Properties

Label 37.2.c.a.26.1
Level $37$
Weight $2$
Character 37.26
Analytic conductor $0.295$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 37.c (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.295446487479\)
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 26.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 37.26
Dual form 37.2.c.a.10.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.00000 + 1.73205i) q^{7} -3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.00000 + 1.73205i) q^{7} -3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +1.00000 q^{10} -2.00000 q^{11} +(1.00000 - 1.73205i) q^{13} +2.00000 q^{14} +(0.500000 + 0.866025i) q^{16} +(-1.50000 - 2.59808i) q^{17} +(1.50000 - 2.59808i) q^{18} +(3.00000 - 5.19615i) q^{19} +(0.500000 + 0.866025i) q^{20} +(1.00000 + 1.73205i) q^{22} -4.00000 q^{23} +(2.00000 + 3.46410i) q^{25} -2.00000 q^{26} +(1.00000 + 1.73205i) q^{28} +9.00000 q^{29} -10.0000 q^{31} +(-2.50000 + 4.33013i) q^{32} +(-1.50000 + 2.59808i) q^{34} +(-1.00000 - 1.73205i) q^{35} +3.00000 q^{36} +(-5.50000 + 2.59808i) q^{37} -6.00000 q^{38} +(1.50000 - 2.59808i) q^{40} +(4.50000 - 7.79423i) q^{41} +2.00000 q^{43} +(-1.00000 + 1.73205i) q^{44} -3.00000 q^{45} +(2.00000 + 3.46410i) q^{46} +6.00000 q^{47} +(1.50000 + 2.59808i) q^{49} +(2.00000 - 3.46410i) q^{50} +(-1.00000 - 1.73205i) q^{52} +(1.00000 + 1.73205i) q^{53} +(1.00000 - 1.73205i) q^{55} +(3.00000 - 5.19615i) q^{56} +(-4.50000 - 7.79423i) q^{58} +(2.00000 + 3.46410i) q^{59} +(-0.500000 + 0.866025i) q^{61} +(5.00000 + 8.66025i) q^{62} -6.00000 q^{63} +7.00000 q^{64} +(1.00000 + 1.73205i) q^{65} +(5.00000 - 8.66025i) q^{67} -3.00000 q^{68} +(-1.00000 + 1.73205i) q^{70} +(-3.00000 + 5.19615i) q^{71} +(-4.50000 - 7.79423i) q^{72} -10.0000 q^{73} +(5.00000 + 3.46410i) q^{74} +(-3.00000 - 5.19615i) q^{76} +(2.00000 - 3.46410i) q^{77} +(-5.00000 + 8.66025i) q^{79} -1.00000 q^{80} +(-4.50000 + 7.79423i) q^{81} -9.00000 q^{82} +(6.00000 + 10.3923i) q^{83} +3.00000 q^{85} +(-1.00000 - 1.73205i) q^{86} +6.00000 q^{88} +(-3.50000 - 6.06218i) q^{89} +(1.50000 + 2.59808i) q^{90} +(2.00000 + 3.46410i) q^{91} +(-2.00000 + 3.46410i) q^{92} +(-3.00000 - 5.19615i) q^{94} +(3.00000 + 5.19615i) q^{95} +7.00000 q^{97} +(1.50000 - 2.59808i) q^{98} +(-3.00000 - 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} + q^{4} - q^{5} - 2q^{7} - 6q^{8} + 3q^{9} + O(q^{10}) \) \( 2q - q^{2} + q^{4} - q^{5} - 2q^{7} - 6q^{8} + 3q^{9} + 2q^{10} - 4q^{11} + 2q^{13} + 4q^{14} + q^{16} - 3q^{17} + 3q^{18} + 6q^{19} + q^{20} + 2q^{22} - 8q^{23} + 4q^{25} - 4q^{26} + 2q^{28} + 18q^{29} - 20q^{31} - 5q^{32} - 3q^{34} - 2q^{35} + 6q^{36} - 11q^{37} - 12q^{38} + 3q^{40} + 9q^{41} + 4q^{43} - 2q^{44} - 6q^{45} + 4q^{46} + 12q^{47} + 3q^{49} + 4q^{50} - 2q^{52} + 2q^{53} + 2q^{55} + 6q^{56} - 9q^{58} + 4q^{59} - q^{61} + 10q^{62} - 12q^{63} + 14q^{64} + 2q^{65} + 10q^{67} - 6q^{68} - 2q^{70} - 6q^{71} - 9q^{72} - 20q^{73} + 10q^{74} - 6q^{76} + 4q^{77} - 10q^{79} - 2q^{80} - 9q^{81} - 18q^{82} + 12q^{83} + 6q^{85} - 2q^{86} + 12q^{88} - 7q^{89} + 3q^{90} + 4q^{91} - 4q^{92} - 6q^{94} + 6q^{95} + 14q^{97} + 3q^{98} - 6q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/37\mathbb{Z}\right)^\times\).

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

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 0.633316 0.773893i \(-0.281693\pi\)
−0.986869 + 0.161521i \(0.948360\pi\)
\(3\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i −0.955901 0.293691i \(-0.905116\pi\)
0.732294 + 0.680989i \(0.238450\pi\)
\(6\) 0 0
\(7\) −1.00000 + 1.73205i −0.377964 + 0.654654i −0.990766 0.135583i \(-0.956709\pi\)
0.612801 + 0.790237i \(0.290043\pi\)
\(8\) −3.00000 −1.06066
\(9\) 1.50000 + 2.59808i 0.500000 + 0.866025i
\(10\) 1.00000 0.316228
\(11\) −2.00000 −0.603023 −0.301511 0.953463i \(-0.597491\pi\)
−0.301511 + 0.953463i \(0.597491\pi\)
\(12\) 0 0
\(13\) 1.00000 1.73205i 0.277350 0.480384i −0.693375 0.720577i \(-0.743877\pi\)
0.970725 + 0.240192i \(0.0772105\pi\)
\(14\) 2.00000 0.534522
\(15\) 0 0
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) −1.50000 2.59808i −0.363803 0.630126i 0.624780 0.780801i \(-0.285189\pi\)
−0.988583 + 0.150675i \(0.951855\pi\)
\(18\) 1.50000 2.59808i 0.353553 0.612372i
\(19\) 3.00000 5.19615i 0.688247 1.19208i −0.284157 0.958778i \(-0.591714\pi\)
0.972404 0.233301i \(-0.0749529\pi\)
\(20\) 0.500000 + 0.866025i 0.111803 + 0.193649i
\(21\) 0 0
\(22\) 1.00000 + 1.73205i 0.213201 + 0.369274i
\(23\) −4.00000 −0.834058 −0.417029 0.908893i \(-0.636929\pi\)
−0.417029 + 0.908893i \(0.636929\pi\)
\(24\) 0 0
\(25\) 2.00000 + 3.46410i 0.400000 + 0.692820i
\(26\) −2.00000 −0.392232
\(27\) 0 0
\(28\) 1.00000 + 1.73205i 0.188982 + 0.327327i
\(29\) 9.00000 1.67126 0.835629 0.549294i \(-0.185103\pi\)
0.835629 + 0.549294i \(0.185103\pi\)
\(30\) 0 0
\(31\) −10.0000 −1.79605 −0.898027 0.439941i \(-0.854999\pi\)
