(-2.12132 + 3.67423i) q^{59} +(1.00000 - 1.73205i) q^{60} +(2.82843 + 4.89898i) q^{61} +1.41421 q^{62} +1.00000 q^{64} +(-2.00000 - 3.46410i) q^{65} +(0.707107 - 1.22474i) q^{66} +(1.00000 - 1.73205i) q^{67} +(2.82843 + 4.89898i) q^{68} +2.82843 q^{69} -10.0000 q^{71} +(-0.500000 - 0.866025i) q^{72} +(7.07107 - 12.2474i) q^{73} +(-1.00000 + 1.73205i) q^{74} +(-2.12132 - 3.67423i) q^{75} +2.82843 q^{76} +4.00000 q^{78} +(4.00000 + 6.92820i) q^{79} +(-0.707107 + 1.22474i) q^{80} +(2.50000 - 4.33013i) q^{81} +(2.82843 + 4.89898i) q^{82} -2.82843 q^{83} -8.00000 q^{85} +(2.00000 + 3.46410i) q^{86} +(-4.24264 + 7.34847i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(3.53553 + 6.12372i) q^{89} +1.41421 q^{90} -2.00000 q^{92} +(-1.00000 - 1.73205i) q^{93} +(2.12132 - 3.67423i) q^{94} +(-2.00000 + 3.46410i) q^{95} +(-0.707107 - 1.22474i) q^{96} -15.5563 q^{97} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{8} + 2 q^{9} + O(q^{10}) \) \( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{8} + 2 q^{9} + 2 q^{11} - 8 q^{15} - 2 q^{16} - 2 q^{18} + 4 q^{22} + 4 q^{23} + 6 q^{25} - 24 q^{29} - 4 q^{30} + 2 q^{32} - 4 q^{36} + 4 q^{37} + 8 q^{39} + 16 q^{43} + 2 q^{44} - 4 q^{46} + 12 q^{50} - 16 q^{51} + 24 q^{53} - 16 q^{57} - 12 q^{58} + 4 q^{60} + 4 q^{64} - 8 q^{65} + 4 q^{67} - 40 q^{71} - 2 q^{72} - 4 q^{74} + 16 q^{78} + 16 q^{79} + 10 q^{81} - 32 q^{85} + 8 q^{86} - 2 q^{88} - 8 q^{92} - 4 q^{93} - 8 q^{95} + 4 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(981\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 0.707107 1.22474i 0.408248 0.707107i −0.586445 0.809989i \(-0.699473\pi\)
0.994694 + 0.102882i \(0.0328064\pi\)
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −0.707107 1.22474i −0.316228 0.547723i 0.663470 0.748203i \(-0.269083\pi\)
−0.979698 + 0.200480i \(0.935750\pi\)
\(6\) 1.41421 0.577350
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 0.707107 1.22474i 0.223607 0.387298i
\(11\) 0.500000 0.866025i 0.150756 0.261116i
\(12\) 0.707107 + 1.22474i 0.204124 + 0.353553i
\(13\) 2.82843 0.784465 0.392232 0.919866i \(-0.371703\pi\)
0.392232 + 0.919866i \(0.371703\pi\)
\(14\) 0 0
\(15\) −2.00000 −0.516398
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 2.82843 4.89898i 0.685994 1.18818i −0.287129 0.957892i \(-0.592701\pi\)
0.973123 0.230285i \(-0.0739659\pi\)
\(18\) −0.500000 + 0.866025i −0.117851 + 0.204124i
\(19\) −1.41421 2.44949i −0.324443 0.561951i 0.656957 0.753928i \(-0.271843\pi\)
−0.981399 + 0.191977i \(0.938510\pi\)
\(20\) 1.41421 0.316228
\(21\) 0 0
\(22\) 1.00000 0.213201
\(23\) 1.00000 + 1.73205i 0.208514 + 0.361158i 0.951247 0.308431i \(-0.0998038\pi\)
−0.742732 + 0.669588i \(0.766471\pi\)
\(24\) −0.707107 + 1.22474i −0.144338 + 0.250000i
\(25\) 1.50000 2.59808i 0.300000 0.519615i
\(26\) 1.41421 + 2.44949i 0.277350 + 0.480384i
\(27\) 5.65685 1.08866
\(28\) 0 0
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) −1.00000 1.73205i −0.182574 0.316228i
\(31\) 0.707107 1.22474i 0.127000 0.219971i −0.795513 0.605937i \(-0.792798\pi\)
0.922513 + 0.385966i \(0.126132\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) −0.707107 1.22474i −0.123091 0.213201i
\(34\) 5.65685 0.970143
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) 1.00000 + 1.73205i 0.164399 + 0.284747i 0.936442 0.350823i \(-0.114098\pi\)
−0.772043 + 0.635571i \(0.780765\pi\)
\(38\) 1.41421 2.44949i 0.229416 0.397360i
\(39\) 2.00000 3.46410i 0.320256 0.554700i
\(40\) 0.707107 + 1.22474i 0.111803 + 0.193649i
\(41\) 5.65685 0.883452 0.441726 0.897150i \(-0.354366\pi\)
0.441726 + 0.897150i \(0.354366\pi\)
\(42\) 0 0
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) 0.500000 + 0.866025i 0.0753778 + 0.130558i
\(45\) 0.707107 1.22474i 0.105409 0.182574i
\(46\) −1.00000 + 1.73205i −0.147442 + 0.255377i
\(47\) −2.12132 3.67423i −0.309426 0.535942i 0.668811 0.743433i \(-0.266804\pi\)
−0.978237 + 0.207491i \(0.933470\pi\)
\(48\) −1.41421 −0.204124
\(49\) 0 0
\(50\) 3.00000 0.424264
\(51\) −4.00000 6.92820i −0.560112 0.970143i
\(52\) −1.41421 + 2.44949i −0.196116 + 0.339683i
\(53\) 6.00000 10.3923i 0.824163 1.42749i −0.0783936 0.996922i \(-0.524979\pi\)
0.902557 0.430570i \(-0.141688\pi\)
\(54\) 2.82843 + 4.89898i 0.384900 + 0.666667i
\(55\) −1.41421 −0.190693
\(56\) 0 0
\(57\) −4.00000 −0.529813
\(58\) −3.00000 5.19615i −0.393919 0.682288i
\(59\) −2.12132 + 3.67423i −0.276172 + 0.478345i −0.970430 0.241382i \(-0.922399\pi\)
0.694258 + 0.719726i \(0.255733\pi\)
\(60\) 1.00000 1.73205i 0.129099 0.223607i
\(61\) 2.82843 + 4.89898i 0.362143 + 0.627250i 0.988313 0.152436i \(-0.0487119\pi\)
−0.626170 + 0.779686i \(0.715379\pi\)
\(62\) 1.41421 0.179605
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −2.00000 3.46410i −0.248069 0.429669i
\(66\) 0.707107 1.22474i 0.0870388 0.150756i
\(67\) 1.00000 1.73205i 0.122169 0.211604i −0.798454 0.602056i \(-0.794348\pi\)
0.920623 + 0.390453i \(0.127682\pi\)
