Properties

Label 65.2.d.b.64.2
Level 65
Weight 2
Character 65.64
Analytic conductor 0.519
Analytic rank 0
Dimension 2
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 65 = 5 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 65.d (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(0.519027613138\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 64.2
Root \(1.00000i\)
Character \(\chi\) = 65.64
Dual form 65.2.d.b.64.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +2.00000i q^{3} -1.00000 q^{4} +(1.00000 - 2.00000i) q^{5} +2.00000i q^{6} -3.00000 q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +2.00000i q^{3} -1.00000 q^{4} +(1.00000 - 2.00000i) q^{5} +2.00000i q^{6} -3.00000 q^{8} -1.00000 q^{9} +(1.00000 - 2.00000i) q^{10} -2.00000i q^{11} -2.00000i q^{12} +(-3.00000 - 2.00000i) q^{13} +(4.00000 + 2.00000i) q^{15} -1.00000 q^{16} -1.00000 q^{18} +6.00000i q^{19} +(-1.00000 + 2.00000i) q^{20} -2.00000i q^{22} +6.00000i q^{23} -6.00000i q^{24} +(-3.00000 - 4.00000i) q^{25} +(-3.00000 - 2.00000i) q^{26} +4.00000i q^{27} +6.00000 q^{29} +(4.00000 + 2.00000i) q^{30} -6.00000i q^{31} +5.00000 q^{32} +4.00000 q^{33} +1.00000 q^{36} -6.00000 q^{37} +6.00000i q^{38} +(4.00000 - 6.00000i) q^{39} +(-3.00000 + 6.00000i) q^{40} +8.00000i q^{41} -6.00000i q^{43} +2.00000i q^{44} +(-1.00000 + 2.00000i) q^{45} +6.00000i q^{46} +8.00000 q^{47} -2.00000i q^{48} -7.00000 q^{49} +(-3.00000 - 4.00000i) q^{50} +(3.00000 + 2.00000i) q^{52} -12.0000i q^{53} +4.00000i q^{54} +(-4.00000 - 2.00000i) q^{55} -12.0000 q^{57} +6.00000 q^{58} -2.00000i q^{59} +(-4.00000 - 2.00000i) q^{60} +6.00000 q^{61} -6.00000i q^{62} +7.00000 q^{64} +(-7.00000 + 4.00000i) q^{65} +4.00000 q^{66} -12.0000 q^{67} -12.0000 q^{69} +2.00000i q^{71} +3.00000 q^{72} +6.00000 q^{73} -6.00000 q^{74} +(8.00000 - 6.00000i) q^{75} -6.00000i q^{76} +(4.00000 - 6.00000i) q^{78} +(-1.00000 + 2.00000i) q^{80} -11.0000 q^{81} +8.00000i q^{82} +4.00000 q^{83} -6.00000i q^{86} +12.0000i q^{87} +6.00000i q^{88} +8.00000i q^{89} +(-1.00000 + 2.00000i) q^{90} -6.00000i q^{92} +12.0000 q^{93} +8.00000 q^{94} +(12.0000 + 6.00000i) q^{95} +10.0000i q^{96} +6.00000 q^{97} -7.00000 q^{98} +2.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{2} - 2q^{4} + 2q^{5} - 6q^{8} - 2q^{9} + O(q^{10}) \) \( 2q + 2q^{2} - 2q^{4} + 2q^{5} - 6q^{8} - 2q^{9} + 2q^{10} - 6q^{13} + 8q^{15} - 2q^{16} - 2q^{18} - 2q^{20} - 6q^{25} - 6q^{26} + 12q^{29} + 8q^{30} + 10q^{32} + 8q^{33} + 2q^{36} - 12q^{37} + 8q^{39} - 6q^{40} - 2q^{45} + 16q^{47} - 14q^{49} - 6q^{50} + 6q^{52} - 8q^{55} - 24q^{57} + 12q^{58} - 8q^{60} + 12q^{61} + 14q^{64} - 14q^{65} + 8q^{66} - 24q^{67} - 24q^{69} + 6q^{72} + 12q^{73} - 12q^{74} + 16q^{75} + 8q^{78} - 2q^{80} - 22q^{81} + 8q^{83} - 2q^{90} + 24q^{93} + 16q^{94} + 24q^{95} + 12q^{97} - 14q^{98} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/65\mathbb{Z}\right)^\times\).