−0.898027 + 0.439941i \(0.854999\pi\)
\(32\) −2.50000 + 4.33013i −0.441942 + 0.765466i
\(33\) 0 0
\(34\) −1.50000 + 2.59808i −0.257248 + 0.445566i
\(35\) −1.00000 1.73205i −0.169031 0.292770i
\(36\) 3.00000 0.500000
\(37\) −5.50000 + 2.59808i −0.904194 + 0.427121i
\(38\) −6.00000 −0.973329
\(39\) 0 0
\(40\) 1.50000 2.59808i 0.237171 0.410792i
\(41\) 4.50000 7.79423i 0.702782 1.21725i −0.264704 0.964330i \(-0.585274\pi\)
0.967486 0.252924i \(-0.0813924\pi\)
\(42\) 0 0
\(43\) 2.00000 0.304997 0.152499 0.988304i \(-0.451268\pi\)
0.152499 + 0.988304i \(0.451268\pi\)
\(44\) −1.00000 + 1.73205i −0.150756 + 0.261116i
\(45\) −3.00000 −0.447214
\(46\) 2.00000 + 3.46410i 0.294884 + 0.510754i
\(47\) 6.00000 0.875190 0.437595 0.899172i \(-0.355830\pi\)
0.437595 + 0.899172i \(0.355830\pi\)
\(48\) 0 0
\(49\) 1.50000 + 2.59808i 0.214286 + 0.371154i
\(50\) 2.00000 3.46410i 0.282843 0.489898i
\(51\) 0 0
\(52\) −1.00000 1.73205i −0.138675 0.240192i
\(53\) 1.00000 + 1.73205i 0.137361 + 0.237915i 0.926497 0.376303i \(-0.122805\pi\)
−0.789136 + 0.614218i \(0.789471\pi\)
\(54\) 0 0
\(55\) 1.00000 1.73205i 0.134840 0.233550i
\(56\) 3.00000 5.19615i 0.400892 0.694365i
\(57\) 0 0
\(58\) −4.50000 7.79423i −0.590879 1.02343i
\(59\) 2.00000 + 3.46410i 0.260378 + 0.450988i 0.966342 0.257260i \(-0.0828195\pi\)
−0.705965 + 0.708247i \(0.749486\pi\)
\(60\) 0 0
\(61\) −0.500000 + 0.866025i −0.0640184 + 0.110883i −0.896258 0.443533i \(-0.853725\pi\)
0.832240 + 0.554416i \(0.187058\pi\)
\(62\) 5.00000 + 8.66025i 0.635001 + 1.09985i
\(63\) −6.00000 −0.755929
\(64\) 7.00000 0.875000
\(65\) 1.00000 + 1.73205i 0.124035 + 0.214834i
\(66\) 0 0
\(67\) 5.00000 8.66025i 0.610847 1.05802i −0.380251 0.924883i \(-0.624162\pi\)
0.991098 0.133135i \(-0.0425044\pi\)
\(68\) −3.00000 −0.363803
\(69\) 0 0
\(70\) −1.00000 + 1.73205i −0.119523 + 0.207020i
\(71\) −3.00000 + 5.19615i −0.356034 + 0.616670i −0.987294 0.158901i \(-0.949205\pi\)
0.631260 + 0.775571i \(0.282538\pi\)
\(72\) −4.50000 7.79423i −0.530330 0.918559i
\(73\) −10.0000 −1.17041 −0.585206 0.810885i \(-0.698986\pi\)
−0.585206 + 0.810885i \(0.698986\pi\)
\(74\) 5.00000 + 3.46410i 0.581238 + 0.402694i
\(75\) 0 0
\(76\) −3.00000 5.19615i −0.344124 0.596040i
\(77\) 2.00000 3.46410i 0.227921 0.394771i
\(78\) 0 0
\(79\) −5.00000 + 8.66025i −0.562544 + 0.974355i 0.434730 + 0.900561i \(0.356844\pi\)
−0.997274 + 0.0737937i \(0.976489\pi\)
\(80\) −1.00000 −0.111803
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) −9.00000 −0.993884
\(83\) 6.00000 + 10.3923i 0.658586 + 1.14070i 0.980982 + 0.194099i \(0.0621783\pi\)
−0.322396 + 0.946605i \(0.604488\pi\)
\(84\) 0 0
\(85\) 3.00000 0.325396
\(86\) −1.00000 1.73205i −0.107833 0.186772i
\(87\) 0 0
\(88\) 6.00000 0.639602
\(89\) −3.50000 6.06218i −0.370999 0.642590i 0.618720 0.785611i \(-0.287651\pi\)
−0.989720 + 0.143022i \(0.954318\pi\)
\(90\) 1.50000 + 2.59808i 0.158114 + 0.273861i
\(91\) 2.00000 + 3.46410i 0.209657 + 0.363137i
\(92\) −2.00000 + 3.46410i −0.208514 + 0.361158i
\(93\) 0 0
\(94\) −3.00000 5.19615i −0.309426 0.535942i
\(95\) 3.00000 + 5.19615i 0.307794 + 0.533114i
\(96\) 0 0
\(97\) 7.00000 0.710742 0.355371 0.934725i \(-0.384354\pi\)
0.355371 + 0.934725i \(0.384354\pi\)
\(98\) 1.50000 2.59808i 0.151523 0.262445i
\(99\) −3.00000 5.19615i −0.301511 0.522233i
\(100\) 4.00000 0.400000
\(101\) −3.00000 −0.298511 −0.149256 0.988799i \(-0.547688\pi\)
−0.149256 + 0.988799i \(0.547688\pi\)
\(102\) 0 0
\(103\) 6.00000 0.591198 0.295599 0.955312i \(-0.404481\pi\)
0.295599 + 0.955312i \(0.404481\pi\)
\(104\) −3.00000 + 5.19615i −0.294174 + 0.509525i
\(105\) 0 0
\(106\) 1.00000 1.73205i 0.0971286 0.168232i
\(107\) 9.00000 15.5885i 0.870063 1.50699i 0.00813215 0.999967i \(-0.497411\pi\)
0.861931 0.507026i \(-0.169255\pi\)
\(108\) 0 0
\(109\) −2.50000 4.33013i −0.239457 0.414751i 0.721102 0.692829i \(-0.243636\pi\)
−0.960558 + 0.278078i \(0.910303\pi\)
\(110\) −2.00000 −0.190693
\(111\) 0 0
\(112\) −2.00000 −0.188982
\(113\) −3.00000 5.19615i −0.282216 0.488813i 0.689714 0.724082i \(-0.257736\pi\)
−0.971930 + 0.235269i \(0.924403\pi\)
\(114\) 0 0
\(115\) 2.00000 3.46410i 0.186501 0.323029i
\(116\) 4.50000 7.79423i 0.417815 0.723676i
\(117\) 6.00000 0.554700
\(118\) 2.00000 3.46410i 0.184115 0.318896i
\(119\) 6.00000 0.550019
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 1.00000 0.0905357
\(123\) 0 0
\(124\) −5.00000 + 8.66025i −0.449013 + 0.777714i
\(125\) −9.00000 −0.804984
\(126\) 3.00000 + 5.19615i 0.267261 + 0.462910i
\(127\) 4.00000 + 6.92820i 0.354943 + 0.614779i 0.987108 0.160055i \(-0.0511671\pi\)
−0.632166 + 0.774833i \(0.717834\pi\)
\(128\) 1.50000 + 2.59808i 0.132583 + 0.229640i
\(129\) 0 0
\(130\) 1.00000 1.73205i 0.0877058 0.151911i
\(131\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(132\) 0 0
\(133\) 6.00000 + 10.3923i 0.520266 + 0.901127i
\(134\) −10.0000 −0.863868
\(135\) 0 0
\(136\) 4.50000 + 7.79423i 0.385872 + 0.668350i
