Properties

Label 770.2.i.a.331.1
Level $770$
Weight $2$
Character 770.331
Analytic conductor $6.148$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 770.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.14848095564\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 331.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 770.331
Dual form 770.2.i.a.221.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(2.50000 - 0.866025i) q^{7} +1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(2.50000 - 0.866025i) q^{7} +1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +(0.500000 + 0.866025i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(-0.500000 + 0.866025i) q^{12} -1.00000 q^{13} +(-0.500000 + 2.59808i) q^{14} -1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{18} +(-1.00000 + 1.73205i) q^{19} -1.00000 q^{20} +(-2.00000 - 1.73205i) q^{21} +1.00000 q^{22} +(3.00000 - 5.19615i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(0.500000 - 0.866025i) q^{26} -5.00000 q^{27} +(-2.00000 - 1.73205i) q^{28} -9.00000 q^{29} +(0.500000 - 0.866025i) q^{30} +(2.00000 + 3.46410i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.500000 + 0.866025i) q^{33} +(0.500000 - 2.59808i) q^{35} -2.00000 q^{36} +(2.00000 - 3.46410i) q^{37} +(-1.00000 - 1.73205i) q^{38} +(0.500000 + 0.866025i) q^{39} +(0.500000 - 0.866025i) q^{40} +12.0000 q^{41} +(2.50000 - 0.866025i) q^{42} -10.0000 q^{43} +(-0.500000 + 0.866025i) q^{44} +(-1.00000 - 1.73205i) q^{45} +(3.00000 + 5.19615i) q^{46} +(6.00000 - 10.3923i) q^{47} +1.00000 q^{48} +(5.50000 - 4.33013i) q^{49} +1.00000 q^{50} +(0.500000 + 0.866025i) q^{52} +(-3.00000 - 5.19615i) q^{53} +(2.50000 - 4.33013i) q^{54} -1.00000 q^{55} +(2.50000 - 0.866025i) q^{56} +2.00000 q^{57} +(4.50000 - 7.79423i) q^{58} +(-1.50000 - 2.59808i) q^{59} +(0.500000 + 0.866025i) q^{60} +(3.50000 - 6.06218i) q^{61} -4.00000 q^{62} +(1.00000 - 5.19615i) q^{63} +1.00000 q^{64} +(-0.500000 + 0.866025i) q^{65} +(-0.500000 - 0.866025i) q^{66} +(6.50000 + 11.2583i) q^{67} -6.00000 q^{69} +(2.00000 + 1.73205i) q^{70} +(1.00000 - 1.73205i) q^{72} +(-7.00000 - 12.1244i) q^{73} +(2.00000 + 3.46410i) q^{74} +(-0.500000 + 0.866025i) q^{75} +2.00000 q^{76} +(-2.00000 - 1.73205i) q^{77} -1.00000 q^{78} +(-8.50000 + 14.7224i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-6.00000 + 10.3923i) q^{82} +6.00000 q^{83} +(-0.500000 + 2.59808i) q^{84} +(5.00000 - 8.66025i) q^{86} +(4.50000 + 7.79423i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(3.00000 - 5.19615i) q^{89} +2.00000 q^{90} +(-2.50000 + 0.866025i) q^{91} -6.00000 q^{92} +(2.00000 - 3.46410i) q^{93} +(6.00000 + 10.3923i) q^{94} +(1.00000 + 1.73205i) q^{95} +(-0.500000 + 0.866025i) q^{96} +5.00000 q^{97} +(1.00000 + 6.92820i) q^{98} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} - q^{3} - q^{4} + q^{5} + 2 q^{6} + 5 q^{7} + 2 q^{8} + 2 q^{9} + O(q^{10}) \) \( 2 q - q^{2} - q^{3} - q^{4} + q^{5} + 2 q^{6} + 5 q^{7} + 2 q^{8} + 2 q^{9} + q^{10} - q^{11} - q^{12} - 2 q^{13} - q^{14} - 2 q^{15} - q^{16} + 2 q^{18} - 2 q^{19} - 2 q^{20} - 4 q^{21} + 2 q^{22} + 6 q^{23} - q^{24} - q^{25} + q^{26} - 10 q^{27} - 4 q^{28} - 18 q^{29} + q^{30} + 4 q^{31} - q^{32} - q^{33} + q^{35} - 4 q^{36} + 4 q^{37} - 2 q^{38} + q^{39} + q^{40} + 24 q^{41} + 5 q^{42} - 20 q^{43} - q^{44} - 2 q^{45} + 6 q^{46} + 12 q^{47} + 2 q^{48} + 11 q^{49} + 2 q^{50} + q^{52} - 6 q^{53} + 5 q^{54} - 2 q^{55} + 5 q^{56} + 4 q^{57} + 9 q^{58} - 3 q^{59} + q^{60} + 7 q^{61} - 8 q^{62} + 2 q^{63} + 2 q^{64} - q^{65} - q^{66} + 13 q^{67} - 12 q^{69} + 4 q^{70} + 2 q^{72} - 14 q^{73} + 4 q^{74} - q^{75} + 4 q^{76} - 4 q^{77} - 2 q^{78} - 17 q^{79} + q^{80} - q^{81} - 12 q^{82} + 12 q^{83} - q^{84} + 10 q^{86} + 9 q^{87} - q^{88} + 6 q^{89} + 4 q^{90} - 5 q^{91} - 12 q^{92} + 4 q^{93} + 12 q^{94} + 2 q^{95} - q^{96} + 10 q^{97} + 2 q^{98} - 4 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/770\mathbb{Z}\right)^\times\).

\(n\) \(211\) \(617\) \(661\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(3\) −0.500000 0.866025i −0.288675 0.500000i 0.684819 0.728714i \(-0.259881\pi\)
−0.973494 + 0.228714i \(0.926548\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 1.00000 0.408248
\(7\) 2.50000 0.866025i 0.944911 0.327327i
\(8\) 1.00000 0.353553
\(9\) 1.00000 1.73205i 0.333333 0.577350i
\(10\) 0.500000 + 0.866025i 0.158114 + 0.273861i
\(11\) −0.500000 0.866025i −0.150756 0.261116i
\(12\) −0.500000 + 0.866025i −0.144338 + 0.250000i
\(13\) −1.00000 −0.277350 −0.138675 0.990338i \(-0.544284\pi\)
−0.138675 + 0.990338i \(0.544284\pi\)
\(14\) −0.500000 + 2.59808i −0.133631 + 0.694365i
\(15\) −1.00000 −0.258199
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(18\) 1.00000 + 1.73205i 0.235702 + 0.408248i
\(19\) −1.00000 + 1.73205i −0.229416 + 0.397360i −0.957635 0.287984i \(-0.907015\pi\)
0.728219 + 0.685344i \(0.240348\pi\)
\(20\) −1.00000 −0.223607
\(21\) −2.00000 1.73205i −0.436436 0.377964i
\(22\) 1.00000 0.213201
\(23\) 3.00000 5.19615i 0.625543 1.08347i −0.362892 0.931831i \(-0.618211\pi\)
0.988436 0.151642i \(-0.0484560\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0.500000 0.866025i 0.0980581 0.169842i
\(27\) −5.00000 −0.962250
\(28\) −2.00000 1.73205i −0.377964 0.327327i
\(29\) −9.00000 −1.67126 −0.835629 0.549294i \(-0.814897\pi\)
−0.835629 + 0.549294i \(0.814897\pi\)
\(30\) 0.500000 0.866025i 0.0912871 0.158114i
\(31\) 2.00000 + 3.46410i 0.359211 + 0.622171i 0.987829 0.155543i \(-0.0497126\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −0.500000 + 0.866025i −0.0870388 + 0.150756i