\(n\) \(27\) \(41\)
\(\chi(n)\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107 0.353553 0.935414i \(-0.384973\pi\)
0.353553 + 0.935414i \(0.384973\pi\)
\(3\) 2.00000i 1.15470i 0.816497 + 0.577350i \(0.195913\pi\)
−0.816497 + 0.577350i \(0.804087\pi\)
\(4\) −1.00000 −0.500000
\(5\) 1.00000 2.00000i 0.447214 0.894427i
\(6\) 2.00000i 0.816497i
\(7\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) −3.00000 −1.06066
\(9\) −1.00000 −0.333333
\(10\) 1.00000 2.00000i 0.316228 0.632456i
\(11\) 2.00000i 0.603023i −0.953463 0.301511i \(-0.902509\pi\)
0.953463 0.301511i \(-0.0974911\pi\)
\(12\) 2.00000i 0.577350i
\(13\) −3.00000 2.00000i −0.832050 0.554700i
\(14\) 0 0
\(15\) 4.00000 + 2.00000i 1.03280 + 0.516398i
\(16\) −1.00000 −0.250000
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) −1.00000 −0.235702
\(19\) 6.00000i 1.37649i 0.725476 + 0.688247i \(0.241620\pi\)
−0.725476 + 0.688247i \(0.758380\pi\)
\(20\) −1.00000 + 2.00000i −0.223607 + 0.447214i
\(21\) 0 0
\(22\) 2.00000i 0.426401i
\(23\) 6.00000i 1.25109i 0.780189 + 0.625543i \(0.215123\pi\)
−0.780189 + 0.625543i \(0.784877\pi\)
\(24\) 6.00000i 1.22474i
\(25\) −3.00000 4.00000i −0.600000 0.800000i
\(26\) −3.00000 2.00000i −0.588348 0.392232i
\(27\) 4.00000i 0.769800i
\(28\) 0 0
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 4.00000 + 2.00000i 0.730297 + 0.365148i
\(31\) 6.00000i 1.07763i −0.842424 0.538816i \(-0.818872\pi\)
0.842424 0.538816i \(-0.181128\pi\)
\(32\) 5.00000 0.883883
\(33\) 4.00000 0.696311
\(34\) 0 0
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −6.00000 −0.986394 −0.493197 0.869918i \(-0.664172\pi\)
−0.493197 + 0.869918i \(0.664172\pi\)
\(38\) 6.00000i 0.973329i
\(39\) 4.00000 6.00000i 0.640513 0.960769i
\(40\) −3.00000 + 6.00000i −0.474342 + 0.948683i
\(41\) 8.00000i 1.24939i 0.780869 + 0.624695i \(0.214777\pi\)
−0.780869 + 0.624695i \(0.785223\pi\)
\(42\) 0 0
\(43\) 6.00000i 0.914991i −0.889212 0.457496i \(-0.848747\pi\)
0.889212 0.457496i \(-0.151253\pi\)
\(44\) 2.00000i 0.301511i
\(45\) −1.00000 + 2.00000i −0.149071 + 0.298142i
\(46\) 6.00000i 0.884652i
\(47\) 8.00000 1.16692 0.583460 0.812142i \(-0.301699\pi\)
0.583460 + 0.812142i \(0.301699\pi\)
\(48\) 2.00000i 0.288675i
\(49\) −7.00000 −1.00000
\(50\) −3.00000 4.00000i −0.424264 0.565685i
\(51\) 0 0
\(52\) 3.00000 + 2.00000i 0.416025 + 0.277350i
\(53\) 12.0000i 1.64833i −0.566352 0.824163i \(-0.691646\pi\)
0.566352 0.824163i \(-0.308354\pi\)
\(54\) 4.00000i 0.544331i
\(55\) −4.00000 2.00000i −0.539360 0.269680i
\(56\) 0 0
\(57\) −12.0000 −1.58944
\(58\) 6.00000 0.787839
\(59\) 2.00000i 0.260378i −0.991489 0.130189i \(-0.958442\pi\)
0.991489 0.130189i \(-0.0415584\pi\)
\(60\) −4.00000 2.00000i −0.516398 0.258199i
\(61\) 6.00000 0.768221 0.384111 0.923287i \(-0.374508\pi\)
0.384111 + 0.923287i \(0.374508\pi\)
\(62\) 6.00000i 0.762001i
\(63\) 0 0
\(64\) 7.00000 0.875000
\(65\) −7.00000 + 4.00000i −0.868243 + 0.496139i
\(66\) 4.00000 0.492366
\(67\) −12.0000 −1.46603 −0.733017 0.680211i \(-0.761888\pi\)
−0.733017 + 0.680211i \(0.761888\pi\)
\(68\) 0 0
\(69\) −12.0000 −1.44463
\(70\) 0 0
\(71\) 2.00000i 0.237356i 0.992933 + 0.118678i \(0.0378657\pi\)
−0.992933 + 0.118678i \(0.962134\pi\)
\(72\) 3.00000 0.353553
\(73\) 6.00000 0.702247 0.351123 0.936329i \(-0.385800\pi\)
0.351123 + 0.936329i \(0.385800\pi\)
\(74\) −6.00000 −0.697486
\(75\) 8.00000 6.00000i 0.923760 0.692820i
\(76\) 6.00000i 0.688247i
\(77\) 0 0
\(78\) 4.00000 6.00000i 0.452911 0.679366i
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) −1.00000 + 2.00000i −0.111803 + 0.223607i
\(81\) −11.0000 −1.22222
\(82\) 8.00000i 0.883452i
\(83\) 4.00000 0.439057 0.219529 0.975606i \(-0.429548\pi\)
0.219529 + 0.975606i \(0.429548\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 6.00000i 0.646997i
\(87\) 12.0000i 1.28654i
\(88\) 6.00000i 0.639602i
\(89\) 8.00000i 0.847998i 0.905663 + 0.423999i \(0.139374\pi\)
−0.905663 + 0.423999i \(0.860626\pi\)
\(90\) −1.00000 + 2.00000i −0.105409 + 0.210819i
\(91\) 0 0