\(68\) 2.82843 + 4.89898i 0.342997 + 0.594089i
\(69\) 2.82843 0.340503
\(70\) 0 0
\(71\) −10.0000 −1.18678 −0.593391 0.804914i \(-0.702211\pi\)
−0.593391 + 0.804914i \(0.702211\pi\)
\(72\) −0.500000 0.866025i −0.0589256 0.102062i
\(73\) 7.07107 12.2474i 0.827606 1.43346i −0.0723054 0.997383i \(-0.523036\pi\)
0.899911 0.436073i \(-0.143631\pi\)
\(74\) −1.00000 + 1.73205i −0.116248 + 0.201347i
\(75\) −2.12132 3.67423i −0.244949 0.424264i
\(76\) 2.82843 0.324443
\(77\) 0 0
\(78\) 4.00000 0.452911
\(79\) 4.00000 + 6.92820i 0.450035 + 0.779484i 0.998388 0.0567635i \(-0.0180781\pi\)
−0.548352 + 0.836247i \(0.684745\pi\)
\(80\) −0.707107 + 1.22474i −0.0790569 + 0.136931i
\(81\) 2.50000 4.33013i 0.277778 0.481125i
\(82\) 2.82843 + 4.89898i 0.312348 + 0.541002i
\(83\) −2.82843 −0.310460 −0.155230 0.987878i \(-0.549612\pi\)
−0.155230 + 0.987878i \(0.549612\pi\)
\(84\) 0 0
\(85\) −8.00000 −0.867722
\(86\) 2.00000 + 3.46410i 0.215666 + 0.373544i
\(87\) −4.24264 + 7.34847i −0.454859 + 0.787839i
\(88\) −0.500000 + 0.866025i −0.0533002 + 0.0923186i
\(89\) 3.53553 + 6.12372i 0.374766 + 0.649113i 0.990292 0.139003i \(-0.0443898\pi\)
−0.615526 + 0.788116i \(0.711056\pi\)
\(90\) 1.41421 0.149071
\(91\) 0 0
\(92\) −2.00000 −0.208514
\(93\) −1.00000 1.73205i −0.103695 0.179605i
\(94\) 2.12132 3.67423i 0.218797 0.378968i
\(95\) −2.00000 + 3.46410i −0.205196 + 0.355409i
\(96\) −0.707107 1.22474i −0.0721688 0.125000i
\(97\) −15.5563 −1.57951 −0.789754 0.613424i \(-0.789792\pi\)
−0.789754 + 0.613424i \(0.789792\pi\)
\(98\) 0 0
\(99\) 1.00000 0.100504
\(100\) 1.50000 + 2.59808i 0.150000 + 0.259808i
\(101\) −1.41421 + 2.44949i −0.140720 + 0.243733i −0.927768 0.373158i \(-0.878275\pi\)
0.787048 + 0.616891i \(0.211608\pi\)
\(102\) 4.00000 6.92820i 0.396059 0.685994i
\(103\) 2.12132 + 3.67423i 0.209020 + 0.362033i 0.951406 0.307939i \(-0.0996393\pi\)
−0.742386 + 0.669972i \(0.766306\pi\)
\(104\) −2.82843 −0.277350
\(105\) 0 0
\(106\) 12.0000 1.16554
\(107\) 10.0000 + 17.3205i 0.966736 + 1.67444i 0.704875 + 0.709331i \(0.251003\pi\)
0.261861 + 0.965106i \(0.415664\pi\)
\(108\) −2.82843 + 4.89898i −0.272166 + 0.471405i
\(109\) −5.00000 + 8.66025i −0.478913 + 0.829502i −0.999708 0.0241802i \(-0.992302\pi\)
0.520794 + 0.853682i \(0.325636\pi\)
\(110\) −0.707107 1.22474i −0.0674200 0.116775i
\(111\) 2.82843 0.268462
\(112\) 0 0
\(113\) −18.0000 −1.69330 −0.846649 0.532152i \(-0.821383\pi\)
−0.846649 + 0.532152i \(0.821383\pi\)
\(114\) −2.00000 3.46410i −0.187317 0.324443i
\(115\) 1.41421 2.44949i 0.131876 0.228416i
\(116\) 3.00000 5.19615i 0.278543 0.482451i
\(117\) 1.41421 + 2.44949i 0.130744 + 0.226455i
\(118\) −4.24264 −0.390567
\(119\) 0 0
\(120\) 2.00000 0.182574
\(121\) −0.500000 0.866025i −0.0454545 0.0787296i
\(122\) −2.82843 + 4.89898i −0.256074 + 0.443533i
\(123\) 4.00000 6.92820i 0.360668 0.624695i
\(124\) 0.707107 + 1.22474i 0.0635001 + 0.109985i
\(125\) −11.3137 −1.01193
\(126\) 0 0
\(127\) 12.0000 1.06483 0.532414 0.846484i \(-0.321285\pi\)
0.532414 + 0.846484i \(0.321285\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 2.82843 4.89898i 0.249029 0.431331i
\(130\) 2.00000 3.46410i 0.175412 0.303822i
\(131\) −5.65685 9.79796i −0.494242 0.856052i 0.505736 0.862688i \(-0.331221\pi\)
−0.999978 + 0.00663646i \(0.997888\pi\)
\(132\) 1.41421 0.123091
\(133\) 0 0
\(134\) 2.00000 0.172774
\(135\) −4.00000 6.92820i −0.344265 0.596285i
\(136\) −2.82843 + 4.89898i −0.242536 + 0.420084i
\(137\) 1.00000 1.73205i 0.0854358 0.147979i −0.820141 0.572161i \(-0.806105\pi\)
0.905577 + 0.424182i \(0.139438\pi\)
\(138\) 1.41421 + 2.44949i 0.120386 + 0.208514i
\(139\) −2.82843 −0.239904 −0.119952 0.992780i \(-0.538274\pi\)
−0.119952 + 0.992780i \(0.538274\pi\)
\(140\) 0 0
\(141\) −6.00000 −0.505291
\(142\) −5.00000 8.66025i −0.419591 0.726752i
\(143\) 1.41421 2.44949i 0.118262 0.204837i
\(144\) 0.500000 0.866025i 0.0416667 0.0721688i
\(145\) 4.24264 + 7.34847i 0.352332 + 0.610257i
\(146\) 14.1421 1.17041
\(147\) 0 0
\(148\) −2.00000 −0.164399
\(149\) 5.00000 + 8.66025i 0.409616 + 0.709476i 0.994847 0.101391i \(-0.0323294\pi\)
−0.585231 + 0.810867i \(0.698996\pi\)
\(150\) 2.12132 3.67423i 0.173205 0.300000i
\(151\) −8.00000 + 13.8564i −0.651031 + 1.12762i 0.331842 + 0.943335i \(0.392330\pi\)
−0.982873 + 0.184284i \(0.941004\pi\)
\(152\) 1.41421 + 2.44949i 0.114708 + 0.198680i
\(153\) 5.65685 0.457330
\(154\) 0 0
\(155\) −2.00000 −0.160644
\(156\) 2.00000 + 3.46410i 0.160128 + 0.277350i
\(157\) −9.19239 + 15.9217i −0.733632 + 1.27069i 0.221688 + 0.975118i \(0.428843\pi\)
−0.955321 + 0.295571i \(0.904490\pi\)
\(158\) −4.00000 + 6.92820i −0.318223 + 0.551178i
\(159\) −8.48528 14.6969i −0.672927 1.16554i
\(160\) −1.41421 −0.111803
\(161\) 0 0
\(162\) 5.00000 0.392837
\(163\) 11.0000 + 19.0526i 0.861586 + 1.49231i 0.870397 + 0.492350i \(0.163862\pi\)
−0.00881059 + 0.999961i \(0.502805\pi\)
\(164\) −2.82843 + 4.89898i −0.220863 + 0.382546i
\(165\) −1.00000 + 1.73205i −0.0778499 + 0.134840i