\(34\) 0 0
\(35\) 0.500000 2.59808i 0.0845154 0.439155i
\(36\) −2.00000 −0.333333
\(37\) 2.00000 3.46410i 0.328798 0.569495i −0.653476 0.756948i \(-0.726690\pi\)
0.982274 + 0.187453i \(0.0600231\pi\)
\(38\) −1.00000 1.73205i −0.162221 0.280976i
\(39\) 0.500000 + 0.866025i 0.0800641 + 0.138675i
\(40\) 0.500000 0.866025i 0.0790569 0.136931i
\(41\) 12.0000 1.87409 0.937043 0.349215i \(-0.113552\pi\)
0.937043 + 0.349215i \(0.113552\pi\)
\(42\) 2.50000 0.866025i 0.385758 0.133631i
\(43\) −10.0000 −1.52499 −0.762493 0.646997i \(-0.776025\pi\)
−0.762493 + 0.646997i \(0.776025\pi\)
\(44\) −0.500000 + 0.866025i −0.0753778 + 0.130558i
\(45\) −1.00000 1.73205i −0.149071 0.258199i
\(46\) 3.00000 + 5.19615i 0.442326 + 0.766131i
\(47\) 6.00000 10.3923i 0.875190 1.51587i 0.0186297 0.999826i \(-0.494070\pi\)
0.856560 0.516047i \(-0.172597\pi\)
\(48\) 1.00000 0.144338
\(49\) 5.50000 4.33013i 0.785714 0.618590i
\(50\) 1.00000 0.141421
\(51\) 0 0
\(52\) 0.500000 + 0.866025i 0.0693375 + 0.120096i
\(53\) −3.00000 5.19615i −0.412082 0.713746i 0.583036 0.812447i \(-0.301865\pi\)
−0.995117 + 0.0987002i \(0.968532\pi\)
\(54\) 2.50000 4.33013i 0.340207 0.589256i
\(55\) −1.00000 −0.134840
\(56\) 2.50000 0.866025i 0.334077 0.115728i
\(57\) 2.00000 0.264906
\(58\) 4.50000 7.79423i 0.590879 1.02343i
\(59\) −1.50000 2.59808i −0.195283 0.338241i 0.751710 0.659494i \(-0.229229\pi\)
−0.946993 + 0.321253i \(0.895896\pi\)
\(60\) 0.500000 + 0.866025i 0.0645497 + 0.111803i
\(61\) 3.50000 6.06218i 0.448129 0.776182i −0.550135 0.835076i \(-0.685424\pi\)
0.998264 + 0.0588933i \(0.0187572\pi\)
\(62\) −4.00000 −0.508001
\(63\) 1.00000 5.19615i 0.125988 0.654654i
\(64\) 1.00000 0.125000
\(65\) −0.500000 + 0.866025i −0.0620174 + 0.107417i
\(66\) −0.500000 0.866025i −0.0615457 0.106600i
\(67\) 6.50000 + 11.2583i 0.794101 + 1.37542i 0.923408 + 0.383819i \(0.125391\pi\)
−0.129307 + 0.991605i \(0.541275\pi\)
\(68\) 0 0
\(69\) −6.00000 −0.722315
\(70\) 2.00000 + 1.73205i 0.239046 + 0.207020i
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 1.00000 1.73205i 0.117851 0.204124i
\(73\) −7.00000 12.1244i −0.819288 1.41905i −0.906208 0.422833i \(-0.861036\pi\)
0.0869195 0.996215i \(-0.472298\pi\)
\(74\) 2.00000 + 3.46410i 0.232495 + 0.402694i
\(75\) −0.500000 + 0.866025i −0.0577350 + 0.100000i
\(76\) 2.00000 0.229416
\(77\) −2.00000 1.73205i −0.227921 0.197386i
\(78\) −1.00000 −0.113228
\(79\) −8.50000 + 14.7224i −0.956325 + 1.65640i −0.225018 + 0.974355i \(0.572244\pi\)
−0.731307 + 0.682048i \(0.761089\pi\)
\(80\) 0.500000 + 0.866025i 0.0559017 + 0.0968246i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −6.00000 + 10.3923i −0.662589 + 1.14764i
\(83\) 6.00000 0.658586 0.329293 0.944228i \(-0.393190\pi\)
0.329293 + 0.944228i \(0.393190\pi\)
\(84\) −0.500000 + 2.59808i −0.0545545 + 0.283473i
\(85\) 0 0
\(86\) 5.00000 8.66025i 0.539164 0.933859i
\(87\) 4.50000 + 7.79423i 0.482451 + 0.835629i
\(88\) −0.500000 0.866025i −0.0533002 0.0923186i
\(89\) 3.00000 5.19615i 0.317999 0.550791i −0.662071 0.749441i \(-0.730322\pi\)
0.980071 + 0.198650i \(0.0636557\pi\)
\(90\) 2.00000 0.210819
\(91\) −2.50000 + 0.866025i −0.262071 + 0.0907841i
\(92\) −6.00000 −0.625543
\(93\) 2.00000 3.46410i 0.207390 0.359211i
\(94\) 6.00000 + 10.3923i 0.618853 + 1.07188i
\(95\) 1.00000 + 1.73205i 0.102598 + 0.177705i
\(96\) −0.500000 + 0.866025i −0.0510310 + 0.0883883i
\(97\) 5.00000 0.507673 0.253837 0.967247i \(-0.418307\pi\)
0.253837 + 0.967247i \(0.418307\pi\)
\(98\) 1.00000 + 6.92820i 0.101015 + 0.699854i
\(99\) −2.00000 −0.201008
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) 4.50000 + 7.79423i 0.447767 + 0.775555i 0.998240 0.0592978i \(-0.0188862\pi\)
−0.550474 + 0.834853i \(0.685553\pi\)
\(102\) 0 0
\(103\) 2.00000 3.46410i 0.197066 0.341328i −0.750510 0.660859i \(-0.770192\pi\)
0.947576 + 0.319531i \(0.103525\pi\)
\(104\) −1.00000 −0.0980581
\(105\) −2.50000 + 0.866025i −0.243975 + 0.0845154i
\(106\) 6.00000 0.582772
\(107\) 3.00000 5.19615i 0.290021 0.502331i −0.683793 0.729676i \(-0.739671\pi\)
0.973814 + 0.227345i \(0.0730044\pi\)
\(108\) 2.50000 + 4.33013i 0.240563 + 0.416667i
\(109\) 5.00000 + 8.66025i 0.478913 + 0.829502i 0.999708 0.0241802i \(-0.00769755\pi\)
−0.520794 + 0.853682i \(0.674364\pi\)
\(110\) 0.500000 0.866025i 0.0476731 0.0825723i
\(111\) −4.00000 −0.379663
\(112\) −0.500000 + 2.59808i −0.0472456 + 0.245495i
\(113\) −9.00000 −0.846649 −0.423324 0.905978i \(-0.639137\pi\)
−0.423324 + 0.905978i \(0.639137\pi\)
\(114\) −1.00000 + 1.73205i −0.0936586 + 0.162221i
\(115\) −3.00000 5.19615i −0.279751 0.484544i
\(116\) 4.50000 + 7.79423i 0.417815 + 0.723676i
\(117\) −1.00000 + 1.73205i −0.0924500 + 0.160128i
\(118\) 3.00000 0.276172
\(119\) 0 0
\(120\) −1.00000 −0.0912871
\(121\) −0.500000 + 0.866025i −0.0454545 + 0.0787296i
\(122\) 3.50000 + 6.06218i 0.316875 + 0.548844i
\(123\) −6.00000 10.3923i −0.541002 0.937043i
\(124\) 2.00000 3.46410i 0.179605 0.311086i
\(125\) −1.00000 −0.0894427
\(126\) 4.00000 + 3.46410i 0.356348 + 0.308607i
\(127\) −13.0000 −1.15356 −0.576782 0.816898i \(-0.695692\pi\)
−0.576782 + 0.816898i \(0.695692\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 5.00000 + 8.66025i 0.440225 + 0.762493i
\(130\) −0.500000 0.866025i −0.0438529 0.0759555i
\(131\) −9.00000 + 15.5885i −0.786334 + 1.36197i 0.141865 + 0.989886i \(0.454690\pi\)
−0.928199 + 0.372084i \(0.878643\pi\)
\(132\) 1.00000 0.0870388
\(133\) −1.00000 + 5.19615i −0.0867110 + 0.450564i