\(92\) 6.00000i 0.625543i
\(93\) 12.0000 1.24434
\(94\) 8.00000 0.825137
\(95\) 12.0000 + 6.00000i 1.23117 + 0.615587i
\(96\) 10.0000i 1.02062i
\(97\) 6.00000 0.609208 0.304604 0.952479i \(-0.401476\pi\)
0.304604 + 0.952479i \(0.401476\pi\)
\(98\) −7.00000 −0.707107
\(99\) 2.00000i 0.201008i
\(100\) 3.00000 + 4.00000i 0.300000 + 0.400000i
\(101\) 6.00000 0.597022 0.298511 0.954406i \(-0.403510\pi\)
0.298511 + 0.954406i \(0.403510\pi\)
\(102\) 0 0
\(103\) 6.00000i 0.591198i 0.955312 + 0.295599i \(0.0955191\pi\)
−0.955312 + 0.295599i \(0.904481\pi\)
\(104\) 9.00000 + 6.00000i 0.882523 + 0.588348i
\(105\) 0 0
\(106\) 12.0000i 1.16554i
\(107\) 6.00000i 0.580042i −0.957020 0.290021i \(-0.906338\pi\)
0.957020 0.290021i \(-0.0936623\pi\)
\(108\) 4.00000i 0.384900i
\(109\) 12.0000i 1.14939i −0.818367 0.574696i \(-0.805120\pi\)
0.818367 0.574696i \(-0.194880\pi\)
\(110\) −4.00000 2.00000i −0.381385 0.190693i
\(111\) 12.0000i 1.13899i
\(112\) 0 0
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) −12.0000 −1.12390
\(115\) 12.0000 + 6.00000i 1.11901 + 0.559503i
\(116\) −6.00000 −0.557086
\(117\) 3.00000 + 2.00000i 0.277350 + 0.184900i
\(118\) 2.00000i 0.184115i
\(119\) 0 0
\(120\) −12.0000 6.00000i −1.09545 0.547723i
\(121\) 7.00000 0.636364
\(122\) 6.00000 0.543214
\(123\) −16.0000 −1.44267
\(124\) 6.00000i 0.538816i
\(125\) −11.0000 + 2.00000i −0.983870 + 0.178885i
\(126\) 0 0
\(127\) 2.00000i 0.177471i −0.996055 0.0887357i \(-0.971717\pi\)
0.996055 0.0887357i \(-0.0282826\pi\)
\(128\) −3.00000 −0.265165
\(129\) 12.0000 1.05654
\(130\) −7.00000 + 4.00000i −0.613941 + 0.350823i
\(131\) −12.0000 −1.04844 −0.524222 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) −4.00000 −0.348155
\(133\) 0 0
\(134\) −12.0000 −1.03664
\(135\) 8.00000 + 4.00000i 0.688530 + 0.344265i
\(136\) 0 0
\(137\) −2.00000 −0.170872 −0.0854358 0.996344i \(-0.527228\pi\)
−0.0854358 + 0.996344i \(0.527228\pi\)
\(138\) −12.0000 −1.02151
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 0 0
\(141\) 16.0000i 1.34744i
\(142\) 2.00000i 0.167836i
\(143\) −4.00000 + 6.00000i −0.334497 + 0.501745i
\(144\) 1.00000 0.0833333
\(145\) 6.00000 12.0000i 0.498273 0.996546i
\(146\) 6.00000 0.496564
\(147\) 14.0000i 1.15470i
\(148\) 6.00000 0.493197
\(149\) 20.0000i 1.63846i −0.573462 0.819232i \(-0.694400\pi\)
0.573462 0.819232i \(-0.305600\pi\)
\(150\) 8.00000 6.00000i 0.653197 0.489898i
\(151\) 18.0000i 1.46482i 0.680864 + 0.732410i \(0.261604\pi\)
−0.680864 + 0.732410i \(0.738396\pi\)
\(152\) 18.0000i 1.45999i
\(153\) 0 0
\(154\) 0 0
\(155\) −12.0000 6.00000i −0.963863 0.481932i
\(156\) −4.00000 + 6.00000i −0.320256 + 0.480384i
\(157\) 12.0000i 0.957704i 0.877896 + 0.478852i \(0.158947\pi\)
−0.877896 + 0.478852i \(0.841053\pi\)
\(158\) 0 0
\(159\) 24.0000 1.90332
\(160\) 5.00000 10.0000i 0.395285 0.790569i
\(161\) 0 0
\(162\) −11.0000 −0.864242
\(163\) −12.0000 −0.939913 −0.469956 0.882690i \(-0.655730\pi\)
−0.469956 + 0.882690i \(0.655730\pi\)
\(164\) 8.00000i 0.624695i
\(165\) 4.00000 8.00000i 0.311400 0.622799i
\(166\) 4.00000 0.310460
\(167\) 16.0000 1.23812 0.619059 0.785345i \(-0.287514\pi\)
0.619059 + 0.785345i \(0.287514\pi\)
\(168\) 0 0
\(169\) 5.00000 + 12.0000i 0.384615 + 0.923077i
\(170\) 0 0
\(171\) 6.00000i 0.458831i
\(172\) 6.00000i 0.457496i
\(173\) 12.0000i 0.912343i 0.889892 + 0.456172i \(0.150780\pi\)
−0.889892 + 0.456172i \(0.849220\pi\)
\(174\) 12.0000i 0.909718i
\(175\) 0 0
\(176\) 2.00000i 0.150756i
\(177\) 4.00000 0.300658
\(178\) 8.00000i 0.599625i
\(179\) −12.0000 −0.896922 −0.448461 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 1.00000 2.00000i 0.0745356 0.149071i
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) 0 0
\(183\) 12.0000i 0.887066i
\(184\) 18.0000i 1.32698i
\(185\) −6.00000 + 12.0000i −0.441129 + 0.882258i
\(186\) 12.0000 0.879883
\(187\) 0 0
\(188\) −8.00000 −0.583460
\(189\) 0 0
\(190\) 12.0000 + 6.00000i 0.870572 + 0.435286i
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 14.0000i 1.01036i