\(166\) −1.41421 2.44949i −0.109764 0.190117i
\(167\) −11.3137 −0.875481 −0.437741 0.899101i \(-0.644221\pi\)
−0.437741 + 0.899101i \(0.644221\pi\)
\(168\) 0 0
\(169\) −5.00000 −0.384615
\(170\) −4.00000 6.92820i −0.306786 0.531369i
\(171\) 1.41421 2.44949i 0.108148 0.187317i
\(172\) −2.00000 + 3.46410i −0.152499 + 0.264135i
\(173\) −7.07107 12.2474i −0.537603 0.931156i −0.999032 0.0439792i \(-0.985996\pi\)
0.461429 0.887177i \(-0.347337\pi\)
\(174\) −8.48528 −0.643268
\(175\) 0 0
\(176\) −1.00000 −0.0753778
\(177\) 3.00000 + 5.19615i 0.225494 + 0.390567i
\(178\) −3.53553 + 6.12372i −0.264999 + 0.458993i
\(179\) −10.0000 + 17.3205i −0.747435 + 1.29460i 0.201613 + 0.979465i \(0.435382\pi\)
−0.949048 + 0.315130i \(0.897952\pi\)
\(180\) 0.707107 + 1.22474i 0.0527046 + 0.0912871i
\(181\) 12.7279 0.946059 0.473029 0.881047i \(-0.343160\pi\)
0.473029 + 0.881047i \(0.343160\pi\)
\(182\) 0 0
\(183\) 8.00000 0.591377
\(184\) −1.00000 1.73205i −0.0737210 0.127688i
\(185\) 1.41421 2.44949i 0.103975 0.180090i
\(186\) 1.00000 1.73205i 0.0733236 0.127000i
\(187\) −2.82843 4.89898i −0.206835 0.358249i
\(188\) 4.24264 0.309426
\(189\) 0 0
\(190\) −4.00000 −0.290191
\(191\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(192\) 0.707107 1.22474i 0.0510310 0.0883883i
\(193\) −3.00000 + 5.19615i −0.215945 + 0.374027i −0.953564 0.301189i \(-0.902616\pi\)
0.737620 + 0.675216i \(0.235950\pi\)
\(194\) −7.77817 13.4722i −0.558440 0.967247i
\(195\) −5.65685 −0.405096
\(196\) 0 0
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 0.500000 + 0.866025i 0.0355335 + 0.0615457i
\(199\) −10.6066 + 18.3712i −0.751882 + 1.30230i 0.195027 + 0.980798i \(0.437520\pi\)
−0.946910 + 0.321500i \(0.895813\pi\)
\(200\) −1.50000 + 2.59808i −0.106066 + 0.183712i
\(201\) −1.41421 2.44949i −0.0997509 0.172774i
\(202\) −2.82843 −0.199007
\(203\) 0 0
\(204\) 8.00000 0.560112
\(205\) −4.00000 6.92820i −0.279372 0.483887i
\(206\) −2.12132 + 3.67423i −0.147799 + 0.255996i
\(207\) −1.00000 + 1.73205i −0.0695048 + 0.120386i
\(208\) −1.41421 2.44949i −0.0980581 0.169842i
\(209\) −2.82843 −0.195646
\(210\) 0 0
\(211\) 28.0000 1.92760 0.963800 0.266627i \(-0.0859092\pi\)
0.963800 + 0.266627i \(0.0859092\pi\)
\(212\) 6.00000 + 10.3923i 0.412082 + 0.713746i
\(213\) −7.07107 + 12.2474i −0.484502 + 0.839181i
\(214\) −10.0000 + 17.3205i −0.683586 + 1.18401i
\(215\) −2.82843 4.89898i −0.192897 0.334108i
\(216\) −5.65685 −0.384900
\(217\) 0 0
\(218\) −10.0000 −0.677285
\(219\) −10.0000 17.3205i −0.675737 1.17041i
\(220\) 0.707107 1.22474i 0.0476731 0.0825723i
\(221\) 8.00000 13.8564i 0.538138 0.932083i
\(222\) 1.41421 + 2.44949i 0.0949158 + 0.164399i
\(223\) −15.5563 −1.04173 −0.520865 0.853639i \(-0.674391\pi\)
−0.520865 + 0.853639i \(0.674391\pi\)
\(224\) 0 0
\(225\) 3.00000 0.200000
\(226\) −9.00000 15.5885i −0.598671 1.03693i
\(227\) 14.1421 24.4949i 0.938647 1.62578i 0.170648 0.985332i \(-0.445414\pi\)
0.767999 0.640451i \(-0.221253\pi\)
\(228\) 2.00000 3.46410i 0.132453 0.229416i
\(229\) 2.12132 + 3.67423i 0.140181 + 0.242800i 0.927565 0.373663i \(-0.121898\pi\)
−0.787384 + 0.616463i \(0.788565\pi\)
\(230\) 2.82843 0.186501
\(231\) 0 0
\(232\) 6.00000 0.393919
\(233\) −3.00000 5.19615i −0.196537 0.340411i 0.750867 0.660454i \(-0.229636\pi\)
−0.947403 + 0.320043i \(0.896303\pi\)
\(234\) −1.41421 + 2.44949i −0.0924500 + 0.160128i
\(235\) −3.00000 + 5.19615i −0.195698 + 0.338960i
\(236\) −2.12132 3.67423i −0.138086 0.239172i
\(237\) 11.3137 0.734904
\(238\) 0 0
\(239\) −16.0000 −1.03495 −0.517477 0.855697i \(-0.673129\pi\)
−0.517477 + 0.855697i \(0.673129\pi\)
\(240\) 1.00000 + 1.73205i 0.0645497 + 0.111803i
\(241\) 2.82843 4.89898i 0.182195 0.315571i −0.760433 0.649417i \(-0.775013\pi\)
0.942628 + 0.333846i \(0.108346\pi\)
\(242\) 0.500000 0.866025i 0.0321412 0.0556702i
\(243\) 4.94975 + 8.57321i 0.317526 + 0.549972i
\(244\) −5.65685 −0.362143
\(245\) 0 0
\(246\) 8.00000 0.510061
\(247\) −4.00000 6.92820i −0.254514 0.440831i
\(248\) −0.707107 + 1.22474i −0.0449013 + 0.0777714i
\(249\) −2.00000 + 3.46410i −0.126745 + 0.219529i
\(250\) −5.65685 9.79796i −0.357771 0.619677i
\(251\) −24.0416 −1.51749 −0.758747 0.651385i \(-0.774188\pi\)
−0.758747 + 0.651385i \(0.774188\pi\)
\(252\) 0 0
\(253\) 2.00000 0.125739
\(254\) 6.00000 + 10.3923i 0.376473 + 0.652071i
\(255\) −5.65685 + 9.79796i −0.354246 + 0.613572i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 4.94975 + 8.57321i 0.308757 + 0.534782i 0.978091 0.208179i \(-0.0667538\pi\)
−0.669334 + 0.742962i \(0.733420\pi\)
\(258\) 5.65685 0.352180
\(259\) 0 0
\(260\) 4.00000 0.248069
\(261\) −3.00000 5.19615i −0.185695 0.321634i
\(262\) 5.65685 9.79796i 0.349482 0.605320i
\(263\) −12.0000 + 20.7846i −0.739952 + 1.28163i 0.212565 + 0.977147i \(0.431818\pi\)
−0.952517 + 0.304487i \(0.901515\pi\)
\(264\) 0.707107 + 1.22474i 0.0435194 + 0.0753778i
\(265\) −16.9706 −1.04249
\(266\) 0 0
\(267\) 10.0000 0.611990