\(134\) −13.0000 −1.12303
\(135\) −2.50000 + 4.33013i −0.215166 + 0.372678i
\(136\) 0 0
\(137\) −4.50000 7.79423i −0.384461 0.665906i 0.607233 0.794524i \(-0.292279\pi\)
−0.991694 + 0.128618i \(0.958946\pi\)
\(138\) 3.00000 5.19615i 0.255377 0.442326i
\(139\) 20.0000 1.69638 0.848189 0.529694i \(-0.177693\pi\)
0.848189 + 0.529694i \(0.177693\pi\)
\(140\) −2.50000 + 0.866025i −0.211289 + 0.0731925i
\(141\) −12.0000 −1.01058
\(142\) 0 0
\(143\) 0.500000 + 0.866025i 0.0418121 + 0.0724207i
\(144\) 1.00000 + 1.73205i 0.0833333 + 0.144338i
\(145\) −4.50000 + 7.79423i −0.373705 + 0.647275i
\(146\) 14.0000 1.15865
\(147\) −6.50000 2.59808i −0.536111 0.214286i
\(148\) −4.00000 −0.328798
\(149\) 3.00000 5.19615i 0.245770 0.425685i −0.716578 0.697507i \(-0.754293\pi\)
0.962348 + 0.271821i \(0.0876260\pi\)
\(150\) −0.500000 0.866025i −0.0408248 0.0707107i
\(151\) 9.50000 + 16.4545i 0.773099 + 1.33905i 0.935857 + 0.352381i \(0.114628\pi\)
−0.162758 + 0.986666i \(0.552039\pi\)
\(152\) −1.00000 + 1.73205i −0.0811107 + 0.140488i
\(153\) 0 0
\(154\) 2.50000 0.866025i 0.201456 0.0697863i
\(155\) 4.00000 0.321288
\(156\) 0.500000 0.866025i 0.0400320 0.0693375i
\(157\) 5.00000 + 8.66025i 0.399043 + 0.691164i 0.993608 0.112884i \(-0.0360089\pi\)
−0.594565 + 0.804048i \(0.702676\pi\)
\(158\) −8.50000 14.7224i −0.676224 1.17125i
\(159\) −3.00000 + 5.19615i −0.237915 + 0.412082i
\(160\) −1.00000 −0.0790569
\(161\) 3.00000 15.5885i 0.236433 1.22854i
\(162\) 1.00000 0.0785674
\(163\) −2.50000 + 4.33013i −0.195815 + 0.339162i −0.947167 0.320740i \(-0.896069\pi\)
0.751352 + 0.659901i \(0.229402\pi\)
\(164\) −6.00000 10.3923i −0.468521 0.811503i
\(165\) 0.500000 + 0.866025i 0.0389249 + 0.0674200i
\(166\) −3.00000 + 5.19615i −0.232845 + 0.403300i
\(167\) −3.00000 −0.232147 −0.116073 0.993241i \(-0.537031\pi\)
−0.116073 + 0.993241i \(0.537031\pi\)
\(168\) −2.00000 1.73205i −0.154303 0.133631i
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) 2.00000 + 3.46410i 0.152944 + 0.264906i
\(172\) 5.00000 + 8.66025i 0.381246 + 0.660338i
\(173\) 10.5000 18.1865i 0.798300 1.38270i −0.122422 0.992478i \(-0.539066\pi\)
0.920722 0.390218i \(-0.127601\pi\)
\(174\) −9.00000 −0.682288
\(175\) −2.00000 1.73205i −0.151186 0.130931i
\(176\) 1.00000 0.0753778
\(177\) −1.50000 + 2.59808i −0.112747 + 0.195283i
\(178\) 3.00000 + 5.19615i 0.224860 + 0.389468i
\(179\) 10.5000 + 18.1865i 0.784807 + 1.35933i 0.929114 + 0.369792i \(0.120571\pi\)
−0.144308 + 0.989533i \(0.546095\pi\)
\(180\) −1.00000 + 1.73205i −0.0745356 + 0.129099i
\(181\) −16.0000 −1.18927 −0.594635 0.803996i \(-0.702704\pi\)
−0.594635 + 0.803996i \(0.702704\pi\)
\(182\) 0.500000 2.59808i 0.0370625 0.192582i
\(183\) −7.00000 −0.517455
\(184\) 3.00000 5.19615i 0.221163 0.383065i
\(185\) −2.00000 3.46410i −0.147043 0.254686i
\(186\) 2.00000 + 3.46410i 0.146647 + 0.254000i
\(187\) 0 0
\(188\) −12.0000 −0.875190
\(189\) −12.5000 + 4.33013i −0.909241 + 0.314970i
\(190\) −2.00000 −0.145095
\(191\) −6.00000 + 10.3923i −0.434145 + 0.751961i −0.997225 0.0744412i \(-0.976283\pi\)
0.563081 + 0.826402i \(0.309616\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) 2.00000 + 3.46410i 0.143963 + 0.249351i 0.928986 0.370116i \(-0.120682\pi\)
−0.785022 + 0.619467i \(0.787349\pi\)
\(194\) −2.50000 + 4.33013i −0.179490 + 0.310885i
\(195\) 1.00000 0.0716115
\(196\) −6.50000 2.59808i −0.464286 0.185577i
\(197\) 9.00000 0.641223 0.320612 0.947211i \(-0.396112\pi\)
0.320612 + 0.947211i \(0.396112\pi\)
\(198\) 1.00000 1.73205i 0.0710669 0.123091i
\(199\) 5.00000 + 8.66025i 0.354441 + 0.613909i 0.987022 0.160585i \(-0.0513380\pi\)
−0.632581 + 0.774494i \(0.718005\pi\)
\(200\) −0.500000 0.866025i −0.0353553 0.0612372i
\(201\) 6.50000 11.2583i 0.458475 0.794101i
\(202\) −9.00000 −0.633238
\(203\) −22.5000 + 7.79423i −1.57919 + 0.547048i
\(204\) 0 0
\(205\) 6.00000 10.3923i 0.419058 0.725830i
\(206\) 2.00000 + 3.46410i 0.139347 + 0.241355i
\(207\) −6.00000 10.3923i −0.417029 0.722315i
\(208\) 0.500000 0.866025i 0.0346688 0.0600481i
\(209\) 2.00000 0.138343
\(210\) 0.500000 2.59808i 0.0345033 0.179284i
\(211\) −16.0000 −1.10149 −0.550743 0.834675i \(-0.685655\pi\)
−0.550743 + 0.834675i \(0.685655\pi\)
\(212\) −3.00000 + 5.19615i −0.206041 + 0.356873i
\(213\) 0 0
\(214\) 3.00000 + 5.19615i 0.205076 + 0.355202i
\(215\) −5.00000 + 8.66025i −0.340997 + 0.590624i
\(216\) −5.00000 −0.340207
\(217\) 8.00000 + 6.92820i 0.543075 + 0.470317i
\(218\) −10.0000 −0.677285
\(219\) −7.00000 + 12.1244i −0.473016 + 0.819288i
\(220\) 0.500000 + 0.866025i 0.0337100 + 0.0583874i
\(221\) 0 0
\(222\) 2.00000 3.46410i 0.134231 0.232495i
\(223\) 20.0000 1.33930 0.669650 0.742677i \(-0.266444\pi\)
0.669650 + 0.742677i \(0.266444\pi\)
\(224\) −2.00000 1.73205i −0.133631 0.115728i
\(225\) −2.00000 −0.133333
\(226\) 4.50000 7.79423i 0.299336 0.518464i
\(227\) 6.00000 + 10.3923i 0.398234 + 0.689761i 0.993508 0.113761i \(-0.0362899\pi\)
−0.595274 + 0.803523i \(0.702957\pi\)
\(228\) −1.00000 1.73205i −0.0662266 0.114708i
\(229\) 5.00000 8.66025i 0.330409 0.572286i −0.652183 0.758062i \(-0.726147\pi\)
0.982592 + 0.185776i \(0.0594799\pi\)
\(230\) 6.00000 0.395628
\(231\) −0.500000 + 2.59808i −0.0328976 + 0.170941i
\(232\) −9.00000 −0.590879
\(233\) 6.00000 10.3923i 0.393073 0.680823i −0.599780 0.800165i \(-0.704745\pi\)
0.992853 + 0.119342i \(0.0380786\pi\)
\(234\) −1.00000 1.73205i −0.0653720 0.113228i
\(235\) −6.00000 10.3923i −0.391397 0.677919i
\(236\) −1.50000 + 2.59808i −0.0976417 + 0.169120i
\(237\) 17.0000 1.10427