\(193\) 6.00000 0.431889 0.215945 0.976406i \(-0.430717\pi\)
0.215945 + 0.976406i \(0.430717\pi\)
\(194\) 6.00000 0.430775
\(195\) −8.00000 14.0000i −0.572892 1.00256i
\(196\) 7.00000 0.500000
\(197\) 2.00000 0.142494 0.0712470 0.997459i \(-0.477302\pi\)
0.0712470 + 0.997459i \(0.477302\pi\)
\(198\) 2.00000i 0.142134i
\(199\) −24.0000 −1.70131 −0.850657 0.525720i \(-0.823796\pi\)
−0.850657 + 0.525720i \(0.823796\pi\)
\(200\) 9.00000 + 12.0000i 0.636396 + 0.848528i
\(201\) 24.0000i 1.69283i
\(202\) 6.00000 0.422159
\(203\) 0 0
\(204\) 0 0
\(205\) 16.0000 + 8.00000i 1.11749 + 0.558744i
\(206\) 6.00000i 0.418040i
\(207\) 6.00000i 0.417029i
\(208\) 3.00000 + 2.00000i 0.208013 + 0.138675i
\(209\) 12.0000 0.830057
\(210\) 0 0
\(211\) −12.0000 −0.826114 −0.413057 0.910705i \(-0.635539\pi\)
−0.413057 + 0.910705i \(0.635539\pi\)
\(212\) 12.0000i 0.824163i
\(213\) −4.00000 −0.274075
\(214\) 6.00000i 0.410152i
\(215\) −12.0000 6.00000i −0.818393 0.409197i
\(216\) 12.0000i 0.816497i
\(217\) 0 0
\(218\) 12.0000i 0.812743i
\(219\) 12.0000i 0.810885i
\(220\) 4.00000 + 2.00000i 0.269680 + 0.134840i
\(221\) 0 0
\(222\) 12.0000i 0.805387i
\(223\) −24.0000 −1.60716 −0.803579 0.595198i \(-0.797074\pi\)
−0.803579 + 0.595198i \(0.797074\pi\)
\(224\) 0 0
\(225\) 3.00000 + 4.00000i 0.200000 + 0.266667i
\(226\) 0 0
\(227\) 4.00000 0.265489 0.132745 0.991150i \(-0.457621\pi\)
0.132745 + 0.991150i \(0.457621\pi\)
\(228\) 12.0000 0.794719
\(229\) 12.0000i 0.792982i 0.918039 + 0.396491i \(0.129772\pi\)
−0.918039 + 0.396491i \(0.870228\pi\)
\(230\) 12.0000 + 6.00000i 0.791257 + 0.395628i
\(231\) 0 0
\(232\) −18.0000 −1.18176
\(233\) 24.0000i 1.57229i −0.618041 0.786146i \(-0.712073\pi\)
0.618041 0.786146i \(-0.287927\pi\)
\(234\) 3.00000 + 2.00000i 0.196116 + 0.130744i
\(235\) 8.00000 16.0000i 0.521862 1.04372i
\(236\) 2.00000i 0.130189i
\(237\) 0 0
\(238\) 0 0
\(239\) 10.0000i 0.646846i 0.946254 + 0.323423i \(0.104834\pi\)
−0.946254 + 0.323423i \(0.895166\pi\)
\(240\) −4.00000 2.00000i −0.258199 0.129099i
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 7.00000 0.449977
\(243\) 10.0000i 0.641500i
\(244\) −6.00000 −0.384111
\(245\) −7.00000 + 14.0000i −0.447214 + 0.894427i
\(246\) −16.0000 −1.02012
\(247\) 12.0000 18.0000i 0.763542 1.14531i
\(248\) 18.0000i 1.14300i
\(249\) 8.00000i 0.506979i
\(250\) −11.0000 + 2.00000i −0.695701 + 0.126491i
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 0 0
\(253\) 12.0000 0.754434
\(254\) 2.00000i 0.125491i
\(255\) 0 0
\(256\) −17.0000 −1.06250
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 12.0000 0.747087
\(259\) 0 0
\(260\) 7.00000 4.00000i 0.434122 0.248069i
\(261\) −6.00000 −0.371391
\(262\) −12.0000 −0.741362
\(263\) 6.00000i 0.369976i 0.982741 + 0.184988i \(0.0592246\pi\)
−0.982741 + 0.184988i \(0.940775\pi\)
\(264\) −12.0000 −0.738549
\(265\) −24.0000 12.0000i −1.47431 0.737154i
\(266\) 0 0
\(267\) −16.0000 −0.979184
\(268\) 12.0000 0.733017
\(269\) −18.0000 −1.09748 −0.548740 0.835993i \(-0.684892\pi\)
−0.548740 + 0.835993i \(0.684892\pi\)
\(270\) 8.00000 + 4.00000i 0.486864 + 0.243432i
\(271\) 6.00000i 0.364474i −0.983255 0.182237i \(-0.941666\pi\)
0.983255 0.182237i \(-0.0583338\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) −2.00000 −0.120824
\(275\) −8.00000 + 6.00000i −0.482418 + 0.361814i
\(276\) 12.0000 0.722315
\(277\) 12.0000i 0.721010i −0.932757 0.360505i \(-0.882604\pi\)
0.932757 0.360505i \(-0.117396\pi\)
\(278\) −4.00000 −0.239904
\(279\) 6.00000i 0.359211i
\(280\) 0 0
\(281\) 8.00000i 0.477240i −0.971113 0.238620i \(-0.923305\pi\)
0.971113 0.238620i \(-0.0766950\pi\)
\(282\) 16.0000i 0.952786i
\(283\) 22.0000i 1.30776i −0.756596 0.653882i \(-0.773139\pi\)
0.756596 0.653882i \(-0.226861\pi\)
\(284\) 2.00000i 0.118678i
\(285\) −12.0000 + 24.0000i −0.710819 + 1.42164i
\(286\) −4.00000 + 6.00000i −0.236525 + 0.354787i
\(287\) 0 0
\(288\) −5.00000 −0.294628
\(289\) 17.0000 1.00000
\(290\) 6.00000 12.0000i 0.352332 0.704664i
\(291\) 12.0000i 0.703452i
\(292\) −6.00000 −0.351123