\(268\) 1.00000 + 1.73205i 0.0610847 + 0.105802i
\(269\) 12.0208 20.8207i 0.732922 1.26946i −0.222707 0.974885i \(-0.571489\pi\)
0.955629 0.294573i \(-0.0951773\pi\)
\(270\) 4.00000 6.92820i 0.243432 0.421637i
\(271\) −4.24264 7.34847i −0.257722 0.446388i 0.707909 0.706303i \(-0.249639\pi\)
−0.965631 + 0.259916i \(0.916305\pi\)
\(272\) −5.65685 −0.342997
\(273\) 0 0
\(274\) 2.00000 0.120824
\(275\) −1.50000 2.59808i −0.0904534 0.156670i
\(276\) −1.41421 + 2.44949i −0.0851257 + 0.147442i
\(277\) 5.00000 8.66025i 0.300421 0.520344i −0.675810 0.737075i \(-0.736206\pi\)
0.976231 + 0.216731i \(0.0695395\pi\)
\(278\) −1.41421 2.44949i −0.0848189 0.146911i
\(279\) 1.41421 0.0846668
\(280\) 0 0
\(281\) 18.0000 1.07379 0.536895 0.843649i \(-0.319597\pi\)
0.536895 + 0.843649i \(0.319597\pi\)
\(282\) −3.00000 5.19615i −0.178647 0.309426i
\(283\) −8.48528 + 14.6969i −0.504398 + 0.873642i 0.495589 + 0.868557i \(0.334952\pi\)
−0.999987 + 0.00508540i \(0.998381\pi\)
\(284\) 5.00000 8.66025i 0.296695 0.513892i
\(285\) 2.82843 + 4.89898i 0.167542 + 0.290191i
\(286\) 2.82843 0.167248
\(287\) 0 0
\(288\) 1.00000 0.0589256
\(289\) −7.50000 12.9904i −0.441176 0.764140i
\(290\) −4.24264 + 7.34847i −0.249136 + 0.431517i
\(291\) −11.0000 + 19.0526i −0.644831 + 1.11688i
\(292\) 7.07107 + 12.2474i 0.413803 + 0.716728i
\(293\) 16.9706 0.991431 0.495715 0.868485i \(-0.334906\pi\)
0.495715 + 0.868485i \(0.334906\pi\)
\(294\) 0 0
\(295\) 6.00000 0.349334
\(296\) −1.00000 1.73205i −0.0581238 0.100673i
\(297\) 2.82843 4.89898i 0.164122 0.284268i
\(298\) −5.00000 + 8.66025i −0.289642 + 0.501675i
\(299\) 2.82843 + 4.89898i 0.163572 + 0.283315i
\(300\) 4.24264 0.244949
\(301\) 0 0
\(302\) −16.0000 −0.920697
\(303\) 2.00000 + 3.46410i 0.114897 + 0.199007i
\(304\) −1.41421 + 2.44949i −0.0811107 + 0.140488i
\(305\) 4.00000 6.92820i 0.229039 0.396708i
\(306\) 2.82843 + 4.89898i 0.161690 + 0.280056i
\(307\) −11.3137 −0.645707 −0.322854 0.946449i \(-0.604642\pi\)
−0.322854 + 0.946449i \(0.604642\pi\)
\(308\) 0 0
\(309\) 6.00000 0.341328
\(310\) −1.00000 1.73205i −0.0567962 0.0983739i
\(311\) 4.94975 8.57321i 0.280674 0.486142i −0.690877 0.722973i \(-0.742775\pi\)
0.971551 + 0.236830i \(0.0761086\pi\)
\(312\) −2.00000 + 3.46410i −0.113228 + 0.196116i
\(313\) −13.4350 23.2702i −0.759393 1.31531i −0.943161 0.332337i \(-0.892163\pi\)
0.183768 0.982970i \(-0.441171\pi\)
\(314\) −18.3848 −1.03751
\(315\) 0 0
\(316\) −8.00000 −0.450035
\(317\) 13.0000 + 22.5167i 0.730153 + 1.26466i 0.956818 + 0.290689i \(0.0938844\pi\)
−0.226665 + 0.973973i \(0.572782\pi\)
\(318\) 8.48528 14.6969i 0.475831 0.824163i
\(319\) −3.00000 + 5.19615i −0.167968 + 0.290929i
\(320\) −0.707107 1.22474i −0.0395285 0.0684653i
\(321\) 28.2843 1.57867
\(322\) 0 0
\(323\) −16.0000 −0.890264
\(324\) 2.50000 + 4.33013i 0.138889 + 0.240563i
\(325\) 4.24264 7.34847i 0.235339 0.407620i
\(326\) −11.0000 + 19.0526i −0.609234 + 1.05522i
\(327\) 7.07107 + 12.2474i 0.391031 + 0.677285i
\(328\) −5.65685 −0.312348
\(329\) 0 0
\(330\) −2.00000 −0.110096
\(331\) −14.0000 24.2487i −0.769510 1.33283i −0.937829 0.347097i \(-0.887167\pi\)
0.168320 0.985732i \(-0.446166\pi\)
\(332\) 1.41421 2.44949i 0.0776151 0.134433i
\(333\) −1.00000 + 1.73205i −0.0547997 + 0.0949158i
\(334\) −5.65685 9.79796i −0.309529 0.536120i
\(335\) −2.82843 −0.154533
\(336\) 0 0
\(337\) −2.00000 −0.108947 −0.0544735 0.998515i \(-0.517348\pi\)
−0.0544735 + 0.998515i \(0.517348\pi\)
\(338\) −2.50000 4.33013i −0.135982 0.235528i
\(339\) −12.7279 + 22.0454i −0.691286 + 1.19734i
\(340\) 4.00000 6.92820i 0.216930 0.375735i
\(341\) −0.707107 1.22474i −0.0382920 0.0663237i
\(342\) 2.82843 0.152944
\(343\) 0 0
\(344\) −4.00000 −0.215666
\(345\) −2.00000 3.46410i −0.107676 0.186501i
\(346\) 7.07107 12.2474i 0.380143 0.658427i
\(347\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(348\) −4.24264 7.34847i −0.227429 0.393919i
\(349\) −5.65685 −0.302804 −0.151402 0.988472i \(-0.548379\pi\)
−0.151402 + 0.988472i \(0.548379\pi\)
\(350\) 0 0
\(351\) 16.0000 0.854017
\(352\) −0.500000 0.866025i −0.0266501 0.0461593i
\(353\) −0.707107 + 1.22474i −0.0376355 + 0.0651866i −0.884230 0.467052i \(-0.845316\pi\)
0.846594 + 0.532239i \(0.178649\pi\)
\(354\) −3.00000 + 5.19615i −0.159448 + 0.276172i
\(355\) 7.07107 + 12.2474i 0.375293 + 0.650027i
\(356\) −7.07107 −0.374766
\(357\) 0 0
\(358\) −20.0000 −1.05703
\(359\) −16.0000 27.7128i −0.844448 1.46263i −0.886100 0.463494i \(-0.846596\pi\)
0.0416523 0.999132i \(-0.486738\pi\)
\(360\) −0.707107 + 1.22474i −0.0372678 + 0.0645497i
\(361\) 5.50000 9.52628i 0.289474 0.501383i
\(362\) 6.36396 + 11.0227i 0.334482 + 0.579340i
\(363\) −1.41421 −0.0742270
\(364\) 0 0
\(365\) −20.0000 −1.04685
\(366\) 4.00000 + 6.92820i 0.209083 + 0.362143i
\(367\) −14.8492 + 25.7196i −0.775124 + 1.34255i 0.159601 + 0.987182i \(0.448979\pi\)
−0.934725 + 0.355373i \(0.884354\pi\)
\(368\) 1.00000 1.73205i 0.0521286 0.0902894i
\(369\) 2.82843 + 4.89898i 0.147242 + 0.255031i