\(238\) 0 0
\(239\) 3.00000 0.194054 0.0970269 0.995282i \(-0.469067\pi\)
0.0970269 + 0.995282i \(0.469067\pi\)
\(240\) 0.500000 0.866025i 0.0322749 0.0559017i
\(241\) 5.00000 + 8.66025i 0.322078 + 0.557856i 0.980917 0.194429i \(-0.0622852\pi\)
−0.658838 + 0.752285i \(0.728952\pi\)
\(242\) −0.500000 0.866025i −0.0321412 0.0556702i
\(243\) −8.00000 + 13.8564i −0.513200 + 0.888889i
\(244\) −7.00000 −0.448129
\(245\) −1.00000 6.92820i −0.0638877 0.442627i
\(246\) 12.0000 0.765092
\(247\) 1.00000 1.73205i 0.0636285 0.110208i
\(248\) 2.00000 + 3.46410i 0.127000 + 0.219971i
\(249\) −3.00000 5.19615i −0.190117 0.329293i
\(250\) 0.500000 0.866025i 0.0316228 0.0547723i
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) −5.00000 + 1.73205i −0.314970 + 0.109109i
\(253\) −6.00000 −0.377217
\(254\) 6.50000 11.2583i 0.407846 0.706410i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −4.50000 + 7.79423i −0.280702 + 0.486191i −0.971558 0.236802i \(-0.923901\pi\)
0.690856 + 0.722993i \(0.257234\pi\)
\(258\) −10.0000 −0.622573
\(259\) 2.00000 10.3923i 0.124274 0.645746i
\(260\) 1.00000 0.0620174
\(261\) −9.00000 + 15.5885i −0.557086 + 0.964901i
\(262\) −9.00000 15.5885i −0.556022 0.963058i
\(263\) −4.50000 7.79423i −0.277482 0.480613i 0.693276 0.720672i \(-0.256167\pi\)
−0.970758 + 0.240059i \(0.922833\pi\)
\(264\) −0.500000 + 0.866025i −0.0307729 + 0.0533002i
\(265\) −6.00000 −0.368577
\(266\) −4.00000 3.46410i −0.245256 0.212398i
\(267\) −6.00000 −0.367194
\(268\) 6.50000 11.2583i 0.397051 0.687712i
\(269\) −3.00000 5.19615i −0.182913 0.316815i 0.759958 0.649972i \(-0.225219\pi\)
−0.942871 + 0.333157i \(0.891886\pi\)
\(270\) −2.50000 4.33013i −0.152145 0.263523i
\(271\) −14.5000 + 25.1147i −0.880812 + 1.52561i −0.0303728 + 0.999539i \(0.509669\pi\)
−0.850439 + 0.526073i \(0.823664\pi\)
\(272\) 0 0
\(273\) 2.00000 + 1.73205i 0.121046 + 0.104828i
\(274\) 9.00000 0.543710
\(275\) −0.500000 + 0.866025i −0.0301511 + 0.0522233i
\(276\) 3.00000 + 5.19615i 0.180579 + 0.312772i
\(277\) 9.50000 + 16.4545i 0.570800 + 0.988654i 0.996484 + 0.0837823i \(0.0267000\pi\)
−0.425684 + 0.904872i \(0.639967\pi\)
\(278\) −10.0000 + 17.3205i −0.599760 + 1.03882i
\(279\) 8.00000 0.478947
\(280\) 0.500000 2.59808i 0.0298807 0.155265i
\(281\) 24.0000 1.43172 0.715860 0.698244i \(-0.246035\pi\)
0.715860 + 0.698244i \(0.246035\pi\)
\(282\) 6.00000 10.3923i 0.357295 0.618853i
\(283\) 11.0000 + 19.0526i 0.653882 + 1.13256i 0.982173 + 0.187980i \(0.0601941\pi\)
−0.328291 + 0.944577i \(0.606473\pi\)
\(284\) 0 0
\(285\) 1.00000 1.73205i 0.0592349 0.102598i
\(286\) −1.00000 −0.0591312
\(287\) 30.0000 10.3923i 1.77084 0.613438i
\(288\) −2.00000 −0.117851
\(289\) 8.50000 14.7224i 0.500000 0.866025i
\(290\) −4.50000 7.79423i −0.264249 0.457693i
\(291\) −2.50000 4.33013i −0.146553 0.253837i
\(292\) −7.00000 + 12.1244i −0.409644 + 0.709524i
\(293\) 6.00000 0.350524 0.175262 0.984522i \(-0.443923\pi\)
0.175262 + 0.984522i \(0.443923\pi\)
\(294\) 5.50000 4.33013i 0.320767 0.252538i
\(295\) −3.00000 −0.174667
\(296\) 2.00000 3.46410i 0.116248 0.201347i
\(297\) 2.50000 + 4.33013i 0.145065 + 0.251259i
\(298\) 3.00000 + 5.19615i 0.173785 + 0.301005i
\(299\) −3.00000 + 5.19615i −0.173494 + 0.300501i
\(300\) 1.00000 0.0577350
\(301\) −25.0000 + 8.66025i −1.44098 + 0.499169i
\(302\) −19.0000 −1.09333
\(303\) 4.50000 7.79423i 0.258518 0.447767i
\(304\) −1.00000 1.73205i −0.0573539 0.0993399i
\(305\) −3.50000 6.06218i −0.200409 0.347119i
\(306\) 0 0
\(307\) 2.00000 0.114146 0.0570730 0.998370i \(-0.481823\pi\)
0.0570730 + 0.998370i \(0.481823\pi\)
\(308\) −0.500000 + 2.59808i −0.0284901 + 0.148039i
\(309\) −4.00000 −0.227552
\(310\) −2.00000 + 3.46410i −0.113592 + 0.196748i
\(311\) −12.0000 20.7846i −0.680458 1.17859i −0.974841 0.222900i \(-0.928448\pi\)
0.294384 0.955687i \(-0.404886\pi\)
\(312\) 0.500000 + 0.866025i 0.0283069 + 0.0490290i
\(313\) 0.500000 0.866025i 0.0282617 0.0489506i −0.851549 0.524276i \(-0.824336\pi\)
0.879810 + 0.475325i \(0.157669\pi\)
\(314\) −10.0000 −0.564333
\(315\) −4.00000 3.46410i −0.225374 0.195180i
\(316\) 17.0000 0.956325
\(317\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(318\) −3.00000 5.19615i −0.168232 0.291386i
\(319\) 4.50000 + 7.79423i 0.251952 + 0.436393i
\(320\) 0.500000 0.866025i 0.0279508 0.0484123i
\(321\) −6.00000 −0.334887
\(322\) 12.0000 + 10.3923i 0.668734 + 0.579141i
\(323\) 0 0
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) 0.500000 + 0.866025i 0.0277350 + 0.0480384i
\(326\) −2.50000 4.33013i −0.138462 0.239824i
\(327\) 5.00000 8.66025i 0.276501 0.478913i
\(328\) 12.0000 0.662589
\(329\) 6.00000 31.1769i 0.330791 1.71884i
\(330\) −1.00000 −0.0550482
\(331\) 3.50000 6.06218i 0.192377 0.333207i −0.753660 0.657264i \(-0.771714\pi\)
0.946038 + 0.324057i \(0.105047\pi\)
\(332\) −3.00000 5.19615i −0.164646 0.285176i
\(333\) −4.00000 6.92820i −0.219199 0.379663i
\(334\) 1.50000 2.59808i 0.0820763 0.142160i
\(335\) 13.0000 0.710266
\(336\) 2.50000 0.866025i 0.136386 0.0472456i
\(337\) 32.0000 1.74315 0.871576 0.490261i \(-0.163099\pi\)
0.871576 + 0.490261i \(0.163099\pi\)
\(338\) 6.00000 10.3923i 0.326357 0.565267i
\(339\) 4.50000 + 7.79423i 0.244406 + 0.423324i
\(340\) 0 0
\(341\) 2.00000 3.46410i 0.108306 0.187592i
\(342\) −4.00000 −0.216295
\(343\) 10.0000 15.5885i 0.539949 0.841698i
\(344\) −10.0000 −0.539164
\(345\) −3.00000 + 5.19615i −0.161515 + 0.279751i
\(346\) 10.5000 + 18.1865i 0.564483 + 0.977714i
\(347\) −9.00000 15.5885i −0.483145 0.836832i 0.516667 0.856186i \(-0.327172\pi\)