\(293\) 26.0000 1.51894 0.759468 0.650545i \(-0.225459\pi\)
0.759468 + 0.650545i \(0.225459\pi\)
\(294\) 14.0000i 0.816497i
\(295\) −4.00000 2.00000i −0.232889 0.116445i
\(296\) 18.0000 1.04623
\(297\) 8.00000 0.464207
\(298\) 20.0000i 1.15857i
\(299\) 12.0000 18.0000i 0.693978 1.04097i
\(300\) −8.00000 + 6.00000i −0.461880 + 0.346410i
\(301\) 0 0
\(302\) 18.0000i 1.03578i
\(303\) 12.0000i 0.689382i
\(304\) 6.00000i 0.344124i
\(305\) 6.00000 12.0000i 0.343559 0.687118i
\(306\) 0 0
\(307\) −12.0000 −0.684876 −0.342438 0.939540i \(-0.611253\pi\)
−0.342438 + 0.939540i \(0.611253\pi\)
\(308\) 0 0
\(309\) −12.0000 −0.682656
\(310\) −12.0000 6.00000i −0.681554 0.340777i
\(311\) 24.0000 1.36092 0.680458 0.732787i \(-0.261781\pi\)
0.680458 + 0.732787i \(0.261781\pi\)
\(312\) −12.0000 + 18.0000i −0.679366 + 1.01905i
\(313\) 8.00000i 0.452187i 0.974106 + 0.226093i \(0.0725954\pi\)
−0.974106 + 0.226093i \(0.927405\pi\)
\(314\) 12.0000i 0.677199i
\(315\) 0 0
\(316\) 0 0
\(317\) 2.00000 0.112331 0.0561656 0.998421i \(-0.482113\pi\)
0.0561656 + 0.998421i \(0.482113\pi\)
\(318\) 24.0000 1.34585
\(319\) 12.0000i 0.671871i
\(320\) 7.00000 14.0000i 0.391312 0.782624i
\(321\) 12.0000 0.669775
\(322\) 0 0
\(323\) 0 0
\(324\) 11.0000 0.611111
\(325\) 1.00000 + 18.0000i 0.0554700 + 0.998460i
\(326\) −12.0000 −0.664619
\(327\) 24.0000 1.32720
\(328\) 24.0000i 1.32518i
\(329\) 0 0
\(330\) 4.00000 8.00000i 0.220193 0.440386i
\(331\) 30.0000i 1.64895i 0.565899 + 0.824475i \(0.308529\pi\)
−0.565899 + 0.824475i \(0.691471\pi\)
\(332\) −4.00000 −0.219529
\(333\) 6.00000 0.328798
\(334\) 16.0000 0.875481
\(335\) −12.0000 + 24.0000i −0.655630 + 1.31126i
\(336\) 0 0
\(337\) 32.0000i 1.74315i 0.490261 + 0.871576i \(0.336901\pi\)
−0.490261 + 0.871576i \(0.663099\pi\)
\(338\) 5.00000 + 12.0000i 0.271964 + 0.652714i
\(339\) 0 0
\(340\) 0 0
\(341\) −12.0000 −0.649836
\(342\) 6.00000i 0.324443i
\(343\) 0 0
\(344\) 18.0000i 0.970495i
\(345\) −12.0000 + 24.0000i −0.646058 + 1.29212i
\(346\) 12.0000i 0.645124i
\(347\) 6.00000i 0.322097i −0.986947 0.161048i \(-0.948512\pi\)
0.986947 0.161048i \(-0.0514875\pi\)
\(348\) 12.0000i 0.643268i
\(349\) 12.0000i 0.642345i −0.947021 0.321173i \(-0.895923\pi\)
0.947021 0.321173i \(-0.104077\pi\)
\(350\) 0 0
\(351\) 8.00000 12.0000i 0.427008 0.640513i
\(352\) 10.0000i 0.533002i
\(353\) 14.0000 0.745145 0.372572 0.928003i \(-0.378476\pi\)
0.372572 + 0.928003i \(0.378476\pi\)
\(354\) 4.00000 0.212598
\(355\) 4.00000 + 2.00000i 0.212298 + 0.106149i
\(356\) 8.00000i 0.423999i
\(357\) 0 0
\(358\) −12.0000 −0.634220
\(359\) 2.00000i 0.105556i 0.998606 + 0.0527780i \(0.0168076\pi\)
−0.998606 + 0.0527780i \(0.983192\pi\)
\(360\) 3.00000 6.00000i 0.158114 0.316228i
\(361\) −17.0000 −0.894737
\(362\) −2.00000 −0.105118
\(363\) 14.0000i 0.734809i
\(364\) 0 0
\(365\) 6.00000 12.0000i 0.314054 0.628109i
\(366\) 12.0000i 0.627250i
\(367\) 18.0000i 0.939592i −0.882775 0.469796i \(-0.844327\pi\)
0.882775 0.469796i \(-0.155673\pi\)
\(368\) 6.00000i 0.312772i
\(369\) 8.00000i 0.416463i
\(370\) −6.00000 + 12.0000i −0.311925 + 0.623850i
\(371\) 0 0
\(372\) −12.0000 −0.622171
\(373\) 4.00000i 0.207112i 0.994624 + 0.103556i \(0.0330221\pi\)
−0.994624 + 0.103556i \(0.966978\pi\)
\(374\) 0 0
\(375\) −4.00000 22.0000i −0.206559 1.13608i
\(376\) −24.0000 −1.23771
\(377\) −18.0000 12.0000i −0.927047 0.618031i
\(378\) 0 0
\(379\) 18.0000i 0.924598i −0.886724 0.462299i \(-0.847025\pi\)
0.886724 0.462299i \(-0.152975\pi\)
\(380\) −12.0000 6.00000i −0.615587 0.307794i
\(381\) 4.00000 0.204926
\(382\) 0 0
\(383\) −8.00000 −0.408781 −0.204390 0.978889i \(-0.565521\pi\)
−0.204390 + 0.978889i \(0.565521\pi\)
\(384\) 6.00000i 0.306186i
\(385\) 0 0
\(386\) 6.00000 0.305392
\(387\) 6.00000i 0.304997i
\(388\) −6.00000 −0.304604
\(389\) 6.00000 0.304212 0.152106 0.988364i \(-0.451394\pi\)
0.152106 + 0.988364i \(0.451394\pi\)
\(390\) −8.00000 14.0000i −0.405096 0.708918i
\(391\) 0 0
\(392\) 21.0000 1.06066
\(393\) 24.0000i 1.21064i
\(394\) 2.00000 0.100759
\(395\) 0 0
\(396\) 2.00000i 0.100504i