\(370\) 2.82843 0.147043
\(371\) 0 0
\(372\) 2.00000 0.103695
\(373\) 7.00000 + 12.1244i 0.362446 + 0.627775i 0.988363 0.152115i \(-0.0486083\pi\)
−0.625917 + 0.779890i \(0.715275\pi\)
\(374\) 2.82843 4.89898i 0.146254 0.253320i
\(375\) −8.00000 + 13.8564i −0.413118 + 0.715542i
\(376\) 2.12132 + 3.67423i 0.109399 + 0.189484i
\(377\) −16.9706 −0.874028
\(378\) 0 0
\(379\) 6.00000 0.308199 0.154100 0.988055i \(-0.450752\pi\)
0.154100 + 0.988055i \(0.450752\pi\)
\(380\) −2.00000 3.46410i −0.102598 0.177705i
\(381\) 8.48528 14.6969i 0.434714 0.752947i
\(382\) 0 0
\(383\) −13.4350 23.2702i −0.686498 1.18905i −0.972964 0.230959i \(-0.925814\pi\)
0.286466 0.958091i \(-0.407520\pi\)
\(384\) 1.41421 0.0721688
\(385\) 0 0
\(386\) −6.00000 −0.305392
\(387\) 2.00000 + 3.46410i 0.101666 + 0.176090i
\(388\) 7.77817 13.4722i 0.394877 0.683947i
\(389\) 14.0000 24.2487i 0.709828 1.22946i −0.255092 0.966917i \(-0.582106\pi\)
0.964921 0.262542i \(-0.0845608\pi\)
\(390\) −2.82843 4.89898i −0.143223 0.248069i
\(391\) 11.3137 0.572159
\(392\) 0 0
\(393\) −16.0000 −0.807093
\(394\) 9.00000 + 15.5885i 0.453413 + 0.785335i
\(395\) 5.65685 9.79796i 0.284627 0.492989i
\(396\) −0.500000 + 0.866025i −0.0251259 + 0.0435194i
\(397\) 12.0208 + 20.8207i 0.603307 + 1.04496i 0.992317 + 0.123725i \(0.0394841\pi\)
−0.389009 + 0.921234i \(0.627183\pi\)
\(398\) −21.2132 −1.06332
\(399\) 0 0
\(400\) −3.00000 −0.150000
\(401\) −18.0000 31.1769i −0.898877 1.55690i −0.828932 0.559350i \(-0.811051\pi\)
−0.0699455 0.997551i \(-0.522283\pi\)
\(402\) 1.41421 2.44949i 0.0705346 0.122169i
\(403\) 2.00000 3.46410i 0.0996271 0.172559i
\(404\) −1.41421 2.44949i −0.0703598 0.121867i
\(405\) −7.07107 −0.351364
\(406\) 0 0
\(407\) 2.00000 0.0991363
\(408\) 4.00000 + 6.92820i 0.198030 + 0.342997i
\(409\) −15.5563 + 26.9444i −0.769212 + 1.33231i 0.168779 + 0.985654i \(0.446018\pi\)
−0.937991 + 0.346660i \(0.887316\pi\)
\(410\) 4.00000 6.92820i 0.197546 0.342160i
\(411\) −1.41421 2.44949i −0.0697580 0.120824i
\(412\) −4.24264 −0.209020
\(413\) 0 0
\(414\) −2.00000 −0.0982946
\(415\) 2.00000 + 3.46410i 0.0981761 + 0.170046i
\(416\) 1.41421 2.44949i 0.0693375 0.120096i
\(417\) −2.00000 + 3.46410i −0.0979404 + 0.169638i
\(418\) −1.41421 2.44949i −0.0691714 0.119808i
\(419\) −12.7279 −0.621800 −0.310900 0.950443i \(-0.600630\pi\)
−0.310900 + 0.950443i \(0.600630\pi\)
\(420\) 0 0
\(421\) 8.00000 0.389896 0.194948 0.980814i \(-0.437546\pi\)
0.194948 + 0.980814i \(0.437546\pi\)
\(422\) 14.0000 + 24.2487i 0.681509 + 1.18041i
\(423\) 2.12132 3.67423i 0.103142 0.178647i
\(424\) −6.00000 + 10.3923i −0.291386 + 0.504695i
\(425\) −8.48528 14.6969i −0.411597 0.712906i
\(426\) −14.1421 −0.685189
\(427\) 0 0
\(428\) −20.0000 −0.966736
\(429\) −2.00000 3.46410i −0.0965609 0.167248i
\(430\) 2.82843 4.89898i 0.136399 0.236250i
\(431\) 10.0000 17.3205i 0.481683 0.834300i −0.518096 0.855323i \(-0.673359\pi\)
0.999779 + 0.0210230i \(0.00669232\pi\)
\(432\) −2.82843 4.89898i −0.136083 0.235702i
\(433\) 38.1838 1.83499 0.917497 0.397742i \(-0.130206\pi\)
0.917497 + 0.397742i \(0.130206\pi\)
\(434\) 0 0
\(435\) 12.0000 0.575356
\(436\) −5.00000 8.66025i −0.239457 0.414751i
\(437\) 2.82843 4.89898i 0.135302 0.234350i
\(438\) 10.0000 17.3205i 0.477818 0.827606i
\(439\) 12.7279 + 22.0454i 0.607471 + 1.05217i 0.991656 + 0.128914i \(0.0411491\pi\)
−0.384185 + 0.923256i \(0.625518\pi\)
\(440\) 1.41421 0.0674200
\(441\) 0 0
\(442\) 16.0000 0.761042
\(443\) 6.00000 + 10.3923i 0.285069 + 0.493753i 0.972626 0.232377i \(-0.0746503\pi\)
−0.687557 + 0.726130i \(0.741317\pi\)
\(444\) −1.41421 + 2.44949i −0.0671156 + 0.116248i
\(445\) 5.00000 8.66025i 0.237023 0.410535i
\(446\) −7.77817 13.4722i −0.368307 0.637927i
\(447\) 14.1421 0.668900
\(448\) 0 0
\(449\) −12.0000 −0.566315 −0.283158 0.959073i \(-0.591382\pi\)
−0.283158 + 0.959073i \(0.591382\pi\)
\(450\) 1.50000 + 2.59808i 0.0707107 + 0.122474i
\(451\) 2.82843 4.89898i 0.133185 0.230684i
\(452\) 9.00000 15.5885i 0.423324 0.733219i
\(453\) 11.3137 + 19.5959i 0.531564 + 0.920697i
\(454\) 28.2843 1.32745
\(455\) 0 0
\(456\) 4.00000 0.187317
\(457\) −1.00000 1.73205i −0.0467780 0.0810219i 0.841688 0.539964i \(-0.181562\pi\)
−0.888466 + 0.458942i \(0.848229\pi\)
\(458\) −2.12132 + 3.67423i −0.0991228 + 0.171686i
\(459\) 16.0000 27.7128i 0.746816 1.29352i
\(460\) 1.41421 + 2.44949i 0.0659380 + 0.114208i
\(461\) 28.2843 1.31733 0.658665 0.752436i \(-0.271121\pi\)
0.658665 + 0.752436i \(0.271121\pi\)
\(462\) 0 0
\(463\) −14.0000 −0.650635 −0.325318 0.945605i \(-0.605471\pi\)
−0.325318 + 0.945605i \(0.605471\pi\)
\(464\) 3.00000 + 5.19615i 0.139272 + 0.241225i
\(465\) −1.41421 + 2.44949i −0.0655826 + 0.113592i
\(466\) 3.00000 5.19615i 0.138972 0.240707i
\(467\) −2.12132 3.67423i −0.0981630 0.170023i 0.812761 0.582597i \(-0.197963\pi\)
−0.910924 + 0.412574i \(0.864630\pi\)
\(468\) −2.82843 −0.130744
\(469\) 0 0
\(470\) −6.00000 −0.276759