\(137\) −9.00000 −0.768922 −0.384461 0.923141i \(-0.625613\pi\)
−0.384461 + 0.923141i \(0.625613\pi\)
\(138\) 0 0
\(139\) −8.00000 13.8564i −0.678551 1.17529i −0.975417 0.220366i \(-0.929275\pi\)
0.296866 0.954919i \(-0.404058\pi\)
\(140\) −2.00000 −0.169031
\(141\) 0 0
\(142\) 6.00000 0.503509
\(143\) −2.00000 + 3.46410i −0.167248 + 0.289683i
\(144\) −1.50000 + 2.59808i −0.125000 + 0.216506i
\(145\) −4.50000 + 7.79423i −0.373705 + 0.647275i
\(146\) 5.00000 + 8.66025i 0.413803 + 0.716728i
\(147\) 0 0
\(148\) −0.500000 + 6.06218i −0.0410997 + 0.498308i
\(149\) −11.0000 −0.901155 −0.450578 0.892737i \(-0.648782\pi\)
−0.450578 + 0.892737i \(0.648782\pi\)
\(150\) 0 0
\(151\) −2.00000 + 3.46410i −0.162758 + 0.281905i −0.935857 0.352381i \(-0.885372\pi\)
0.773099 + 0.634285i \(0.218706\pi\)
\(152\) −9.00000 + 15.5885i −0.729996 + 1.26439i
\(153\) 4.50000 7.79423i 0.363803 0.630126i
\(154\) −4.00000 −0.322329
\(155\) 5.00000 8.66025i 0.401610 0.695608i
\(156\) 0 0
\(157\) −8.50000 14.7224i −0.678374 1.17498i −0.975470 0.220131i \(-0.929352\pi\)
0.297097 0.954847i \(-0.403982\pi\)
\(158\) 10.0000 0.795557
\(159\) 0 0
\(160\) −2.50000 4.33013i −0.197642 0.342327i
\(161\) 4.00000 6.92820i 0.315244 0.546019i
\(162\) 9.00000 0.707107
\(163\) 3.00000 + 5.19615i 0.234978 + 0.406994i 0.959266 0.282503i \(-0.0911648\pi\)
−0.724288 + 0.689497i \(0.757831\pi\)
\(164\) −4.50000 7.79423i −0.351391 0.608627i
\(165\) 0 0
\(166\) 6.00000 10.3923i 0.465690 0.806599i
\(167\) −6.00000 + 10.3923i −0.464294 + 0.804181i −0.999169 0.0407502i \(-0.987025\pi\)
0.534875 + 0.844931i \(0.320359\pi\)
\(168\) 0 0
\(169\) 4.50000 + 7.79423i 0.346154 + 0.599556i
\(170\) −1.50000 2.59808i −0.115045 0.199263i
\(171\) 18.0000 1.37649
\(172\) 1.00000 1.73205i 0.0762493 0.132068i
\(173\) −10.5000 18.1865i −0.798300 1.38270i −0.920722 0.390218i \(-0.872399\pi\)
0.122422 0.992478i \(-0.460934\pi\)
\(174\) 0 0
\(175\) −8.00000 −0.604743
\(176\) −1.00000 1.73205i −0.0753778 0.130558i
\(177\) 0 0
\(178\) −3.50000 + 6.06218i −0.262336 + 0.454379i
\(179\) 12.0000 0.896922 0.448461 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) −1.50000 + 2.59808i −0.111803 + 0.193649i
\(181\) −2.50000 + 4.33013i −0.185824 + 0.321856i −0.943854 0.330364i \(-0.892829\pi\)
0.758030 + 0.652219i \(0.226162\pi\)
\(182\) 2.00000 3.46410i 0.148250 0.256776i
\(183\) 0 0
\(184\) 12.0000 0.884652
\(185\) 0.500000 6.06218i 0.0367607 0.445700i
\(186\) 0 0
\(187\) 3.00000 + 5.19615i 0.219382 + 0.379980i
\(188\) 3.00000 5.19615i 0.218797 0.378968i
\(189\) 0 0
\(190\) 3.00000 5.19615i 0.217643 0.376969i
\(191\) −4.00000 −0.289430 −0.144715 0.989473i \(-0.546227\pi\)
−0.144715 + 0.989473i \(0.546227\pi\)
\(192\) 0 0
\(193\) 19.0000 1.36765 0.683825 0.729646i \(-0.260315\pi\)
0.683825 + 0.729646i \(0.260315\pi\)
\(194\) −3.50000 6.06218i −0.251285 0.435239i
\(195\) 0 0
\(196\) 3.00000 0.214286
\(197\) 7.50000 + 12.9904i 0.534353 + 0.925526i 0.999194 + 0.0401324i \(0.0127780\pi\)
−0.464841 + 0.885394i \(0.653889\pi\)
\(198\) −3.00000 + 5.19615i −0.213201 + 0.369274i
\(199\) −10.0000 −0.708881 −0.354441 0.935079i \(-0.615329\pi\)
−0.354441 + 0.935079i \(0.615329\pi\)
\(200\) −6.00000 10.3923i −0.424264 0.734847i
\(201\) 0 0
\(202\) 1.50000 + 2.59808i 0.105540 + 0.182800i
\(203\) −9.00000 + 15.5885i −0.631676 + 1.09410i
\(204\) 0 0
\(205\) 4.50000 + 7.79423i 0.314294 + 0.544373i
\(206\) −3.00000 5.19615i −0.209020 0.362033i
\(207\) −6.00000 10.3923i −0.417029 0.722315i
\(208\) 2.00000 0.138675
\(209\) −6.00000 + 10.3923i −0.415029 + 0.718851i
\(210\) 0 0
\(211\) 2.00000 0.137686 0.0688428 0.997628i \(-0.478069\pi\)
0.0688428 + 0.997628i \(0.478069\pi\)
\(212\) 2.00000 0.137361
\(213\) 0 0
\(214\) −18.0000 −1.23045
\(215\) −1.00000 + 1.73205i −0.0681994 + 0.118125i
\(216\) 0 0
\(217\) 10.0000 17.3205i 0.678844 1.17579i
\(218\) −2.50000 + 4.33013i −0.169321 + 0.293273i
\(219\) 0 0
\(220\) −1.00000 1.73205i −0.0674200 0.116775i
\(221\) −6.00000 −0.403604
\(222\) 0 0
\(223\) 28.0000 1.87502 0.937509 0.347960i \(-0.113126\pi\)
0.937509 + 0.347960i \(0.113126\pi\)
\(224\) −5.00000 8.66025i −0.334077 0.578638i
\(225\) −6.00000 + 10.3923i −0.400000 + 0.692820i
\(226\) −3.00000 + 5.19615i −0.199557 + 0.345643i
\(227\) −7.00000 + 12.1244i −0.464606 + 0.804722i −0.999184 0.0403978i \(-0.987137\pi\)
0.534577 + 0.845120i \(0.320471\pi\)
\(228\) 0 0
\(229\) −0.500000 + 0.866025i −0.0330409 + 0.0572286i −0.882073 0.471113i \(-0.843853\pi\)
0.849032 + 0.528341i \(0.177186\pi\)
\(230\) −4.00000 −0.263752
\(231\) 0 0
\(232\) −27.0000 −1.77264
\(233\) 3.00000 0.196537 0.0982683 0.995160i \(-0.468670\pi\)
0.0982683 + 0.995160i \(0.468670\pi\)
\(234\) −3.00000 5.19615i −0.196116 0.339683i
\(235\) −3.00000 + 5.19615i −0.195698 + 0.338960i
\(236\) 4.00000 0.260378
\(237\) 0 0
\(238\) −3.00000 5.19615i −0.194461 0.336817i
\(239\) −3.00000 5.19615i −0.194054 0.336111i 0.752536 0.658551i \(-0.228830\pi\)