\(397\) 18.0000 0.903394 0.451697 0.892171i \(-0.350819\pi\)
0.451697 + 0.892171i \(0.350819\pi\)
\(398\) −24.0000 −1.20301
\(399\) 0 0
\(400\) 3.00000 + 4.00000i 0.150000 + 0.200000i
\(401\) 16.0000i 0.799002i −0.916733 0.399501i \(-0.869183\pi\)
0.916733 0.399501i \(-0.130817\pi\)
\(402\) 24.0000i 1.19701i
\(403\) −12.0000 + 18.0000i −0.597763 + 0.896644i
\(404\) −6.00000 −0.298511
\(405\) −11.0000 + 22.0000i −0.546594 + 1.09319i
\(406\) 0 0
\(407\) 12.0000i 0.594818i
\(408\) 0 0
\(409\) 24.0000i 1.18672i 0.804936 + 0.593362i \(0.202200\pi\)
−0.804936 + 0.593362i \(0.797800\pi\)
\(410\) 16.0000 + 8.00000i 0.790184 + 0.395092i
\(411\) 4.00000i 0.197305i
\(412\) 6.00000i 0.295599i
\(413\) 0 0
\(414\) 6.00000i 0.294884i
\(415\) 4.00000 8.00000i 0.196352 0.392705i
\(416\) −15.0000 10.0000i −0.735436 0.490290i
\(417\) 8.00000i 0.391762i
\(418\) 12.0000 0.586939
\(419\) −12.0000 −0.586238 −0.293119 0.956076i \(-0.594693\pi\)
−0.293119 + 0.956076i \(0.594693\pi\)
\(420\) 0 0
\(421\) 36.0000i 1.75453i −0.480004 0.877266i \(-0.659365\pi\)
0.480004 0.877266i \(-0.340635\pi\)
\(422\) −12.0000 −0.584151
\(423\) −8.00000 −0.388973
\(424\) 36.0000i 1.74831i
\(425\) 0 0
\(426\) −4.00000 −0.193801
\(427\) 0 0
\(428\) 6.00000i 0.290021i
\(429\) −12.0000 8.00000i −0.579365 0.386244i
\(430\) −12.0000 6.00000i −0.578691 0.289346i
\(431\) 10.0000i 0.481683i 0.970564 + 0.240842i \(0.0774234\pi\)
−0.970564 + 0.240842i \(0.922577\pi\)
\(432\) 4.00000i 0.192450i
\(433\) 16.0000i 0.768911i 0.923144 + 0.384455i \(0.125611\pi\)
−0.923144 + 0.384455i \(0.874389\pi\)
\(434\) 0 0
\(435\) 24.0000 + 12.0000i 1.15071 + 0.575356i
\(436\) 12.0000i 0.574696i
\(437\) −36.0000 −1.72211
\(438\) 12.0000i 0.573382i
\(439\) 8.00000 0.381819 0.190910 0.981608i \(-0.438856\pi\)
0.190910 + 0.981608i \(0.438856\pi\)
\(440\) 12.0000 + 6.00000i 0.572078 + 0.286039i
\(441\) 7.00000 0.333333
\(442\) 0 0
\(443\) 6.00000i 0.285069i −0.989790 0.142534i \(-0.954475\pi\)
0.989790 0.142534i \(-0.0455251\pi\)
\(444\) 12.0000i 0.569495i
\(445\) 16.0000 + 8.00000i 0.758473 + 0.379236i
\(446\) −24.0000 −1.13643
\(447\) 40.0000 1.89194
\(448\) 0 0
\(449\) 16.0000i 0.755087i 0.925992 + 0.377543i \(0.123231\pi\)
−0.925992 + 0.377543i \(0.876769\pi\)
\(450\) 3.00000 + 4.00000i 0.141421 + 0.188562i
\(451\) 16.0000 0.753411
\(452\) 0 0
\(453\) −36.0000 −1.69143
\(454\) 4.00000 0.187729
\(455\) 0 0
\(456\) 36.0000 1.68585
\(457\) 30.0000 1.40334 0.701670 0.712502i \(-0.252438\pi\)
0.701670 + 0.712502i \(0.252438\pi\)
\(458\) 12.0000i 0.560723i
\(459\) 0 0
\(460\) −12.0000 6.00000i −0.559503 0.279751i
\(461\) 4.00000i 0.186299i 0.995652 + 0.0931493i \(0.0296934\pi\)
−0.995652 + 0.0931493i \(0.970307\pi\)
\(462\) 0 0
\(463\) 24.0000 1.11537 0.557687 0.830051i \(-0.311689\pi\)
0.557687 + 0.830051i \(0.311689\pi\)
\(464\) −6.00000 −0.278543
\(465\) 12.0000 24.0000i 0.556487 1.11297i
\(466\) 24.0000i 1.11178i
\(467\) 18.0000i 0.832941i 0.909149 + 0.416470i \(0.136733\pi\)
−0.909149 + 0.416470i \(0.863267\pi\)
\(468\) −3.00000 2.00000i −0.138675 0.0924500i
\(469\) 0 0
\(470\) 8.00000 16.0000i 0.369012 0.738025i
\(471\) −24.0000 −1.10586
\(472\) 6.00000i 0.276172i
\(473\) −12.0000 −0.551761
\(474\) 0 0
\(475\) 24.0000 18.0000i 1.10120 0.825897i
\(476\) 0 0
\(477\) 12.0000i 0.549442i
\(478\) 10.0000i 0.457389i
\(479\) 22.0000i 1.00521i −0.864517 0.502603i \(-0.832376\pi\)
0.864517 0.502603i \(-0.167624\pi\)
\(480\) 20.0000 + 10.0000i 0.912871 + 0.456435i
\(481\) 18.0000 + 12.0000i 0.820729 + 0.547153i
\(482\) 0 0
\(483\) 0 0
\(484\) −7.00000 −0.318182
\(485\) 6.00000 12.0000i 0.272446 0.544892i
\(486\) 10.0000i 0.453609i
\(487\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(488\) −18.0000 −0.814822
\(489\) 24.0000i 1.08532i
\(490\) −7.00000 + 14.0000i −0.316228 + 0.632456i
\(491\) 12.0000 0.541552 0.270776 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) 16.0000 0.721336
\(493\) 0 0
\(494\) 12.0000 18.0000i 0.539906 0.809858i
\(495\) 4.00000 + 2.00000i 0.179787 + 0.0898933i