\(471\) 13.0000 + 22.5167i 0.599008 + 1.03751i
\(472\) 2.12132 3.67423i 0.0976417 0.169120i
\(473\) 2.00000 3.46410i 0.0919601 0.159280i
\(474\) 5.65685 + 9.79796i 0.259828 + 0.450035i
\(475\) −8.48528 −0.389331
\(476\) 0 0
\(477\) 12.0000 0.549442
\(478\) −8.00000 13.8564i −0.365911 0.633777i
\(479\) −12.7279 + 22.0454i −0.581554 + 1.00728i 0.413742 + 0.910394i \(0.364222\pi\)
−0.995295 + 0.0968862i \(0.969112\pi\)
\(480\) −1.00000 + 1.73205i −0.0456435 + 0.0790569i
\(481\) 2.82843 + 4.89898i 0.128965 + 0.223374i
\(482\) 5.65685 0.257663
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) 11.0000 + 19.0526i 0.499484 + 0.865132i
\(486\) −4.94975 + 8.57321i −0.224525 + 0.388889i
\(487\) −5.00000 + 8.66025i −0.226572 + 0.392434i −0.956790 0.290780i \(-0.906085\pi\)
0.730218 + 0.683214i \(0.239418\pi\)
\(488\) −2.82843 4.89898i −0.128037 0.221766i
\(489\) 31.1127 1.40696
\(490\) 0 0
\(491\) 4.00000 0.180517 0.0902587 0.995918i \(-0.471231\pi\)
0.0902587 + 0.995918i \(0.471231\pi\)
\(492\) 4.00000 + 6.92820i 0.180334 + 0.312348i
\(493\) −16.9706 + 29.3939i −0.764316 + 1.32383i
\(494\) 4.00000 6.92820i 0.179969 0.311715i
\(495\) −0.707107 1.22474i −0.0317821 0.0550482i
\(496\) −1.41421 −0.0635001
\(497\) 0 0
\(498\) −4.00000 −0.179244
\(499\) 15.0000 + 25.9808i 0.671492 + 1.16306i 0.977481 + 0.211024i \(0.0676797\pi\)
−0.305989 + 0.952035i \(0.598987\pi\)
\(500\) 5.65685 9.79796i 0.252982 0.438178i
\(501\) −8.00000 + 13.8564i −0.357414 + 0.619059i
\(502\) −12.0208 20.8207i −0.536515 0.929272i
\(503\) 19.7990 0.882793 0.441397 0.897312i \(-0.354483\pi\)
0.441397 + 0.897312i \(0.354483\pi\)
\(504\) 0 0
\(505\) 4.00000 0.177998
\(506\) 1.00000 + 1.73205i 0.0444554 + 0.0769991i
\(507\) −3.53553 + 6.12372i −0.157019 + 0.271964i
\(508\) −6.00000 + 10.3923i −0.266207 + 0.461084i
\(509\) −2.12132 3.67423i −0.0940259 0.162858i 0.815176 0.579214i \(-0.196640\pi\)
−0.909202 + 0.416356i \(0.863307\pi\)
\(510\) −11.3137 −0.500979
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) −8.00000 13.8564i −0.353209 0.611775i
\(514\) −4.94975 + 8.57321i −0.218324 + 0.378148i
\(515\) 3.00000 5.19615i 0.132196 0.228970i
\(516\) 2.82843 + 4.89898i 0.124515 + 0.215666i
\(517\) −4.24264 −0.186591
\(518\) 0 0
\(519\) −20.0000 −0.877903
\(520\) 2.00000 + 3.46410i 0.0877058 + 0.151911i
\(521\) 7.77817 13.4722i 0.340768 0.590228i −0.643808 0.765187i \(-0.722646\pi\)
0.984576 + 0.174960i \(0.0559796\pi\)
\(522\) 3.00000 5.19615i 0.131306 0.227429i
\(523\) 8.48528 + 14.6969i 0.371035 + 0.642652i 0.989725 0.142983i \(-0.0456695\pi\)
−0.618690 + 0.785635i \(0.712336\pi\)
\(524\) 11.3137 0.494242
\(525\) 0 0
\(526\) −24.0000 −1.04645
\(527\) −4.00000 6.92820i −0.174243 0.301797i
\(528\) −0.707107 + 1.22474i −0.0307729 + 0.0533002i
\(529\) 9.50000 16.4545i 0.413043 0.715412i
\(530\) −8.48528 14.6969i −0.368577 0.638394i
\(531\) −4.24264 −0.184115
\(532\) 0 0
\(533\) 16.0000 0.693037
\(534\) 5.00000 + 8.66025i 0.216371 + 0.374766i
\(535\) 14.1421 24.4949i 0.611418 1.05901i
\(536\) −1.00000 + 1.73205i −0.0431934 + 0.0748132i
\(537\) 14.1421 + 24.4949i 0.610278 + 1.05703i
\(538\) 24.0416 1.03651
\(539\) 0 0
\(540\) 8.00000 0.344265
\(541\) 9.00000 + 15.5885i 0.386940 + 0.670200i 0.992036 0.125952i \(-0.0401986\pi\)
−0.605096 + 0.796152i \(0.706865\pi\)
\(542\) 4.24264 7.34847i 0.182237 0.315644i
\(543\) 9.00000 15.5885i 0.386227 0.668965i
\(544\) −2.82843 4.89898i −0.121268 0.210042i
\(545\) 14.1421 0.605783
\(546\) 0 0
\(547\) 28.0000 1.19719 0.598597 0.801050i \(-0.295725\pi\)
0.598597 + 0.801050i \(0.295725\pi\)
\(548\) 1.00000 + 1.73205i 0.0427179 + 0.0739895i
\(549\) −2.82843 + 4.89898i −0.120714 + 0.209083i
\(550\) 1.50000 2.59808i 0.0639602 0.110782i
\(551\) 8.48528 + 14.6969i 0.361485 + 0.626111i
\(552\) −2.82843 −0.120386
\(553\) 0 0
\(554\) 10.0000 0.424859
\(555\) −2.00000 3.46410i −0.0848953 0.147043i
\(556\) 1.41421 2.44949i 0.0599760 0.103882i
\(557\) 9.00000 15.5885i 0.381342 0.660504i −0.609912 0.792469i \(-0.708795\pi\)
0.991254 + 0.131965i \(0.0421286\pi\)
\(558\) 0.707107 + 1.22474i 0.0299342 + 0.0518476i
\(559\) 11.3137 0.478519
\(560\) 0 0
\(561\) −8.00000 −0.337760
\(562\) 9.00000 + 15.5885i 0.379642 + 0.657559i
\(563\) 7.07107 12.2474i 0.298010 0.516168i −0.677671 0.735366i \(-0.737010\pi\)
0.975681 + 0.219197i \(0.0703438\pi\)
\(564\) 3.00000 5.19615i 0.126323 0.218797i
\(565\) 12.7279 + 22.0454i 0.535468 + 0.927457i
\(566\) −16.9706 −0.713326
\(567\) 0 0
\(568\) 10.0000 0.419591
\(569\) 3.00000 + 5.19615i 0.125767 + 0.217834i 0.922032 0.387113i \(-0.126528\pi\)
−0.796266 + 0.604947i \(0.793194\pi\)
\(570\) −2.82843 + 4.89898i −0.118470 + 0.205196i
\(571\) −4.00000 + 6.92820i −0.167395 + 0.289936i −0.937503 0.347977i \(-0.886869\pi\)
0.770108 + 0.637913i \(0.220202\pi\)
\(572\) 1.41421 + 2.44949i 0.0591312 + 0.102418i
\(573\) 0 0
\(574\) 0 0
\(575\) 6.00000 0.250217
\(576\) 0.500000 + 0.866025i 0.0208333 + 0.0360844i