−0.946590 + 0.322440i \(0.895497\pi\)
\(240\) 0 0
\(241\) −7.00000 + 12.1244i −0.450910 + 0.780998i −0.998443 0.0557856i \(-0.982234\pi\)
0.547533 + 0.836784i \(0.315567\pi\)
\(242\) 3.50000 + 6.06218i 0.224989 + 0.389692i
\(243\) 0 0
\(244\) 0.500000 + 0.866025i 0.0320092 + 0.0554416i
\(245\) −3.00000 −0.191663
\(246\) 0 0
\(247\) −6.00000 10.3923i −0.381771 0.661247i
\(248\) 30.0000 1.90500
\(249\) 0 0
\(250\) 4.50000 + 7.79423i 0.284605 + 0.492950i
\(251\) −14.0000 −0.883672 −0.441836 0.897096i \(-0.645673\pi\)
−0.441836 + 0.897096i \(0.645673\pi\)
\(252\) −3.00000 + 5.19615i −0.188982 + 0.327327i
\(253\) 8.00000 0.502956
\(254\) 4.00000 6.92820i 0.250982 0.434714i
\(255\) 0 0
\(256\) 8.50000 14.7224i 0.531250 0.920152i
\(257\) 10.5000 + 18.1865i 0.654972 + 1.13444i 0.981901 + 0.189396i \(0.0606529\pi\)
−0.326929 + 0.945049i \(0.606014\pi\)
\(258\) 0 0
\(259\) 1.00000 12.1244i 0.0621370 0.753371i
\(260\) 2.00000 0.124035
\(261\) 13.5000 + 23.3827i 0.835629 + 1.44735i
\(262\) 0 0
\(263\) −2.00000 + 3.46410i −0.123325 + 0.213606i −0.921077 0.389380i \(-0.872689\pi\)
0.797752 + 0.602986i \(0.206023\pi\)
\(264\) 0 0
\(265\) −2.00000 −0.122859
\(266\) 6.00000 10.3923i 0.367884 0.637193i
\(267\) 0 0
\(268\) −5.00000 8.66025i −0.305424 0.529009i
\(269\) 18.0000 1.09748 0.548740 0.835993i \(-0.315108\pi\)
0.548740 + 0.835993i \(0.315108\pi\)
\(270\) 0 0
\(271\) −7.00000 12.1244i −0.425220 0.736502i 0.571221 0.820796i \(-0.306470\pi\)
−0.996441 + 0.0842940i \(0.973137\pi\)
\(272\) 1.50000 2.59808i 0.0909509 0.157532i
\(273\) 0 0
\(274\) 4.50000 + 7.79423i 0.271855 + 0.470867i
\(275\) −4.00000 6.92820i −0.241209 0.417786i
\(276\) 0 0
\(277\) 1.50000 2.59808i 0.0901263 0.156103i −0.817438 0.576017i \(-0.804606\pi\)
0.907564 + 0.419914i \(0.137940\pi\)
\(278\) −8.00000 + 13.8564i −0.479808 + 0.831052i
\(279\) −15.0000 25.9808i −0.898027 1.55543i
\(280\) 3.00000 + 5.19615i 0.179284 + 0.310530i
\(281\) −13.5000 23.3827i −0.805342 1.39489i −0.916060 0.401042i \(-0.868648\pi\)
0.110717 0.993852i \(-0.464685\pi\)
\(282\) 0 0
\(283\) 7.00000 12.1244i 0.416107 0.720718i −0.579437 0.815017i \(-0.696728\pi\)
0.995544 + 0.0942988i \(0.0300609\pi\)
\(284\) 3.00000 + 5.19615i 0.178017 + 0.308335i
\(285\) 0 0
\(286\) 4.00000 0.236525
\(287\) 9.00000 + 15.5885i 0.531253 + 0.920158i
\(288\) −15.0000 −0.883883
\(289\) 4.00000 6.92820i 0.235294 0.407541i
\(290\) 9.00000 0.528498
\(291\) 0 0
\(292\) −5.00000 + 8.66025i −0.292603 + 0.506803i
\(293\) 11.5000 19.9186i 0.671837 1.16366i −0.305545 0.952177i \(-0.598839\pi\)
0.977383 0.211479i \(-0.0678279\pi\)
\(294\) 0 0
\(295\) −4.00000 −0.232889
\(296\) 16.5000 7.79423i 0.959043 0.453030i
\(297\) 0 0
\(298\) 5.50000 + 9.52628i 0.318606 + 0.551843i
\(299\) −4.00000 + 6.92820i −0.231326 + 0.400668i
\(300\) 0 0
\(301\) −2.00000 + 3.46410i −0.115278 + 0.199667i
\(302\) 4.00000 0.230174
\(303\) 0 0
\(304\) 6.00000 0.344124
\(305\) −0.500000 0.866025i −0.0286299 0.0495885i
\(306\) −9.00000 −0.514496
\(307\) −14.0000 −0.799022 −0.399511 0.916728i \(-0.630820\pi\)
−0.399511 + 0.916728i \(0.630820\pi\)
\(308\) −2.00000 3.46410i −0.113961 0.197386i
\(309\) 0 0
\(310\) −10.0000 −0.567962
\(311\) 9.00000 + 15.5885i 0.510343 + 0.883940i 0.999928 + 0.0119847i \(0.00381495\pi\)
−0.489585 + 0.871956i \(0.662852\pi\)
\(312\) 0 0
\(313\) −3.50000 6.06218i −0.197832 0.342655i 0.749993 0.661445i \(-0.230057\pi\)
−0.947825 + 0.318791i \(0.896723\pi\)
\(314\) −8.50000 + 14.7224i −0.479683 + 0.830835i
\(315\) 3.00000 5.19615i 0.169031 0.292770i
\(316\) 5.00000 + 8.66025i 0.281272 + 0.487177i
\(317\) −0.500000 0.866025i −0.0280828 0.0486408i 0.851642 0.524123i \(-0.175607\pi\)
−0.879725 + 0.475482i \(0.842274\pi\)
\(318\) 0 0
\(319\) −18.0000 −1.00781
\(320\) −3.50000 + 6.06218i −0.195656 + 0.338886i
\(321\) 0 0
\(322\) −8.00000 −0.445823
\(323\) −18.0000 −1.00155
\(324\) 4.50000 + 7.79423i 0.250000 + 0.433013i
\(325\) 8.00000 0.443760
\(326\) 3.00000 5.19615i 0.166155 0.287788i
\(327\) 0 0
\(328\) −13.5000 + 23.3827i −0.745413 + 1.29109i
\(329\) −6.00000 + 10.3923i −0.330791 + 0.572946i
\(330\) 0 0
\(331\) 10.0000 + 17.3205i 0.549650 + 0.952021i 0.998298 + 0.0583130i \(0.0185721\pi\)
−0.448649 + 0.893708i \(0.648095\pi\)
\(332\) 12.0000 0.658586
\(333\) −15.0000 10.3923i −0.821995 0.569495i
\(334\) 12.0000 0.656611
\(335\) 5.00000 + 8.66025i 0.273179 + 0.473160i
\(336\) 0 0
\(337\) 0.500000 0.866025i 0.0272367 0.0471754i −0.852086 0.523402i \(-0.824663\pi\)
0.879322 + 0.476227i \(0.157996\pi\)
\(338\) 4.50000 7.79423i 0.244768 0.423950i
\(339\) 0 0
\(340\) 1.50000 2.59808i 0.0813489 0.140900i
\(341\) 20.0000 1.08306
\(342\) −9.00000 15.5885i −0.486664 0.842927i
\(343\) −20.0000 −1.07990
\(344\) −6.00000 −0.323498
\(345\) 0 0
\(346\) −10.5000 + 18.1865i −0.564483 + 0.977714i
\(347\) −16.0000 −0.858925 −0.429463 0.903085i \(-0.641297\pi\)
−0.429463 + 0.903085i \(0.641297\pi\)
\(348\) 0 0