\(496\) 6.00000i 0.269408i
\(497\) 0 0
\(498\) 8.00000i 0.358489i
\(499\) 6.00000i 0.268597i 0.990941 + 0.134298i \(0.0428781\pi\)
−0.990941 + 0.134298i \(0.957122\pi\)
\(500\) 11.0000 2.00000i 0.491935 0.0894427i
\(501\) 32.0000i 1.42965i
\(502\) 12.0000 0.535586
\(503\) 6.00000i 0.267527i 0.991013 + 0.133763i \(0.0427062\pi\)
−0.991013 + 0.133763i \(0.957294\pi\)
\(504\) 0 0
\(505\) 6.00000 12.0000i 0.266996 0.533993i
\(506\) 12.0000 0.533465
\(507\) −24.0000 + 10.0000i −1.06588 + 0.444116i
\(508\) 2.00000i 0.0887357i
\(509\) 20.0000i 0.886484i 0.896402 + 0.443242i \(0.146172\pi\)
−0.896402 + 0.443242i \(0.853828\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −11.0000 −0.486136
\(513\) −24.0000 −1.05963
\(514\) 0 0
\(515\) 12.0000 + 6.00000i 0.528783 + 0.264392i
\(516\) −12.0000 −0.528271
\(517\) 16.0000i 0.703679i
\(518\) 0 0
\(519\) −24.0000 −1.05348
\(520\) 21.0000 12.0000i 0.920911 0.526235i
\(521\) −30.0000 −1.31432 −0.657162 0.753749i \(-0.728243\pi\)
−0.657162 + 0.753749i \(0.728243\pi\)
\(522\) −6.00000 −0.262613
\(523\) 42.0000i 1.83653i 0.395964 + 0.918266i \(0.370410\pi\)
−0.395964 + 0.918266i \(0.629590\pi\)
\(524\) 12.0000 0.524222
\(525\) 0 0
\(526\) 6.00000i 0.261612i
\(527\) 0 0
\(528\) −4.00000 −0.174078
\(529\) −13.0000 −0.565217
\(530\) −24.0000 12.0000i −1.04249 0.521247i
\(531\) 2.00000i 0.0867926i
\(532\) 0 0
\(533\) 16.0000 24.0000i 0.693037 1.03956i
\(534\) −16.0000 −0.692388
\(535\) −12.0000 6.00000i −0.518805 0.259403i
\(536\) 36.0000 1.55496
\(537\) 24.0000i 1.03568i
\(538\) −18.0000 −0.776035
\(539\) 14.0000i 0.603023i
\(540\) −8.00000 4.00000i −0.344265 0.172133i
\(541\) 12.0000i 0.515920i −0.966156 0.257960i \(-0.916950\pi\)
0.966156 0.257960i \(-0.0830503\pi\)
\(542\) 6.00000i 0.257722i
\(543\) 4.00000i 0.171656i
\(544\) 0 0
\(545\) −24.0000 12.0000i −1.02805 0.514024i
\(546\) 0 0
\(547\) 18.0000i 0.769624i 0.922995 + 0.384812i \(0.125734\pi\)
−0.922995 + 0.384812i \(0.874266\pi\)
\(548\) 2.00000 0.0854358
\(549\) −6.00000 −0.256074
\(550\) −8.00000 + 6.00000i −0.341121 + 0.255841i
\(551\) 36.0000i 1.53365i
\(552\) 36.0000 1.53226
\(553\) 0 0
\(554\) 12.0000i 0.509831i
\(555\) −24.0000 12.0000i −1.01874 0.509372i
\(556\) 4.00000 0.169638
\(557\) −14.0000 −0.593199 −0.296600 0.955002i \(-0.595853\pi\)
−0.296600 + 0.955002i \(0.595853\pi\)
\(558\) 6.00000i 0.254000i
\(559\) −12.0000 + 18.0000i −0.507546 + 0.761319i
\(560\) 0 0
\(561\) 0 0
\(562\) 8.00000i 0.337460i
\(563\) 30.0000i 1.26435i −0.774826 0.632175i \(-0.782163\pi\)
0.774826 0.632175i \(-0.217837\pi\)
\(564\) 16.0000i 0.673722i
\(565\) 0 0
\(566\) 22.0000i 0.924729i
\(567\) 0 0
\(568\) 6.00000i 0.251754i
\(569\) 18.0000 0.754599 0.377300 0.926091i \(-0.376853\pi\)
0.377300 + 0.926091i \(0.376853\pi\)
\(570\) −12.0000 + 24.0000i −0.502625 + 1.00525i
\(571\) 12.0000 0.502184 0.251092 0.967963i \(-0.419210\pi\)
0.251092 + 0.967963i \(0.419210\pi\)
\(572\) 4.00000 6.00000i 0.167248 0.250873i
\(573\) 0 0
\(574\) 0 0
\(575\) 24.0000 18.0000i 1.00087 0.750652i
\(576\) −7.00000 −0.291667
\(577\) −18.0000 −0.749350 −0.374675 0.927156i \(-0.622246\pi\)
−0.374675 + 0.927156i \(0.622246\pi\)
\(578\) 17.0000 0.707107
\(579\) 12.0000i 0.498703i
\(580\) −6.00000 + 12.0000i −0.249136 + 0.498273i
\(581\) 0 0
\(582\) 12.0000i 0.497416i
\(583\) −24.0000 −0.993978
\(584\) −18.0000 −0.744845
\(585\) 7.00000 4.00000i 0.289414 0.165380i
\(586\) 26.0000 1.07405
\(587\) −20.0000 −0.825488 −0.412744 0.910847i \(-0.635430\pi\)
−0.412744 + 0.910847i \(0.635430\pi\)
\(588\) 14.0000i 0.577350i
\(589\) 36.0000 1.48335
\(590\) −4.00000 2.00000i −0.164677 0.0823387i
\(591\) 4.00000i 0.164538i
\(592\) 6.00000 0.246598
\(593\) 22.0000 0.903432 0.451716 0.892162i \(-0.350812\pi\)
0.451716 + 0.892162i \(0.350812\pi\)
\(594\) 8.00000 0.328244
\(595\) 0 0
\(596\) 20.0000i 0.819232i
\(597\) 48.0000i 1.96451i
\(598\) 12.0000 18.0000i 0.490716 0.736075i
\(599\) 24.0000 0.980613 0.490307 0.871550i \(-0.336885\pi\)
0.490307 + 0.871550i \(0.336885\pi\)