−0.999813 + 0.0193540i \(0.993839\pi\)
\(348\) 4.50000 7.79423i 0.241225 0.417815i
\(349\) 26.0000 1.39175 0.695874 0.718164i \(-0.255017\pi\)
0.695874 + 0.718164i \(0.255017\pi\)
\(350\) 2.50000 0.866025i 0.133631 0.0462910i
\(351\) 5.00000 0.266880
\(352\) −0.500000 + 0.866025i −0.0266501 + 0.0461593i
\(353\) 3.00000 + 5.19615i 0.159674 + 0.276563i 0.934751 0.355303i \(-0.115622\pi\)
−0.775077 + 0.631867i \(0.782289\pi\)
\(354\) −1.50000 2.59808i −0.0797241 0.138086i
\(355\) 0 0
\(356\) −6.00000 −0.317999
\(357\) 0 0
\(358\) −21.0000 −1.10988
\(359\) 13.5000 23.3827i 0.712503 1.23409i −0.251412 0.967880i \(-0.580895\pi\)
0.963915 0.266211i \(-0.0857717\pi\)
\(360\) −1.00000 1.73205i −0.0527046 0.0912871i
\(361\) 7.50000 + 12.9904i 0.394737 + 0.683704i
\(362\) 8.00000 13.8564i 0.420471 0.728277i
\(363\) 1.00000 0.0524864
\(364\) 2.00000 + 1.73205i 0.104828 + 0.0907841i
\(365\) −14.0000 −0.732793
\(366\) 3.50000 6.06218i 0.182948 0.316875i
\(367\) 14.0000 + 24.2487i 0.730794 + 1.26577i 0.956544 + 0.291587i \(0.0941834\pi\)
−0.225750 + 0.974185i \(0.572483\pi\)
\(368\) 3.00000 + 5.19615i 0.156386 + 0.270868i
\(369\) 12.0000 20.7846i 0.624695 1.08200i
\(370\) 4.00000 0.207950
\(371\) −12.0000 10.3923i −0.623009 0.539542i
\(372\) −4.00000 −0.207390
\(373\) −14.5000 + 25.1147i −0.750782 + 1.30039i 0.196663 + 0.980471i \(0.436990\pi\)
−0.947444 + 0.319921i \(0.896344\pi\)
\(374\) 0 0
\(375\) 0.500000 + 0.866025i 0.0258199 + 0.0447214i
\(376\) 6.00000 10.3923i 0.309426 0.535942i
\(377\) 9.00000 0.463524
\(378\) 2.50000 12.9904i 0.128586 0.668153i
\(379\) 5.00000 0.256833 0.128416 0.991720i \(-0.459011\pi\)
0.128416 + 0.991720i \(0.459011\pi\)
\(380\) 1.00000 1.73205i 0.0512989 0.0888523i
\(381\) 6.50000 + 11.2583i 0.333005 + 0.576782i
\(382\) −6.00000 10.3923i −0.306987 0.531717i
\(383\) −18.0000 + 31.1769i −0.919757 + 1.59307i −0.119974 + 0.992777i \(0.538281\pi\)
−0.799783 + 0.600289i \(0.795052\pi\)
\(384\) 1.00000 0.0510310
\(385\) −2.50000 + 0.866025i −0.127412 + 0.0441367i
\(386\) −4.00000 −0.203595
\(387\) −10.0000 + 17.3205i −0.508329 + 0.880451i
\(388\) −2.50000 4.33013i −0.126918 0.219829i
\(389\) −6.00000 10.3923i −0.304212 0.526911i 0.672874 0.739758i \(-0.265060\pi\)
−0.977086 + 0.212847i \(0.931726\pi\)
\(390\) −0.500000 + 0.866025i −0.0253185 + 0.0438529i
\(391\) 0 0
\(392\) 5.50000 4.33013i 0.277792 0.218704i
\(393\) 18.0000 0.907980
\(394\) −4.50000 + 7.79423i −0.226707 + 0.392668i
\(395\) 8.50000 + 14.7224i 0.427681 + 0.740766i
\(396\) 1.00000 + 1.73205i 0.0502519 + 0.0870388i
\(397\) −1.00000 + 1.73205i −0.0501886 + 0.0869291i −0.890028 0.455905i \(-0.849316\pi\)
0.839840 + 0.542834i \(0.182649\pi\)
\(398\) −10.0000 −0.501255
\(399\) 5.00000 1.73205i 0.250313 0.0867110i
\(400\) 1.00000 0.0500000
\(401\) −7.50000 + 12.9904i −0.374532 + 0.648709i −0.990257 0.139253i \(-0.955530\pi\)
0.615725 + 0.787961i \(0.288863\pi\)
\(402\) 6.50000 + 11.2583i 0.324191 + 0.561514i
\(403\) −2.00000 3.46410i −0.0996271 0.172559i
\(404\) 4.50000 7.79423i 0.223883 0.387777i
\(405\) −1.00000 −0.0496904
\(406\) 4.50000 23.3827i 0.223331 1.16046i
\(407\) −4.00000 −0.198273
\(408\) 0 0
\(409\) −10.0000 17.3205i −0.494468 0.856444i 0.505511 0.862820i \(-0.331304\pi\)
−0.999980 + 0.00637586i \(0.997970\pi\)
\(410\) 6.00000 + 10.3923i 0.296319 + 0.513239i
\(411\) −4.50000 + 7.79423i −0.221969 + 0.384461i
\(412\) −4.00000 −0.197066
\(413\) −6.00000 5.19615i −0.295241 0.255686i
\(414\) 12.0000 0.589768
\(415\) 3.00000 5.19615i 0.147264 0.255069i
\(416\) 0.500000 + 0.866025i 0.0245145 + 0.0424604i
\(417\) −10.0000 17.3205i −0.489702 0.848189i
\(418\) −1.00000 + 1.73205i −0.0489116 + 0.0847174i
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 2.00000 + 1.73205i 0.0975900 + 0.0845154i
\(421\) 32.0000 1.55958 0.779792 0.626038i \(-0.215325\pi\)
0.779792 + 0.626038i \(0.215325\pi\)
\(422\) 8.00000 13.8564i 0.389434 0.674519i
\(423\) −12.0000 20.7846i −0.583460 1.01058i
\(424\) −3.00000 5.19615i −0.145693 0.252347i
\(425\) 0 0
\(426\) 0 0
\(427\) 3.50000 18.1865i 0.169377 0.880108i
\(428\) −6.00000 −0.290021
\(429\) 0.500000 0.866025i 0.0241402 0.0418121i
\(430\) −5.00000 8.66025i −0.241121 0.417635i
\(431\) 7.50000 + 12.9904i 0.361262 + 0.625725i 0.988169 0.153370i \(-0.0490126\pi\)
−0.626907 + 0.779094i \(0.715679\pi\)
\(432\) 2.50000 4.33013i 0.120281 0.208333i
\(433\) 2.00000 0.0961139 0.0480569 0.998845i \(-0.484697\pi\)
0.0480569 + 0.998845i \(0.484697\pi\)
\(434\) −10.0000 + 3.46410i −0.480015 + 0.166282i
\(435\) 9.00000 0.431517
\(436\) 5.00000 8.66025i 0.239457 0.414751i
\(437\) 6.00000 + 10.3923i 0.287019 + 0.497131i
\(438\) −7.00000 12.1244i −0.334473 0.579324i
\(439\) 6.50000 11.2583i 0.310228 0.537331i −0.668184 0.743996i \(-0.732928\pi\)
0.978412 + 0.206666i \(0.0662612\pi\)
\(440\) −1.00000 −0.0476731
\(441\) −2.00000 13.8564i −0.0952381 0.659829i
\(442\) 0 0
\(443\) 12.0000 20.7846i 0.570137 0.987507i −0.426414 0.904528i \(-0.640223\pi\)
0.996551 0.0829786i \(-0.0264433\pi\)
\(444\) 2.00000 + 3.46410i 0.0949158 + 0.164399i
\(445\) −3.00000 5.19615i −0.142214 0.246321i
\(446\) −10.0000 + 17.3205i −0.473514 + 0.820150i
\(447\) −6.00000 −0.283790
\(448\) 2.50000 0.866025i 0.118114 0.0409159i
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) 1.00000 1.73205i 0.0471405 0.0816497i
\(451\) −6.00000 10.3923i −0.282529 0.489355i
\(452\) 4.50000 + 7.79423i 0.211662 + 0.366610i
\(453\) 9.50000 16.4545i 0.446349 0.773099i
\(454\) −12.0000 −0.563188