\(349\) −4.50000 7.79423i −0.240879 0.417215i 0.720086 0.693885i \(-0.244103\pi\)
−0.960965 + 0.276670i \(0.910769\pi\)
\(350\) 4.00000 + 6.92820i 0.213809 + 0.370328i
\(351\) 0 0
\(352\) 5.00000 8.66025i 0.266501 0.461593i
\(353\) 12.5000 + 21.6506i 0.665308 + 1.15235i 0.979202 + 0.202889i \(0.0650330\pi\)
−0.313894 + 0.949458i \(0.601634\pi\)
\(354\) 0 0
\(355\) −3.00000 5.19615i −0.159223 0.275783i
\(356\) −7.00000 −0.370999
\(357\) 0 0
\(358\) −6.00000 10.3923i −0.317110 0.549250i
\(359\) 24.0000 1.26667 0.633336 0.773877i \(-0.281685\pi\)
0.633336 + 0.773877i \(0.281685\pi\)
\(360\) 9.00000 0.474342
\(361\) −8.50000 14.7224i −0.447368 0.774865i
\(362\) 5.00000 0.262794
\(363\) 0 0
\(364\) 4.00000 0.209657
\(365\) 5.00000 8.66025i 0.261712 0.453298i
\(366\) 0 0
\(367\) 14.0000 24.2487i 0.730794 1.26577i −0.225750 0.974185i \(-0.572483\pi\)
0.956544 0.291587i \(-0.0941834\pi\)
\(368\) −2.00000 3.46410i −0.104257 0.180579i
\(369\) 27.0000 1.40556
\(370\) −5.50000 + 2.59808i −0.285931 + 0.135068i
\(371\) −4.00000 −0.207670
\(372\) 0 0
\(373\) −8.50000 + 14.7224i −0.440113 + 0.762299i −0.997697 0.0678218i \(-0.978395\pi\)
0.557584 + 0.830120i \(0.311728\pi\)
\(374\) 3.00000 5.19615i 0.155126 0.268687i
\(375\) 0 0
\(376\) −18.0000 −0.928279
\(377\) 9.00000 15.5885i 0.463524 0.802846i
\(378\) 0 0
\(379\) −3.00000 5.19615i −0.154100 0.266908i 0.778631 0.627482i \(-0.215914\pi\)
−0.932731 + 0.360573i \(0.882581\pi\)
\(380\) 6.00000 0.307794
\(381\) 0 0
\(382\) 2.00000 + 3.46410i 0.102329 + 0.177239i
\(383\) 17.0000 29.4449i 0.868659 1.50456i 0.00529229 0.999986i \(-0.498315\pi\)
0.863367 0.504576i \(-0.168351\pi\)
\(384\) 0 0
\(385\) 2.00000 + 3.46410i 0.101929 + 0.176547i
\(386\) −9.50000 16.4545i −0.483537 0.837511i
\(387\) 3.00000 + 5.19615i 0.152499 + 0.264135i
\(388\) 3.50000 6.06218i 0.177686 0.307760i
\(389\) −12.5000 + 21.6506i −0.633775 + 1.09773i 0.352998 + 0.935624i \(0.385162\pi\)
−0.986773 + 0.162107i \(0.948171\pi\)
\(390\) 0 0
\(391\) 6.00000 + 10.3923i 0.303433 + 0.525561i
\(392\) −4.50000 7.79423i −0.227284 0.393668i
\(393\) 0 0
\(394\) 7.50000 12.9904i 0.377845 0.654446i
\(395\) −5.00000 8.66025i −0.251577 0.435745i
\(396\) −6.00000 −0.301511
\(397\) 13.0000 0.652451 0.326226 0.945292i \(-0.394223\pi\)
0.326226 + 0.945292i \(0.394223\pi\)
\(398\) 5.00000 + 8.66025i 0.250627 + 0.434099i
\(399\) 0 0
\(400\) −2.00000 + 3.46410i −0.100000 + 0.173205i
\(401\) −18.0000 −0.898877 −0.449439 0.893311i \(-0.648376\pi\)
−0.449439 + 0.893311i \(0.648376\pi\)
\(402\) 0 0
\(403\) −10.0000 + 17.3205i −0.498135 + 0.862796i
\(404\) −1.50000 + 2.59808i −0.0746278 + 0.129259i
\(405\) −4.50000 7.79423i −0.223607 0.387298i
\(406\) 18.0000 0.893325
\(407\) 11.0000 5.19615i 0.545250 0.257564i
\(408\) 0 0
\(409\) 12.5000 + 21.6506i 0.618085 + 1.07056i 0.989835 + 0.142222i \(0.0454247\pi\)
−0.371750 + 0.928333i \(0.621242\pi\)
\(410\) 4.50000 7.79423i 0.222239 0.384930i
\(411\) 0 0
\(412\) 3.00000 5.19615i 0.147799 0.255996i
\(413\) −8.00000 −0.393654
\(414\) −6.00000 + 10.3923i −0.294884 + 0.510754i
\(415\) −12.0000 −0.589057
\(416\) 5.00000 + 8.66025i 0.245145 + 0.424604i
\(417\) 0 0
\(418\) 12.0000 0.586939
\(419\) 13.0000 + 22.5167i 0.635092 + 1.10001i 0.986496 + 0.163787i \(0.0523710\pi\)
−0.351404 + 0.936224i \(0.614296\pi\)
\(420\) 0 0
\(421\) 9.00000 0.438633 0.219317 0.975654i \(-0.429617\pi\)
0.219317 + 0.975654i \(0.429617\pi\)
\(422\) −1.00000 1.73205i −0.0486792 0.0843149i
\(423\) 9.00000 + 15.5885i 0.437595 + 0.757937i
\(424\) −3.00000 5.19615i −0.145693 0.252347i
\(425\) 6.00000 10.3923i 0.291043 0.504101i
\(426\) 0 0
\(427\) −1.00000 1.73205i −0.0483934 0.0838198i
\(428\) −9.00000 15.5885i −0.435031 0.753497i
\(429\) 0 0
\(430\) 2.00000 0.0964486
\(431\) −9.00000 + 15.5885i −0.433515 + 0.750870i −0.997173 0.0751385i \(-0.976060\pi\)
0.563658 + 0.826008i \(0.309393\pi\)
\(432\) 0 0
\(433\) −21.0000 −1.00920 −0.504598 0.863355i \(-0.668359\pi\)
−0.504598 + 0.863355i \(0.668359\pi\)
\(434\) −20.0000 −0.960031
\(435\) 0 0
\(436\) −5.00000 −0.239457
\(437\) −12.0000 + 20.7846i −0.574038 + 0.994263i
\(438\) 0 0
\(439\) 10.0000 17.3205i 0.477274 0.826663i −0.522387 0.852709i \(-0.674958\pi\)
0.999661 + 0.0260459i \(0.00829161\pi\)
\(440\) −3.00000 + 5.19615i −0.143019 + 0.247717i
\(441\) −4.50000 + 7.79423i −0.214286 + 0.371154i
\(442\) 3.00000 + 5.19615i 0.142695 + 0.247156i
\(443\) −32.0000 −1.52037 −0.760183 0.649709i \(-0.774891\pi\)
−0.760183 + 0.649709i \(0.774891\pi\)
\(444\) 0 0
\(445\) 7.00000 0.331832
\(446\) −14.0000 24.2487i −0.662919 1.14821i
\(447\) 0 0
\(448\) −7.00000 + 12.1244i −0.330719 + 0.572822i
\(449\) −3.00000 + 5.19615i −0.141579 + 0.245222i −0.928091 0.372353i \(-0.878551\pi\)
0.786513 + 0.617574i \(0.211885\pi\)
\(450\) 12.0000 0.565685
\(451\) −9.00000 + 15.5885i −0.423793 + 0.734032i
\(452\) −6.00000 −0.282216
\(453\) 0 0
\(454\) 14.0000 0.657053
\(455\) −4.00000 −0.187523