\(577\) 14.8492 25.7196i 0.618182 1.07072i −0.371635 0.928379i \(-0.621203\pi\)
0.989817 0.142344i \(-0.0454639\pi\)
\(578\) 7.50000 12.9904i 0.311959 0.540329i
\(579\) 4.24264 + 7.34847i 0.176318 + 0.305392i
\(580\) −8.48528 −0.352332
\(581\) 0 0
\(582\) −22.0000 −0.911929
\(583\) −6.00000 10.3923i −0.248495 0.430405i
\(584\) −7.07107 + 12.2474i −0.292603 + 0.506803i
\(585\) 2.00000 3.46410i 0.0826898 0.143223i
\(586\) 8.48528 + 14.6969i 0.350524 + 0.607125i
\(587\) −1.41421 −0.0583708 −0.0291854 0.999574i \(-0.509291\pi\)
−0.0291854 + 0.999574i \(0.509291\pi\)
\(588\) 0 0
\(589\) −4.00000 −0.164817
\(590\) 3.00000 + 5.19615i 0.123508 + 0.213922i
\(591\) 12.7279 22.0454i 0.523557 0.906827i
\(592\) 1.00000 1.73205i 0.0410997 0.0711868i
\(593\) −9.89949 17.1464i −0.406524 0.704119i 0.587974 0.808880i \(-0.299926\pi\)
−0.994497 + 0.104760i \(0.966592\pi\)
\(594\) 5.65685 0.232104
\(595\) 0 0
\(596\) −10.0000 −0.409616
\(597\) 15.0000 + 25.9808i 0.613909 + 1.06332i
\(598\) −2.82843 + 4.89898i −0.115663 + 0.200334i
\(599\) −9.00000 + 15.5885i −0.367730 + 0.636927i −0.989210 0.146503i \(-0.953198\pi\)
0.621480 + 0.783430i \(0.286532\pi\)
\(600\) 2.12132 + 3.67423i 0.0866025 + 0.150000i
\(601\) 45.2548 1.84598 0.922992 0.384820i \(-0.125737\pi\)
0.922992 + 0.384820i \(0.125737\pi\)
\(602\) 0 0
\(603\) 2.00000 0.0814463
\(604\) −8.00000 13.8564i −0.325515 0.563809i
\(605\) −0.707107 + 1.22474i −0.0287480 + 0.0497930i
\(606\) −2.00000 + 3.46410i −0.0812444 + 0.140720i
\(607\) 16.9706 + 29.3939i 0.688814 + 1.19306i 0.972222 + 0.234061i \(0.0752016\pi\)
−0.283408 + 0.958999i \(0.591465\pi\)
\(608\) −2.82843 −0.114708
\(609\) 0 0
\(610\) 8.00000 0.323911
\(611\) −6.00000 10.3923i −0.242734 0.420428i
\(612\) −2.82843 + 4.89898i −0.114332 + 0.198030i
\(613\) 17.0000 29.4449i 0.686624 1.18927i −0.286300 0.958140i \(-0.592425\pi\)
0.972924 0.231127i \(-0.0742412\pi\)
\(614\) −5.65685 9.79796i −0.228292 0.395413i
\(615\) −11.3137 −0.456213
\(616\) 0 0
\(617\) −6.00000 −0.241551 −0.120775 0.992680i \(-0.538538\pi\)
−0.120775 + 0.992680i \(0.538538\pi\)
\(618\) 3.00000 + 5.19615i 0.120678 + 0.209020i
\(619\) −6.36396 + 11.0227i −0.255789 + 0.443040i −0.965110 0.261846i \(-0.915669\pi\)
0.709320 + 0.704886i \(0.249002\pi\)
\(620\) 1.00000 1.73205i 0.0401610 0.0695608i
\(621\) 5.65685 + 9.79796i 0.227002 + 0.393179i
\(622\) 9.89949 0.396934
\(623\) 0 0
\(624\) −4.00000 −0.160128
\(625\) 0.500000 + 0.866025i 0.0200000 + 0.0346410i
\(626\) 13.4350 23.2702i 0.536972 0.930062i
\(627\) −2.00000 + 3.46410i −0.0798723 + 0.138343i
\(628\) −9.19239 15.9217i −0.366816 0.635344i
\(629\) 11.3137 0.451107
\(630\) 0 0
\(631\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) −4.00000 6.92820i −0.159111 0.275589i
\(633\) 19.7990 34.2929i 0.786939 1.36302i
\(634\) −13.0000 + 22.5167i −0.516296 + 0.894251i
\(635\) −8.48528 14.6969i −0.336728 0.583230i
\(636\) 16.9706 0.672927
\(637\) 0 0
\(638\) −6.00000 −0.237542
\(639\) −5.00000 8.66025i −0.197797 0.342594i
\(640\) 0.707107 1.22474i 0.0279508 0.0484123i
\(641\) −15.0000 + 25.9808i −0.592464 + 1.02618i 0.401435 + 0.915888i \(0.368512\pi\)
−0.993899 + 0.110291i \(0.964822\pi\)
\(642\) 14.1421 + 24.4949i 0.558146 + 0.966736i
\(643\) −12.7279 −0.501940 −0.250970 0.967995i \(-0.580750\pi\)
−0.250970 + 0.967995i \(0.580750\pi\)
\(644\) 0 0
\(645\) −8.00000 −0.315000
\(646\) −8.00000 13.8564i −0.314756 0.545173i
\(647\) −20.5061 + 35.5176i −0.806178 + 1.39634i 0.109315 + 0.994007i \(0.465134\pi\)
−0.915493 + 0.402334i \(0.868199\pi\)
\(648\) −2.50000 + 4.33013i −0.0982093 + 0.170103i
\(649\) 2.12132 + 3.67423i 0.0832691 + 0.144226i
\(650\) 8.48528 0.332820
\(651\) 0 0
\(652\) −22.0000 −0.861586
\(653\) 24.0000 + 41.5692i 0.939193 + 1.62673i 0.766982 + 0.641669i \(0.221758\pi\)
0.172211 + 0.985060i \(0.444909\pi\)
\(654\) −7.07107 + 12.2474i −0.276501 + 0.478913i
\(655\) −8.00000 + 13.8564i −0.312586 + 0.541415i
\(656\) −2.82843 4.89898i −0.110432 0.191273i
\(657\) 14.1421 0.551737
\(658\) 0 0
\(659\) −4.00000 −0.155818 −0.0779089 0.996960i \(-0.524824\pi\)
−0.0779089 + 0.996960i \(0.524824\pi\)
\(660\) −1.00000 1.73205i −0.0389249 0.0674200i
\(661\) −19.0919 + 33.0681i −0.742588 + 1.28620i 0.208725 + 0.977974i \(0.433069\pi\)
−0.951313 + 0.308226i \(0.900265\pi\)
\(662\) 14.0000 24.2487i 0.544125 0.942453i
\(663\) −11.3137 19.5959i −0.439388 0.761042i
\(664\) 2.82843 0.109764
\(665\) 0 0
\(666\) −2.00000 −0.0774984
\(667\) −6.00000 10.3923i −0.232321 0.402392i
\(668\) 5.65685 9.79796i 0.218870 0.379094i
\(669\) −11.0000 + 19.0526i −0.425285 + 0.736614i
\(670\) −1.41421 2.44949i −0.0546358 0.0946320i
\(671\) 5.65685 0.218380
\(672\) 0 0
\(673\) 2.00000 0.0770943 0.0385472 0.999257i \(-0.487727\pi\)
0.0385472 + 0.999257i \(0.487727\pi\)
\(674\) −1.00000 1.73205i −0.0385186 0.0667161i
\(675\) 8.48528 14.6969i 0.326599 0.565685i
\(676\) 2.50000 4.33013i 0.0961538 0.166543i
\(677\) −15.5563 26.9444i −0.597879 1.03556i −0.993134 0.116985i \(-0.962677\pi\)