\(455\) −0.500000 + 2.59808i −0.0234404 + 0.121800i
\(456\) 2.00000 0.0936586
\(457\) 2.00000 3.46410i 0.0935561 0.162044i −0.815449 0.578829i \(-0.803510\pi\)
0.909005 + 0.416785i \(0.136843\pi\)
\(458\) 5.00000 + 8.66025i 0.233635 + 0.404667i
\(459\) 0 0
\(460\) −3.00000 + 5.19615i −0.139876 + 0.242272i
\(461\) 15.0000 0.698620 0.349310 0.937007i \(-0.386416\pi\)
0.349310 + 0.937007i \(0.386416\pi\)
\(462\) −2.00000 1.73205i −0.0930484 0.0805823i
\(463\) 20.0000 0.929479 0.464739 0.885448i \(-0.346148\pi\)
0.464739 + 0.885448i \(0.346148\pi\)
\(464\) 4.50000 7.79423i 0.208907 0.361838i
\(465\) −2.00000 3.46410i −0.0927478 0.160644i
\(466\) 6.00000 + 10.3923i 0.277945 + 0.481414i
\(467\) −6.00000 + 10.3923i −0.277647 + 0.480899i −0.970799 0.239892i \(-0.922888\pi\)
0.693153 + 0.720791i \(0.256221\pi\)
\(468\) 2.00000 0.0924500
\(469\) 26.0000 + 22.5167i 1.20057 + 1.03972i
\(470\) 12.0000 0.553519
\(471\) 5.00000 8.66025i 0.230388 0.399043i
\(472\) −1.50000 2.59808i −0.0690431 0.119586i
\(473\) 5.00000 + 8.66025i 0.229900 + 0.398199i
\(474\) −8.50000 + 14.7224i −0.390418 + 0.676224i
\(475\) 2.00000 0.0917663
\(476\) 0 0
\(477\) −12.0000 −0.549442
\(478\) −1.50000 + 2.59808i −0.0686084 + 0.118833i
\(479\) 10.5000 + 18.1865i 0.479757 + 0.830964i 0.999730 0.0232187i \(-0.00739140\pi\)
−0.519973 + 0.854183i \(0.674058\pi\)
\(480\) 0.500000 + 0.866025i 0.0228218 + 0.0395285i
\(481\) −2.00000 + 3.46410i −0.0911922 + 0.157949i
\(482\) −10.0000 −0.455488
\(483\) −15.0000 + 5.19615i −0.682524 + 0.236433i
\(484\) 1.00000 0.0454545
\(485\) 2.50000 4.33013i 0.113519 0.196621i
\(486\) −8.00000 13.8564i −0.362887 0.628539i
\(487\) −1.00000 1.73205i −0.0453143 0.0784867i 0.842479 0.538730i \(-0.181096\pi\)
−0.887793 + 0.460243i \(0.847762\pi\)
\(488\) 3.50000 6.06218i 0.158438 0.274422i
\(489\) 5.00000 0.226108
\(490\) 6.50000 + 2.59808i 0.293640 + 0.117369i
\(491\) −24.0000 −1.08310 −0.541552 0.840667i \(-0.682163\pi\)
−0.541552 + 0.840667i \(0.682163\pi\)
\(492\) −6.00000 + 10.3923i −0.270501 + 0.468521i
\(493\) 0 0
\(494\) 1.00000 + 1.73205i 0.0449921 + 0.0779287i
\(495\) −1.00000 + 1.73205i −0.0449467 + 0.0778499i
\(496\) −4.00000 −0.179605
\(497\) 0 0
\(498\) 6.00000 0.268866
\(499\) −10.0000 + 17.3205i −0.447661 + 0.775372i −0.998233 0.0594153i \(-0.981076\pi\)
0.550572 + 0.834788i \(0.314410\pi\)
\(500\) 0.500000 + 0.866025i 0.0223607 + 0.0387298i
\(501\) 1.50000 + 2.59808i 0.0670151 + 0.116073i
\(502\) −6.00000 + 10.3923i −0.267793 + 0.463831i
\(503\) −3.00000 −0.133763 −0.0668817 0.997761i \(-0.521305\pi\)
−0.0668817 + 0.997761i \(0.521305\pi\)
\(504\) 1.00000 5.19615i 0.0445435 0.231455i
\(505\) 9.00000 0.400495
\(506\) 3.00000 5.19615i 0.133366 0.230997i
\(507\) 6.00000 + 10.3923i 0.266469 + 0.461538i
\(508\) 6.50000 + 11.2583i 0.288391 + 0.499508i
\(509\) 3.00000 5.19615i 0.132973 0.230315i −0.791849 0.610718i \(-0.790881\pi\)
0.924821 + 0.380402i \(0.124214\pi\)
\(510\) 0 0
\(511\) −28.0000 24.2487i −1.23865 1.07270i
\(512\) 1.00000 0.0441942
\(513\) 5.00000 8.66025i 0.220755 0.382360i
\(514\) −4.50000 7.79423i −0.198486 0.343789i
\(515\) −2.00000 3.46410i −0.0881305 0.152647i
\(516\) 5.00000 8.66025i 0.220113 0.381246i
\(517\) −12.0000 −0.527759
\(518\) 8.00000 + 6.92820i 0.351500 + 0.304408i
\(519\) −21.0000 −0.921798
\(520\) −0.500000 + 0.866025i −0.0219265 + 0.0379777i
\(521\) −3.00000 5.19615i −0.131432 0.227648i 0.792797 0.609486i \(-0.208624\pi\)
−0.924229 + 0.381839i \(0.875291\pi\)
\(522\) −9.00000 15.5885i −0.393919 0.682288i
\(523\) −1.00000 + 1.73205i −0.0437269 + 0.0757373i −0.887061 0.461653i \(-0.847256\pi\)
0.843334 + 0.537390i \(0.180590\pi\)
\(524\) 18.0000 0.786334
\(525\) −0.500000 + 2.59808i −0.0218218 + 0.113389i
\(526\) 9.00000 0.392419
\(527\) 0 0
\(528\) −0.500000 0.866025i −0.0217597 0.0376889i
\(529\) −6.50000 11.2583i −0.282609 0.489493i
\(530\) 3.00000 5.19615i 0.130312 0.225706i
\(531\) −6.00000 −0.260378
\(532\) 5.00000 1.73205i 0.216777 0.0750939i
\(533\) −12.0000 −0.519778
\(534\) 3.00000 5.19615i 0.129823 0.224860i
\(535\) −3.00000 5.19615i −0.129701 0.224649i
\(536\) 6.50000 + 11.2583i 0.280757 + 0.486286i
\(537\) 10.5000 18.1865i 0.453108 0.784807i
\(538\) 6.00000 0.258678
\(539\) −6.50000 2.59808i −0.279975 0.111907i
\(540\) 5.00000 0.215166
\(541\) −2.50000 + 4.33013i −0.107483 + 0.186167i −0.914750 0.404020i \(-0.867613\pi\)
0.807267 + 0.590187i \(0.200946\pi\)
\(542\) −14.5000 25.1147i −0.622828 1.07877i
\(543\) 8.00000 + 13.8564i 0.343313 + 0.594635i
\(544\) 0 0
\(545\) 10.0000 0.428353
\(546\) −2.50000 + 0.866025i −0.106990 + 0.0370625i
\(547\) 8.00000 0.342055 0.171028 0.985266i \(-0.445291\pi\)
0.171028 + 0.985266i \(0.445291\pi\)
\(548\) −4.50000 + 7.79423i −0.192230 + 0.332953i
\(549\) −7.00000 12.1244i −0.298753 0.517455i
\(550\) −0.500000 0.866025i −0.0213201 0.0369274i
\(551\) 9.00000 15.5885i 0.383413 0.664091i
\(552\) −6.00000 −0.255377
\(553\) −8.50000 + 44.1673i −0.361457 + 1.87818i
\(554\) −19.0000 −0.807233
\(555\) −2.00000 + 3.46410i −0.0848953 + 0.147043i
\(556\) −10.0000 17.3205i −0.424094 0.734553i
\(557\) −9.00000 15.5885i −0.381342 0.660504i 0.609912 0.792469i \(-0.291205\pi\)
−0.991254 + 0.131965i \(0.957871\pi\)
\(558\) −4.00000 + 6.92820i −0.169334 + 0.293294i
\(559\) 10.0000 0.422955
\(560\) 2.00000 + 1.73205i 0.0845154 + 0.0731925i
\(561\) 0 0
\(562\) −12.0000 + 20.7846i −0.506189 + 0.876746i
\(563\) −3.00000 5.19615i −0.126435 0.218992i 0.795858 0.605483i \(-0.207020\pi\)
−0.922293 + 0.386492i \(0.873687\pi\)
\(564\) 6.00000 + 10.3923i 0.252646 + 0.437595i