\(456\) 0 0
\(457\) −1.50000 + 2.59808i −0.0701670 + 0.121533i −0.898974 0.438001i \(-0.855687\pi\)
0.828807 + 0.559534i \(0.189020\pi\)
\(458\) 1.00000 0.0467269
\(459\) 0 0
\(460\) −2.00000 3.46410i −0.0932505 0.161515i
\(461\) −15.0000 25.9808i −0.698620 1.21004i −0.968945 0.247276i \(-0.920465\pi\)
0.270326 0.962769i \(-0.412869\pi\)
\(462\) 0 0
\(463\) 11.0000 19.0526i 0.511213 0.885448i −0.488702 0.872451i \(-0.662530\pi\)
0.999916 0.0129968i \(-0.00413714\pi\)
\(464\) 4.50000 + 7.79423i 0.208907 + 0.361838i
\(465\) 0 0
\(466\) −1.50000 2.59808i −0.0694862 0.120354i
\(467\) −8.00000 −0.370196 −0.185098 0.982720i \(-0.559260\pi\)
−0.185098 + 0.982720i \(0.559260\pi\)
\(468\) 3.00000 5.19615i 0.138675 0.240192i
\(469\) 10.0000 + 17.3205i 0.461757 + 0.799787i
\(470\) 6.00000 0.276759
\(471\) 0 0
\(472\) −6.00000 10.3923i −0.276172 0.478345i
\(473\) −4.00000 −0.183920
\(474\) 0 0
\(475\) 24.0000 1.10120
\(476\) 3.00000 5.19615i 0.137505 0.238165i
\(477\) −3.00000 + 5.19615i −0.137361 + 0.237915i
\(478\) −3.00000 + 5.19615i −0.137217 + 0.237666i
\(479\) 2.00000 + 3.46410i 0.0913823 + 0.158279i 0.908093 0.418769i \(-0.137538\pi\)
−0.816711 + 0.577047i \(0.804205\pi\)
\(480\) 0 0
\(481\) −1.00000 + 12.1244i −0.0455961 + 0.552823i
\(482\) 14.0000 0.637683
\(483\) 0 0
\(484\) −3.50000 + 6.06218i −0.159091 + 0.275554i
\(485\) −3.50000 + 6.06218i −0.158927 + 0.275269i
\(486\) 0 0
\(487\) 12.0000 0.543772 0.271886 0.962329i \(-0.412353\pi\)
0.271886 + 0.962329i \(0.412353\pi\)
\(488\) 1.50000 2.59808i 0.0679018 0.117609i
\(489\) 0 0
\(490\) 1.50000 + 2.59808i 0.0677631 + 0.117369i
\(491\) 2.00000 0.0902587 0.0451294 0.998981i \(-0.485630\pi\)
0.0451294 + 0.998981i \(0.485630\pi\)
\(492\) 0 0
\(493\) −13.5000 23.3827i −0.608009 1.05310i
\(494\) −6.00000 + 10.3923i −0.269953 + 0.467572i
\(495\) 6.00000 0.269680
\(496\) −5.00000 8.66025i −0.224507 0.388857i
\(497\) −6.00000 10.3923i −0.269137 0.466159i
\(498\) 0 0
\(499\) 9.00000 15.5885i 0.402895 0.697835i −0.591179 0.806541i \(-0.701337\pi\)
0.994074 + 0.108705i \(0.0346705\pi\)
\(500\) −4.50000 + 7.79423i −0.201246 + 0.348569i
\(501\) 0 0
\(502\) 7.00000 + 12.1244i 0.312425 + 0.541136i
\(503\) 13.0000 + 22.5167i 0.579641 + 1.00397i 0.995520 + 0.0945483i \(0.0301407\pi\)
−0.415879 + 0.909420i \(0.636526\pi\)
\(504\) 18.0000 0.801784
\(505\) 1.50000 2.59808i 0.0667491 0.115613i
\(506\) −4.00000 6.92820i −0.177822 0.307996i
\(507\) 0 0
\(508\) 8.00000 0.354943
\(509\) 3.50000 + 6.06218i 0.155135 + 0.268701i 0.933108 0.359596i \(-0.117085\pi\)
−0.777973 + 0.628297i \(0.783752\pi\)
\(510\) 0 0
\(511\) 10.0000 17.3205i 0.442374 0.766214i
\(512\) −11.0000 −0.486136
\(513\) 0 0
\(514\) 10.5000 18.1865i 0.463135 0.802174i
\(515\) −3.00000 + 5.19615i −0.132196 + 0.228970i
\(516\) 0 0
\(517\) −12.0000 −0.527759
\(518\) −11.0000 + 5.19615i −0.483312 + 0.228306i
\(519\) 0 0
\(520\) −3.00000 5.19615i −0.131559 0.227866i
\(521\) 21.0000 36.3731i 0.920027 1.59353i 0.120656 0.992694i \(-0.461500\pi\)
0.799370 0.600839i \(-0.205167\pi\)
\(522\) 13.5000 23.3827i 0.590879 1.02343i
\(523\) −4.00000 + 6.92820i −0.174908 + 0.302949i −0.940129 0.340818i \(-0.889296\pi\)
0.765222 + 0.643767i \(0.222629\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 4.00000 0.174408
\(527\) 15.0000 + 25.9808i 0.653410 + 1.13174i
\(528\) 0 0
\(529\) −7.00000 −0.304348
\(530\) 1.00000 + 1.73205i 0.0434372 + 0.0752355i
\(531\) −6.00000 + 10.3923i −0.260378 + 0.450988i
\(532\) 12.0000 0.520266
\(533\) −9.00000 15.5885i −0.389833 0.675211i
\(534\) 0 0
\(535\) 9.00000 + 15.5885i 0.389104 + 0.673948i
\(536\) −15.0000 + 25.9808i −0.647901 + 1.12220i
\(537\) 0 0
\(538\) −9.00000 15.5885i −0.388018 0.672066i
\(539\) −3.00000 5.19615i −0.129219 0.223814i
\(540\) 0 0
\(541\) 17.0000 0.730887 0.365444 0.930834i \(-0.380917\pi\)
0.365444 + 0.930834i \(0.380917\pi\)
\(542\) −7.00000 + 12.1244i −0.300676 + 0.520786i
\(543\) 0 0
\(544\) 15.0000 0.643120
\(545\) 5.00000 0.214176
\(546\) 0 0
\(547\) 2.00000 0.0855138 0.0427569 0.999086i \(-0.486386\pi\)
0.0427569 + 0.999086i \(0.486386\pi\)
\(548\) −4.50000 + 7.79423i −0.192230 + 0.332953i
\(549\) −3.00000 −0.128037
\(550\) −4.00000 + 6.92820i −0.170561 + 0.295420i
\(551\) 27.0000 46.7654i 1.15024 1.99227i
\(552\) 0 0
\(553\) −10.0000 17.3205i −0.425243 0.736543i
\(554\) −3.00000 −0.127458
\(555\) 0 0
\(556\) −16.0000 −0.678551
\(557\) −16.5000 28.5788i −0.699127 1.21092i −0.968769 0.247964i \(-0.920239\pi\)
0.269642 0.962961i \(-0.413095\pi\)
\(558\) −15.0000 + 25.9808i −0.635001 + 1.09985i
\(559\) 2.00000 3.46410i 0.0845910 0.146516i
\(560\) 1.00000 1.73205i 0.0422577 0.0731925i
\(561\) 0 0
\(562\) −13.5000 + 23.3827i −0.569463 + 0.986339i
\(563\) −24.0000 −1.01148 −0.505740 0.862686i \(-0.668780\pi\)
−0.505740 + 0.862686i \(0.668780\pi\)
\(564\) 0 0
\(565\) 6.00000 0.252422
\(566\) −14.0000 −0.588464
\(567\) −9.00000 15.5885i −0.377964 0.654654i