0.395255 0.918572i \(-0.370656\pi\)
\(678\) −25.4558 −0.977626
\(679\) 0 0
\(680\) 8.00000 0.306786
\(681\) −20.0000 34.6410i −0.766402 1.32745i
\(682\) 0.707107 1.22474i 0.0270765 0.0468979i
\(683\) 6.00000 10.3923i 0.229584 0.397650i −0.728101 0.685470i \(-0.759597\pi\)
0.957685 + 0.287819i \(0.0929302\pi\)
\(684\) 1.41421 + 2.44949i 0.0540738 + 0.0936586i
\(685\) −2.82843 −0.108069
\(686\) 0 0
\(687\) 6.00000 0.228914
\(688\) −2.00000 3.46410i −0.0762493 0.132068i
\(689\) 16.9706 29.3939i 0.646527 1.11982i
\(690\) 2.00000 3.46410i 0.0761387 0.131876i
\(691\) 16.2635 + 28.1691i 0.618691 + 1.07160i 0.989725 + 0.142985i \(0.0456700\pi\)
−0.371034 + 0.928619i \(0.620997\pi\)
\(692\) 14.1421 0.537603
\(693\) 0 0
\(694\) 0 0
\(695\) 2.00000 + 3.46410i 0.0758643 + 0.131401i
\(696\) 4.24264 7.34847i 0.160817 0.278543i
\(697\) 16.0000 27.7128i 0.606043 1.04970i
\(698\) −2.82843 4.89898i −0.107058 0.185429i
\(699\) −8.48528 −0.320943
\(700\) 0 0
\(701\) −10.0000 −0.377695 −0.188847 0.982006i \(-0.560475\pi\)
−0.188847 + 0.982006i \(0.560475\pi\)
\(702\) 8.00000 + 13.8564i 0.301941 + 0.522976i
\(703\) 2.82843 4.89898i 0.106676 0.184769i
\(704\) 0.500000 0.866025i 0.0188445 0.0326396i
\(705\) 4.24264 + 7.34847i 0.159787 + 0.276759i
\(706\) −1.41421 −0.0532246
\(707\) 0 0
\(708\) −6.00000 −0.225494
\(709\) 4.00000 + 6.92820i 0.150223 + 0.260194i 0.931309 0.364229i \(-0.118667\pi\)
−0.781086 + 0.624423i \(0.785334\pi\)
\(710\) −7.07107 + 12.2474i −0.265372 + 0.459639i
\(711\) −4.00000 + 6.92820i −0.150012 + 0.259828i
\(712\) −3.53553 6.12372i −0.132500 0.229496i
\(713\) 2.82843 0.105925
\(714\) 0 0
\(715\) −4.00000 −0.149592
\(716\) −10.0000 17.3205i −0.373718 0.647298i
\(717\) −11.3137 + 19.5959i −0.422518 + 0.731823i
\(718\) 16.0000 27.7128i 0.597115 1.03423i
\(719\) 7.77817 + 13.4722i 0.290077 + 0.502428i 0.973828 0.227288i \(-0.0729858\pi\)
−0.683751 + 0.729716i \(0.739652\pi\)
\(720\) −1.41421 −0.0527046
\(721\) 0 0
\(722\) 11.0000 0.409378
\(723\) −4.00000 6.92820i −0.148762 0.257663i
\(724\) −6.36396 + 11.0227i −0.236515 + 0.409656i
\(725\) −9.00000 + 15.5885i −0.334252 + 0.578941i
\(726\) −0.707107 1.22474i −0.0262432 0.0454545i
\(727\) −32.5269 −1.20636 −0.603178 0.797606i \(-0.706099\pi\)
−0.603178 + 0.797606i \(0.706099\pi\)
\(728\) 0 0
\(729\) 29.0000 1.07407
\(730\) −10.0000 17.3205i −0.370117 0.641061i
\(731\) 11.3137 19.5959i 0.418453 0.724781i
\(732\) −4.00000 + 6.92820i −0.147844 + 0.256074i
\(733\) 8.48528 + 14.6969i 0.313411 + 0.542844i 0.979098 0.203387i \(-0.0651949\pi\)
−0.665687 + 0.746231i \(0.731862\pi\)
\(734\) −29.6985 −1.09619
\(735\) 0 0
\(736\) 2.00000 0.0737210
\(737\) −1.00000 1.73205i −0.0368355 0.0638009i
\(738\) −2.82843 + 4.89898i −0.104116 + 0.180334i
\(739\) 12.0000 20.7846i 0.441427 0.764574i −0.556369 0.830936i \(-0.687806\pi\)
0.997796 + 0.0663614i \(0.0211390\pi\)
\(740\) 1.41421 + 2.44949i 0.0519875 + 0.0900450i
\(741\) −11.3137 −0.415619
\(742\) 0 0
\(743\) −48.0000 −1.76095 −0.880475 0.474093i \(-0.842776\pi\)
−0.880475 + 0.474093i \(0.842776\pi\)
\(744\) 1.00000 + 1.73205i 0.0366618 + 0.0635001i
\(745\) 7.07107 12.2474i 0.259064 0.448712i
\(746\) −7.00000 + 12.1244i −0.256288 + 0.443904i
\(747\) −1.41421 2.44949i −0.0517434 0.0896221i
\(748\) 5.65685 0.206835
\(749\) 0 0
\(750\) −16.0000 −0.584237
\(751\) −13.0000 22.5167i −0.474377 0.821645i 0.525193 0.850983i \(-0.323993\pi\)
−0.999570 + 0.0293387i \(0.990660\pi\)
\(752\) −2.12132 + 3.67423i −0.0773566 + 0.133986i
\(753\) −17.0000 + 29.4449i −0.619514 + 1.07303i
\(754\) −8.48528 14.6969i −0.309016 0.535231i
\(755\) 22.6274 0.823496
\(756\) 0 0
\(757\) −44.0000 −1.59921 −0.799604 0.600528i \(-0.794957\pi\)
−0.799604 + 0.600528i \(0.794957\pi\)
\(758\) 3.00000 + 5.19615i 0.108965 + 0.188733i
\(759\) 1.41421 2.44949i 0.0513327 0.0889108i
\(760\) 2.00000 3.46410i 0.0725476 0.125656i
\(761\) −12.7279 22.0454i −0.461387 0.799145i 0.537644 0.843172i \(-0.319315\pi\)
−0.999030 + 0.0440268i \(0.985981\pi\)
\(762\) 16.9706 0.614779
\(763\) 0 0
\(764\) 0 0
\(765\) −4.00000 6.92820i −0.144620 0.250490i
\(766\) 13.4350 23.2702i 0.485427 0.840785i
\(767\) −6.00000 + 10.3923i −0.216647 + 0.375244i
\(768\) 0.707107 + 1.22474i 0.0255155 + 0.0441942i
\(769\) 8.48528 0.305987 0.152994 0.988227i \(-0.451109\pi\)
0.152994 + 0.988227i \(0.451109\pi\)
\(770\) 0 0
\(771\) 14.0000 0.504198
\(772\) −3.00000 5.19615i −0.107972 0.187014i
\(773\) 0.707107 1.22474i 0.0254329 0.0440510i −0.853029 0.521864i \(-0.825237\pi\)
0.878462 + 0.477813i \(0.158570\pi\)
\(774\) −2.00000 + 3.46410i −0.0718885 + 0.124515i
\(775\) −2.12132 3.67423i −0.0762001 0.131982i
\(776\) 15.5563 0.558440
\(777\) 0 0
\(778\) 28.0000 1.00385
\(779\) −8.00000 13.8564i −0.286630 0.496457i
\(780\) 2.82843 4.89898i 0.101274 0.175412i
\(781\) −5.00000 + 8.66025i −0.178914 + 0.309888i
\(782\) 5.65685 + 9.79796i 0.202289 + 0.350374i
\(783\) −33.9411 −1.21296
\(784\) 0 0
\(785\) 26.0000