\(565\) −4.50000 + 7.79423i −0.189316 + 0.327906i
\(566\) −22.0000 −0.924729
\(567\) −2.00000 1.73205i −0.0839921 0.0727393i
\(568\) 0 0
\(569\) −21.0000 + 36.3731i −0.880366 + 1.52484i −0.0294311 + 0.999567i \(0.509370\pi\)
−0.850935 + 0.525271i \(0.823964\pi\)
\(570\) 1.00000 + 1.73205i 0.0418854 + 0.0725476i
\(571\) −10.0000 17.3205i −0.418487 0.724841i 0.577301 0.816532i \(-0.304106\pi\)
−0.995788 + 0.0916910i \(0.970773\pi\)
\(572\) 0.500000 0.866025i 0.0209061 0.0362103i
\(573\) 12.0000 0.501307
\(574\) −6.00000 + 31.1769i −0.250435 + 1.30130i
\(575\) −6.00000 −0.250217
\(576\) 1.00000 1.73205i 0.0416667 0.0721688i
\(577\) −5.50000 9.52628i −0.228968 0.396584i 0.728535 0.685009i \(-0.240202\pi\)
−0.957503 + 0.288425i \(0.906868\pi\)
\(578\) 8.50000 + 14.7224i 0.353553 + 0.612372i
\(579\) 2.00000 3.46410i 0.0831172 0.143963i
\(580\) 9.00000 0.373705
\(581\) 15.0000 5.19615i 0.622305 0.215573i
\(582\) 5.00000 0.207257
\(583\) −3.00000 + 5.19615i −0.124247 + 0.215203i
\(584\) −7.00000 12.1244i −0.289662 0.501709i
\(585\) 1.00000 + 1.73205i 0.0413449 + 0.0716115i
\(586\) −3.00000 + 5.19615i −0.123929 + 0.214651i
\(587\) −15.0000 −0.619116 −0.309558 0.950881i \(-0.600181\pi\)
−0.309558 + 0.950881i \(0.600181\pi\)
\(588\) 1.00000 + 6.92820i 0.0412393 + 0.285714i
\(589\) −8.00000 −0.329634
\(590\) 1.50000 2.59808i 0.0617540 0.106961i
\(591\) −4.50000 7.79423i −0.185105 0.320612i
\(592\) 2.00000 + 3.46410i 0.0821995 + 0.142374i
\(593\) −21.0000 + 36.3731i −0.862367 + 1.49366i 0.00727173 + 0.999974i \(0.497685\pi\)
−0.869638 + 0.493689i \(0.835648\pi\)
\(594\) −5.00000 −0.205152
\(595\) 0 0
\(596\) −6.00000 −0.245770
\(597\) 5.00000 8.66025i 0.204636 0.354441i
\(598\) −3.00000 5.19615i −0.122679 0.212486i
\(599\) −12.0000 20.7846i −0.490307 0.849236i 0.509631 0.860393i \(-0.329782\pi\)
−0.999938 + 0.0111569i \(0.996449\pi\)
\(600\) −0.500000 + 0.866025i −0.0204124 + 0.0353553i
\(601\) −28.0000 −1.14214 −0.571072 0.820900i \(-0.693472\pi\)
−0.571072 + 0.820900i \(0.693472\pi\)
\(602\) 5.00000 25.9808i 0.203785 1.05890i
\(603\) 26.0000 1.05880
\(604\) 9.50000 16.4545i 0.386550 0.669523i
\(605\) 0.500000 + 0.866025i 0.0203279 + 0.0352089i
\(606\) 4.50000 + 7.79423i 0.182800 + 0.316619i
\(607\) 8.00000 13.8564i 0.324710 0.562414i −0.656744 0.754114i \(-0.728067\pi\)
0.981454 + 0.191700i \(0.0614000\pi\)
\(608\) 2.00000 0.0811107
\(609\) 18.0000 + 15.5885i 0.729397 + 0.631676i
\(610\) 7.00000 0.283422
\(611\) −6.00000 + 10.3923i −0.242734 + 0.420428i
\(612\) 0 0
\(613\) −1.00000 1.73205i −0.0403896 0.0699569i 0.845124 0.534570i \(-0.179527\pi\)
−0.885514 + 0.464614i \(0.846193\pi\)
\(614\) −1.00000 + 1.73205i −0.0403567 + 0.0698999i
\(615\) −12.0000 −0.483887
\(616\) −2.00000 1.73205i −0.0805823 0.0697863i
\(617\) 15.0000 0.603877 0.301939 0.953327i \(-0.402366\pi\)
0.301939 + 0.953327i \(0.402366\pi\)
\(618\) 2.00000 3.46410i 0.0804518 0.139347i
\(619\) −4.00000 6.92820i −0.160774 0.278468i 0.774373 0.632730i \(-0.218066\pi\)
−0.935146 + 0.354262i \(0.884732\pi\)
\(620\) −2.00000 3.46410i −0.0803219 0.139122i
\(621\) −15.0000 + 25.9808i −0.601929 + 1.04257i
\(622\) 24.0000 0.962312
\(623\) 3.00000 15.5885i 0.120192 0.624538i
\(624\) −1.00000 −0.0400320
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0.500000 + 0.866025i 0.0199840 + 0.0346133i
\(627\) −1.00000 1.73205i −0.0399362 0.0691714i
\(628\) 5.00000 8.66025i 0.199522 0.345582i
\(629\) 0 0
\(630\) 5.00000 1.73205i 0.199205 0.0690066i
\(631\) 2.00000 0.0796187 0.0398094 0.999207i \(-0.487325\pi\)
0.0398094 + 0.999207i \(0.487325\pi\)
\(632\) −8.50000 + 14.7224i −0.338112 + 0.585627i
\(633\) 8.00000 + 13.8564i 0.317971 + 0.550743i
\(634\) 0 0
\(635\) −6.50000 + 11.2583i −0.257945 + 0.446773i
\(636\) 6.00000 0.237915
\(637\) −5.50000 + 4.33013i −0.217918 + 0.171566i
\(638\) −9.00000 −0.356313
\(639\) 0 0
\(640\) 0.500000 + 0.866025i 0.0197642 + 0.0342327i
\(641\) −4.50000 7.79423i −0.177739 0.307854i 0.763367 0.645966i \(-0.223545\pi\)
−0.941106 + 0.338112i \(0.890212\pi\)
\(642\) 3.00000 5.19615i 0.118401 0.205076i
\(643\) −19.0000 −0.749287 −0.374643 0.927169i \(-0.622235\pi\)
−0.374643 + 0.927169i \(0.622235\pi\)
\(644\) −15.0000 + 5.19615i −0.591083 + 0.204757i
\(645\) 10.0000 0.393750
\(646\) 0 0
\(647\) 21.0000 + 36.3731i 0.825595 + 1.42997i 0.901464 + 0.432855i \(0.142494\pi\)
−0.0758684 + 0.997118i \(0.524173\pi\)
\(648\) −0.500000 0.866025i −0.0196419 0.0340207i
\(649\) −1.50000 + 2.59808i −0.0588802 + 0.101983i
\(650\) −1.00000 −0.0392232
\(651\) 2.00000 10.3923i 0.0783862 0.407307i
\(652\) 5.00000 0.195815
\(653\) −9.00000 + 15.5885i −0.352197 + 0.610023i −0.986634 0.162951i \(-0.947899\pi\)
0.634437 + 0.772975i \(0.281232\pi\)
\(654\) 5.00000 + 8.66025i 0.195515 + 0.338643i
\(655\) 9.00000 + 15.5885i 0.351659 + 0.609091i
\(656\) −6.00000 + 10.3923i −0.234261 + 0.405751i
\(657\) −28.0000 −1.09238
\(658\) 24.0000 + 20.7846i 0.935617 + 0.810268i
\(659\) −6.00000 −0.233727 −0.116863 0.993148i \(-0.537284\pi\)
−0.116863 + 0.993148i \(0.537284\pi\)
\(660\) 0.500000 0.866025i 0.0194625 0.0337100i
\(661\) −13.0000 22.5167i −0.505641 0.875797i −0.999979 0.00652642i \(-0.997923\pi\)
0.494337 0.869270i \(-0.335411\pi\)
\(662\) 3.50000 + 6.06218i 0.136031 + 0.235613i
\(663\) 0 0
\(664\) 6.00000 0.232845
\(665\) 4.00000 + 3.46410i 0.155113 + 0.134332i
\(666\) 8.00000 0.309994
\(667\) −27.0000 + 46.7654i −1.04544 + 1.81076i
\(668\) 1.50000 + 2.59808i 0.0580367 + 0.100523i
\(669\) −10.0000 17.3205i −0.386622 0.669650i