\(568\) 9.00000 15.5885i 0.377632 0.654077i
\(569\) 3.00000 0.125767 0.0628833 0.998021i \(-0.479970\pi\)
0.0628833 + 0.998021i \(0.479970\pi\)
\(570\) 0 0
\(571\) 22.0000 + 38.1051i 0.920671 + 1.59465i 0.798379 + 0.602155i \(0.205691\pi\)
0.122292 + 0.992494i \(0.460975\pi\)
\(572\) 2.00000 + 3.46410i 0.0836242 + 0.144841i
\(573\) 0 0
\(574\) 9.00000 15.5885i 0.375653 0.650650i
\(575\) −8.00000 13.8564i −0.333623 0.577852i
\(576\) 10.5000 + 18.1865i 0.437500 + 0.757772i
\(577\) 9.00000 + 15.5885i 0.374675 + 0.648956i 0.990278 0.139100i \(-0.0444210\pi\)
−0.615603 + 0.788056i \(0.711088\pi\)
\(578\) −8.00000 −0.332756
\(579\) 0 0
\(580\) 4.50000 + 7.79423i 0.186852 + 0.323638i
\(581\) −24.0000 −0.995688
\(582\) 0 0
\(583\) −2.00000 3.46410i −0.0828315 0.143468i
\(584\) 30.0000 1.24141
\(585\) −3.00000 + 5.19615i −0.124035 + 0.214834i
\(586\) −23.0000 −0.950121
\(587\) −20.0000 + 34.6410i −0.825488 + 1.42979i 0.0760572 + 0.997103i \(0.475767\pi\)
−0.901546 + 0.432684i \(0.857566\pi\)
\(588\) 0 0
\(589\) −30.0000 + 51.9615i −1.23613 + 2.14104i
\(590\) 2.00000 + 3.46410i 0.0823387 + 0.142615i
\(591\) 0 0
\(592\) −5.00000 3.46410i −0.205499 0.142374i
\(593\) −29.0000 −1.19089 −0.595444 0.803397i \(-0.703024\pi\)
−0.595444 + 0.803397i \(0.703024\pi\)
\(594\) 0 0
\(595\) −3.00000 + 5.19615i −0.122988 + 0.213021i
\(596\) −5.50000 + 9.52628i −0.225289 + 0.390212i
\(597\) 0 0
\(598\) 8.00000 0.327144
\(599\) 19.0000 32.9090i 0.776319 1.34462i −0.157731 0.987482i \(-0.550418\pi\)
0.934050 0.357142i \(-0.116249\pi\)
\(600\) 0 0
\(601\) −11.5000 19.9186i −0.469095 0.812496i 0.530281 0.847822i \(-0.322086\pi\)
−0.999376 + 0.0353259i \(0.988753\pi\)
\(602\) 4.00000 0.163028
\(603\) 30.0000 1.22169
\(604\) 2.00000 + 3.46410i 0.0813788 + 0.140952i
\(605\) 3.50000 6.06218i 0.142295 0.246463i
\(606\) 0 0
\(607\) 7.00000 + 12.1244i 0.284121 + 0.492112i 0.972396 0.233338i \(-0.0749648\pi\)
−0.688274 + 0.725450i \(0.741632\pi\)
\(608\) 15.0000 + 25.9808i 0.608330 + 1.05366i
\(609\) 0 0
\(610\) −0.500000 + 0.866025i −0.0202444 + 0.0350643i
\(611\) 6.00000 10.3923i 0.242734 0.420428i
\(612\) −4.50000 7.79423i −0.181902 0.315063i
\(613\) −16.5000 28.5788i −0.666429 1.15429i −0.978896 0.204360i \(-0.934489\pi\)
0.312467 0.949929i \(-0.398845\pi\)
\(614\) 7.00000 + 12.1244i 0.282497 + 0.489299i
\(615\) 0 0
\(616\) −6.00000 + 10.3923i −0.241747 + 0.418718i
\(617\) 11.0000 + 19.0526i 0.442843 + 0.767027i 0.997899 0.0647859i \(-0.0206365\pi\)
−0.555056 + 0.831813i \(0.687303\pi\)
\(618\) 0 0
\(619\) −10.0000 −0.401934 −0.200967 0.979598i \(-0.564408\pi\)
−0.200967 + 0.979598i \(0.564408\pi\)
\(620\) −5.00000 8.66025i −0.200805 0.347804i
\(621\) 0 0
\(622\) 9.00000 15.5885i 0.360867 0.625040i
\(623\) 14.0000 0.560898
\(624\) 0 0
\(625\) −5.50000 + 9.52628i −0.220000 + 0.381051i
\(626\) −3.50000 + 6.06218i −0.139888 + 0.242293i
\(627\) 0 0
\(628\) −17.0000 −0.678374
\(629\) 15.0000 + 10.3923i 0.598089 + 0.414368i
\(630\) −6.00000 −0.239046
\(631\) −10.0000 17.3205i −0.398094 0.689519i 0.595397 0.803432i \(-0.296995\pi\)
−0.993491 + 0.113913i \(0.963661\pi\)
\(632\) 15.0000 25.9808i 0.596668 1.03346i
\(633\) 0 0
\(634\) −0.500000 + 0.866025i −0.0198575 + 0.0343943i
\(635\) −8.00000 −0.317470
\(636\) 0 0
\(637\) 6.00000 0.237729
\(638\) 9.00000 + 15.5885i 0.356313 + 0.617153i
\(639\) −18.0000 −0.712069
\(640\) −3.00000 −0.118585
\(641\) 18.5000 + 32.0429i 0.730706 + 1.26562i 0.956582 + 0.291464i \(0.0941423\pi\)
−0.225876 + 0.974156i \(0.572524\pi\)
\(642\) 0 0
\(643\) 14.0000 0.552106 0.276053 0.961142i \(-0.410973\pi\)
0.276053 + 0.961142i \(0.410973\pi\)
\(644\) −4.00000 6.92820i −0.157622 0.273009i
\(645\) 0 0
\(646\) 9.00000 + 15.5885i 0.354100 + 0.613320i
\(647\) 7.00000 12.1244i 0.275198 0.476658i −0.694987 0.719023i \(-0.744590\pi\)
0.970185 + 0.242365i \(0.0779231\pi\)
\(648\) 13.5000 23.3827i 0.530330 0.918559i
\(649\) −4.00000 6.92820i −0.157014 0.271956i
\(650\) −4.00000 6.92820i −0.156893 0.271746i
\(651\) 0 0
\(652\) 6.00000 0.234978
\(653\) 19.5000 33.7750i 0.763094 1.32172i −0.178154 0.984003i \(-0.557013\pi\)
0.941248 0.337715i \(-0.109654\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 9.00000 0.351391
\(657\) −15.0000 25.9808i −0.585206 1.01361i
\(658\) 12.0000 0.467809
\(659\) 18.0000 31.1769i 0.701180 1.21448i −0.266872 0.963732i \(-0.585990\pi\)
0.968052 0.250748i \(-0.0806766\pi\)
\(660\) 0 0
\(661\) 3.50000 6.06218i 0.136134 0.235791i −0.789896 0.613241i \(-0.789865\pi\)
0.926030 + 0.377450i \(0.123199\pi\)
\(662\) 10.0000 17.3205i 0.388661 0.673181i
\(663\) 0 0
\(664\) −18.0000 31.1769i −0.698535 1.20990i
\(665\) −12.0000 −0.465340
\(666\) −1.50000 + 18.1865i −0.0581238 + 0.704714i
\(667\) −36.0000 −1.39393
\(668\) 6.00000 + 10.3923i 0.232147 + 0.402090i
\(669\) 0 0
\(670\) 5.00000 8.66025i 0.193167 0.334575i
\(671\) 1.00000 1.73205i 0.0386046 0.0668651i
\(672\) 0 0