\(670\) −6.50000 + 11.2583i −0.251117 + 0.434947i
\(671\) −7.00000 −0.270232
\(672\) −0.500000 + 2.59808i −0.0192879 + 0.100223i
\(673\) −34.0000 −1.31060 −0.655302 0.755367i \(-0.727459\pi\)
−0.655302 + 0.755367i \(0.727459\pi\)
\(674\) −16.0000 + 27.7128i −0.616297 + 1.06746i
\(675\) 2.50000 + 4.33013i 0.0962250 + 0.166667i
\(676\) 6.00000 + 10.3923i 0.230769 + 0.399704i
\(677\) 21.0000 36.3731i 0.807096 1.39793i −0.107772 0.994176i \(-0.534372\pi\)
0.914867 0.403755i \(-0.132295\pi\)
\(678\) −9.00000 −0.345643
\(679\) 12.5000 4.33013i 0.479706 0.166175i
\(680\) 0 0
\(681\) 6.00000 10.3923i 0.229920 0.398234i
\(682\) 2.00000 + 3.46410i 0.0765840 + 0.132647i
\(683\) −19.5000 33.7750i −0.746147 1.29236i −0.949657 0.313291i \(-0.898568\pi\)
0.203510 0.979073i \(-0.434765\pi\)
\(684\) 2.00000 3.46410i 0.0764719 0.132453i
\(685\) −9.00000 −0.343872
\(686\) 8.50000 + 16.4545i 0.324532 + 0.628235i
\(687\) −10.0000 −0.381524
\(688\) 5.00000 8.66025i 0.190623 0.330169i
\(689\) 3.00000 + 5.19615i 0.114291 + 0.197958i
\(690\) −3.00000 5.19615i −0.114208 0.197814i
\(691\) −8.50000 + 14.7224i −0.323355 + 0.560068i −0.981178 0.193105i \(-0.938144\pi\)
0.657823 + 0.753173i \(0.271478\pi\)
\(692\) −21.0000 −0.798300
\(693\) −5.00000 + 1.73205i −0.189934 + 0.0657952i
\(694\) 18.0000 0.683271
\(695\) 10.0000 17.3205i 0.379322 0.657004i
\(696\) 4.50000 + 7.79423i 0.170572 + 0.295439i
\(697\) 0 0
\(698\) −13.0000 + 22.5167i −0.492057 + 0.852268i
\(699\) −12.0000 −0.453882
\(700\) −0.500000 + 2.59808i −0.0188982 + 0.0981981i
\(701\) 21.0000 0.793159 0.396580 0.918000i \(-0.370197\pi\)
0.396580 + 0.918000i \(0.370197\pi\)
\(702\) −2.50000 + 4.33013i −0.0943564 + 0.163430i
\(703\) 4.00000 + 6.92820i 0.150863 + 0.261302i
\(704\) −0.500000 0.866025i −0.0188445 0.0326396i
\(705\) −6.00000 + 10.3923i −0.225973 + 0.391397i
\(706\) −6.00000 −0.225813
\(707\) 18.0000 + 15.5885i 0.676960 + 0.586264i
\(708\) 3.00000 0.112747
\(709\) 5.00000 8.66025i 0.187779 0.325243i −0.756730 0.653727i \(-0.773204\pi\)
0.944509 + 0.328484i \(0.106538\pi\)
\(710\) 0 0
\(711\) 17.0000 + 29.4449i 0.637550 + 1.10427i
\(712\) 3.00000 5.19615i 0.112430 0.194734i
\(713\) 24.0000 0.898807
\(714\) 0 0
\(715\) 1.00000 0.0373979
\(716\) 10.5000 18.1865i 0.392403 0.679663i
\(717\) −1.50000 2.59808i −0.0560185 0.0970269i
\(718\) 13.5000 + 23.3827i 0.503816 + 0.872634i
\(719\) −12.0000 + 20.7846i −0.447524 + 0.775135i −0.998224 0.0595683i \(-0.981028\pi\)
0.550700 + 0.834703i \(0.314361\pi\)
\(720\) 2.00000 0.0745356
\(721\) 2.00000 10.3923i 0.0744839 0.387030i
\(722\) −15.0000 −0.558242
\(723\) 5.00000 8.66025i 0.185952 0.322078i
\(724\) 8.00000 + 13.8564i 0.297318 + 0.514969i
\(725\) 4.50000 + 7.79423i 0.167126 + 0.289470i
\(726\) −0.500000 + 0.866025i −0.0185567 + 0.0321412i
\(727\) −34.0000 −1.26099 −0.630495 0.776193i \(-0.717148\pi\)
−0.630495 + 0.776193i \(0.717148\pi\)
\(728\) −2.50000 + 0.866025i −0.0926562 + 0.0320970i
\(729\) 13.0000 0.481481
\(730\) 7.00000 12.1244i 0.259082 0.448743i
\(731\) 0 0
\(732\) 3.50000 + 6.06218i 0.129364 + 0.224065i
\(733\) −5.50000 + 9.52628i −0.203147 + 0.351861i −0.949541 0.313644i \(-0.898450\pi\)
0.746394 + 0.665505i \(0.231784\pi\)
\(734\) −28.0000 −1.03350
\(735\) −5.50000 + 4.33013i −0.202871 + 0.159719i
\(736\) −6.00000 −0.221163
\(737\) 6.50000 11.2583i 0.239431 0.414706i
\(738\) 12.0000 + 20.7846i 0.441726 + 0.765092i
\(739\) 8.00000 + 13.8564i 0.294285 + 0.509716i 0.974818 0.223001i \(-0.0715853\pi\)
−0.680534 + 0.732717i \(0.738252\pi\)
\(740\) −2.00000 + 3.46410i −0.0735215 + 0.127343i
\(741\) −2.00000 −0.0734718
\(742\) 15.0000 5.19615i 0.550667 0.190757i
\(743\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(744\) 2.00000 3.46410i 0.0733236 0.127000i
\(745\) −3.00000 5.19615i −0.109911 0.190372i
\(746\) −14.5000 25.1147i −0.530883 0.919516i
\(747\) 6.00000 10.3923i 0.219529 0.380235i
\(748\) 0 0
\(749\) 3.00000 15.5885i 0.109618 0.569590i
\(750\) −1.00000 −0.0365148
\(751\) 23.0000 39.8372i 0.839282 1.45368i −0.0512140 0.998688i \(-0.516309\pi\)
0.890496 0.454991i \(-0.150358\pi\)
\(752\) 6.00000 + 10.3923i 0.218797 + 0.378968i
\(753\) −6.00000 10.3923i −0.218652 0.378717i
\(754\) −4.50000 + 7.79423i −0.163880 + 0.283849i
\(755\) 19.0000 0.691481
\(756\) 10.0000 + 8.66025i 0.363696 + 0.314970i
\(757\) −46.0000 −1.67190 −0.835949 0.548807i \(-0.815082\pi\)
−0.835949 + 0.548807i \(0.815082\pi\)
\(758\) −2.50000 + 4.33013i −0.0908041 + 0.157277i
\(759\) 3.00000 + 5.19615i 0.108893 + 0.188608i
\(760\) 1.00000 + 1.73205i 0.0362738 + 0.0628281i
\(761\) −9.00000 + 15.5885i −0.326250 + 0.565081i −0.981764 0.190101i \(-0.939118\pi\)
0.655515 + 0.755182i \(0.272452\pi\)
\(762\) −13.0000 −0.470940
\(763\) 20.0000 + 17.3205i 0.724049 + 0.627044i
\(764\) 12.0000 0.434145
\(765\) 0 0
\(766\) −18.0000 31.1769i −0.650366 1.12647i
\(767\) 1.50000 + 2.59808i 0.0541619 + 0.0938111i
\(768\) −0.500000 + 0.866025i −0.0180422 + 0.0312500i
\(769\) −4.00000 −0.144244 −0.0721218 0.997396i \(-0.522977\pi\)
−0.0721218 + 0.997396i \(0.522977\pi\)
\(770\) 0.500000 2.59808i 0.0180187 0.0936282i
\(771\) 9.00000 0.324127
\(772\) 2.00000 3.46410i 0.0719816 0.124676i
\(773\) 27.0000 + 46.7654i 0.971123 + 1.68203i 0.692179 + 0.721726i \(0.256651\pi\)
0.278944 + 0.960307i \(0.410016\pi\)
\(774\) −10.0000 17.3205i −0.359443 0.622573i
\(775\) 2.00000 3.46410i 0.0718421 0.124434i
\(776\) 5.00000 0.179490
\(777\) −10.0000 + 3.46410i −0.358748 + 0.124274i
\(778\) 12.0000 0.430221
\(779\) −12.0000 + 20.7846i −0.429945 +