\(673\) −3.00000 + 5.19615i −0.115642 + 0.200297i −0.918036 0.396497i \(-0.870226\pi\)
0.802395 + 0.596794i \(0.203559\pi\)
\(674\) −1.00000 −0.0385186
\(675\) 0 0
\(676\) 9.00000 0.346154
\(677\) 13.0000 0.499631 0.249815 0.968294i \(-0.419630\pi\)
0.249815 + 0.968294i \(0.419630\pi\)
\(678\) 0 0
\(679\) −7.00000 + 12.1244i −0.268635 + 0.465290i
\(680\) −9.00000 −0.345134
\(681\) 0 0
\(682\) −10.0000 17.3205i −0.382920 0.663237i
\(683\) 15.0000 + 25.9808i 0.573959 + 0.994126i 0.996154 + 0.0876211i \(0.0279265\pi\)
−0.422195 + 0.906505i \(0.638740\pi\)
\(684\) 9.00000 15.5885i 0.344124 0.596040i
\(685\) 4.50000 7.79423i 0.171936 0.297802i
\(686\) 10.0000 + 17.3205i 0.381802 + 0.661300i
\(687\) 0 0
\(688\) 1.00000 + 1.73205i 0.0381246 + 0.0660338i
\(689\) 4.00000 0.152388
\(690\) 0 0
\(691\) 7.00000 + 12.1244i 0.266293 + 0.461232i 0.967901 0.251330i \(-0.0808679\pi\)
−0.701609 + 0.712562i \(0.747535\pi\)
\(692\) −21.0000 −0.798300
\(693\) 12.0000 0.455842
\(694\) 8.00000 + 13.8564i 0.303676 + 0.525982i
\(695\) 16.0000 0.606915
\(696\) 0 0
\(697\) −27.0000 −1.02270
\(698\) −4.50000 + 7.79423i −0.170328 + 0.295016i
\(699\) 0 0
\(700\) −4.00000 + 6.92820i −0.151186 + 0.261861i
\(701\) −3.00000 5.19615i −0.113308 0.196256i 0.803794 0.594908i \(-0.202811\pi\)
−0.917102 + 0.398652i \(0.869478\pi\)
\(702\) 0 0
\(703\) −3.00000 + 36.3731i −0.113147 + 1.37184i
\(704\) −14.0000 −0.527645
\(705\) 0 0
\(706\) 12.5000 21.6506i 0.470444 0.814832i
\(707\) 3.00000 5.19615i 0.112827 0.195421i
\(708\) 0 0
\(709\) 10.0000 0.375558 0.187779 0.982211i \(-0.439871\pi\)
0.187779 + 0.982211i \(0.439871\pi\)
\(710\) −3.00000 + 5.19615i −0.112588 + 0.195008i
\(711\) −30.0000 −1.12509
\(712\) 10.5000 + 18.1865i 0.393504 + 0.681569i
\(713\) 40.0000 1.49801
\(714\) 0 0
\(715\) −2.00000 3.46410i −0.0747958 0.129550i
\(716\) 6.00000 10.3923i 0.224231 0.388379i
\(717\) 0 0
\(718\) −12.0000 20.7846i −0.447836 0.775675i
\(719\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(720\) −1.50000 2.59808i −0.0559017 0.0968246i
\(721\) −6.00000 + 10.3923i −0.223452 + 0.387030i
\(722\) −8.50000 + 14.7224i −0.316337 + 0.547912i
\(723\) 0 0
\(724\) 2.50000 + 4.33013i 0.0929118 + 0.160928i
\(725\) 18.0000 + 31.1769i 0.668503 + 1.15788i
\(726\) 0 0
\(727\) −20.0000 + 34.6410i −0.741759 + 1.28476i 0.209935 + 0.977715i \(0.432675\pi\)
−0.951694 + 0.307049i \(0.900659\pi\)
\(728\) −6.00000 10.3923i −0.222375 0.385164i
\(729\) −27.0000 −1.00000
\(730\) −10.0000 −0.370117
\(731\) −3.00000 5.19615i −0.110959 0.192187i
\(732\) 0 0
\(733\) −11.0000 + 19.0526i −0.406294 + 0.703722i −0.994471 0.105010i \(-0.966513\pi\)
0.588177 + 0.808732i \(0.299846\pi\)
\(734\) −28.0000 −1.03350
\(735\) 0 0
\(736\) 10.0000 17.3205i 0.368605 0.638442i
\(737\) −10.0000 + 17.3205i −0.368355 + 0.638009i
\(738\) −13.5000 23.3827i −0.496942 0.860729i
\(739\) 12.0000 0.441427 0.220714 0.975339i \(-0.429161\pi\)
0.220714 + 0.975339i \(0.429161\pi\)
\(740\) −5.00000 3.46410i −0.183804 0.127343i
\(741\) 0 0
\(742\) 2.00000 + 3.46410i 0.0734223 + 0.127171i
\(743\) −3.00000 + 5.19615i −0.110059 + 0.190628i −0.915794 0.401648i \(-0.868437\pi\)
0.805735 + 0.592277i \(0.201771\pi\)
\(744\) 0 0
\(745\) 5.50000 9.52628i 0.201504 0.349016i
\(746\) 17.0000 0.622414
\(747\) −18.0000 + 31.1769i −0.658586 + 1.14070i
\(748\) 6.00000 0.219382
\(749\) 18.0000 + 31.1769i 0.657706 + 1.13918i
\(750\) 0 0
\(751\) 10.0000 0.364905 0.182453 0.983215i \(-0.441596\pi\)
0.182453 + 0.983215i \(0.441596\pi\)
\(752\) 3.00000 + 5.19615i 0.109399 + 0.189484i
\(753\) 0 0
\(754\) −18.0000 −0.655521
\(755\) −2.00000 3.46410i −0.0727875 0.126072i
\(756\) 0 0
\(757\) −6.50000 11.2583i −0.236247 0.409191i 0.723388 0.690442i \(-0.242584\pi\)
−0.959634 + 0.281251i \(0.909251\pi\)
\(758\) −3.00000 + 5.19615i −0.108965 + 0.188733i
\(759\) 0 0
\(760\) −9.00000 15.5885i −0.326464 0.565453i
\(761\) −3.50000 6.06218i −0.126875 0.219754i 0.795589 0.605836i \(-0.207161\pi\)
−0.922464 + 0.386082i \(0.873828\pi\)
\(762\) 0 0
\(763\) 10.0000 0.362024
\(764\) −2.00000 + 3.46410i −0.0723575 + 0.125327i
\(765\) 4.50000 + 7.79423i 0.162698 + 0.281801i
\(766\) −34.0000 −1.22847
\(767\) 8.00000 0.288863
\(768\) 0 0
\(769\) 14.0000 0.504853 0.252426 0.967616i \(-0.418771\pi\)
0.252426 + 0.967616i \(0.418771\pi\)
\(770\) 2.00000 3.46410i 0.0720750 0.124838i
\(771\) 0 0
\(772\) 9.50000 16.4545i 0.341912 0.592210i
\(773\) −10.5000 + 18.1865i −0.377659 + 0.654124i −0.990721 0.135910i \(-0.956604\pi\)
0.613062 + 0.790034i \(0.289937\pi\)
\(774\) 3.00000 5.19615i 0.107833 0.186772i
\(775\) −20.0000 34.6410i −0.718421 1.24434i
\(776\) −21.0000 −0.753856
\(777\) 0 0
\(778\) 25.0000 0.896293
\(779\) −27.0000 46.7654i −0.967375 1.67554i
\(780\) 0 0
\(781\) 6.00000 10.3923i 0.214697 0.371866i
\(782\) 6.00000 10.3923i 0.214560 0.371628i
\(783\) 0 0
\(784\) −1.50000 + 2.59808i −0.0535714 + 0.0927884i
\(785\) 17.0000 0.606756
\(786\) 0 0
\(787\) 4.00000 0.142585