\(600\) −24.0000 + 18.0000i −0.979796 + 0.734847i
\(601\) −6.00000 −0.244745 −0.122373 0.992484i \(-0.539050\pi\)
−0.122373 + 0.992484i \(0.539050\pi\)
\(602\) 0 0
\(603\) 12.0000 0.488678
\(604\) 18.0000i 0.732410i
\(605\) 7.00000 14.0000i 0.284590 0.569181i
\(606\) 12.0000i 0.487467i
\(607\) 18.0000i 0.730597i −0.930890 0.365299i \(-0.880967\pi\)
0.930890 0.365299i \(-0.119033\pi\)
\(608\) 30.0000i 1.21666i
\(609\) 0 0
\(610\) 6.00000 12.0000i 0.242933 0.485866i
\(611\) −24.0000 16.0000i −0.970936 0.647291i
\(612\) 0 0
\(613\) −30.0000 −1.21169 −0.605844 0.795583i \(-0.707165\pi\)
−0.605844 + 0.795583i \(0.707165\pi\)
\(614\) −12.0000 −0.484281
\(615\) −16.0000 + 32.0000i −0.645182 + 1.29036i
\(616\) 0 0
\(617\) −34.0000 −1.36879 −0.684394 0.729112i \(-0.739933\pi\)
−0.684394 + 0.729112i \(0.739933\pi\)
\(618\) −12.0000 −0.482711
\(619\) 18.0000i 0.723481i −0.932279 0.361741i \(-0.882183\pi\)
0.932279 0.361741i \(-0.117817\pi\)
\(620\) 12.0000 + 6.00000i 0.481932 + 0.240966i
\(621\) −24.0000 −0.963087
\(622\) 24.0000 0.962312
\(623\) 0 0
\(624\) −4.00000 + 6.00000i −0.160128 + 0.240192i
\(625\) −7.00000 + 24.0000i −0.280000 + 0.960000i
\(626\) 8.00000i 0.319744i
\(627\) 24.0000i 0.958468i
\(628\) 12.0000i 0.478852i
\(629\) 0 0
\(630\) 0 0
\(631\) 30.0000i 1.19428i −0.802137 0.597141i \(-0.796303\pi\)
0.802137 0.597141i \(-0.203697\pi\)
\(632\) 0 0
\(633\) 24.0000i 0.953914i
\(634\) 2.00000 0.0794301
\(635\) −4.00000 2.00000i −0.158735 0.0793676i
\(636\) −24.0000 −0.951662
\(637\) 21.0000 + 14.0000i 0.832050 + 0.554700i
\(638\) 12.0000i 0.475085i
\(639\) 2.00000i 0.0791188i
\(640\) −3.00000 + 6.00000i −0.118585 + 0.237171i
\(641\) −30.0000 −1.18493 −0.592464 0.805597i \(-0.701845\pi\)
−0.592464 + 0.805597i \(0.701845\pi\)
\(642\) 12.0000 0.473602
\(643\) 36.0000 1.41970 0.709851 0.704352i \(-0.248762\pi\)
0.709851 + 0.704352i \(0.248762\pi\)
\(644\) 0 0
\(645\) 12.0000 24.0000i 0.472500 0.944999i
\(646\) 0 0
\(647\) 6.00000i 0.235884i 0.993020 + 0.117942i \(0.0376297\pi\)
−0.993020 + 0.117942i \(0.962370\pi\)
\(648\) 33.0000 1.29636
\(649\) −4.00000 −0.157014
\(650\) 1.00000 + 18.0000i 0.0392232 + 0.706018i
\(651\) 0 0
\(652\) 12.0000 0.469956
\(653\) 36.0000i 1.40879i −0.709809 0.704394i \(-0.751219\pi\)
0.709809 0.704394i \(-0.248781\pi\)
\(654\) 24.0000 0.938474
\(655\) −12.0000 + 24.0000i −0.468879 + 0.937758i
\(656\) 8.00000i 0.312348i
\(657\) −6.00000 −0.234082
\(658\) 0 0
\(659\) 36.0000 1.40236 0.701180 0.712984i \(-0.252657\pi\)
0.701180 + 0.712984i \(0.252657\pi\)
\(660\) −4.00000 + 8.00000i −0.155700 + 0.311400i
\(661\) 12.0000i 0.466746i 0.972387 + 0.233373i \(0.0749763\pi\)
−0.972387 + 0.233373i \(0.925024\pi\)
\(662\) 30.0000i 1.16598i
\(663\) 0 0
\(664\) −12.0000 −0.465690
\(665\) 0 0
\(666\) 6.00000 0.232495
\(667\) 36.0000i 1.39393i
\(668\) −16.0000 −0.619059
\(669\) 48.0000i 1.85579i
\(670\) −12.0000 + 24.0000i −0.463600 + 0.927201i
\(671\) 12.0000i 0.463255i
\(672\) 0 0
\(673\) 48.0000i 1.85026i 0.379646 + 0.925132i \(0.376046\pi\)
−0.379646 + 0.925132i \(0.623954\pi\)
\(674\) 32.0000i 1.23259i
\(675\) 16.0000 12.0000i 0.615840 0.461880i
\(676\) −5.00000 12.0000i −0.192308 0.461538i
\(677\) 36.0000i 1.38359i 0.722093 + 0.691796i \(0.243180\pi\)
−0.722093 + 0.691796i \(0.756820\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 8.00000i 0.306561i
\(682\) −12.0000 −0.459504
\(683\) 44.0000 1.68361 0.841807 0.539779i \(-0.181492\pi\)
0.841807 + 0.539779i \(0.181492\pi\)
\(684\) 6.00000i 0.229416i
\(685\) −2.00000 + 4.00000i −0.0764161 + 0.152832i
\(686\) 0 0
\(687\) −24.0000 −0.915657
\(688\) 6.00000i 0.228748i
\(689\) −24.0000 + 36.0000i −0.914327 + 1.37149i
\(690\) −12.0000 + 24.0000i −0.456832 + 0.913664i
\(691\) 42.0000i 1.59776i −0.601494 0.798878i \(-0.705427\pi\)
0.601494 0.798878i \(-0.294573\pi\)
\(692\) 12.0000i 0.456172i
\(693\) 0 0
\(694\) 6.00000i 0.227757i
\(695\) −4.00000 + 8.00000i −0.151729 + 0.303457i
\(696\) 36.0000i 1.36458i
\(697\) 0 0
\(698\) 12.0000i 0.454207i
\(699\) 48.0000 1.81553
\(700\) 0 0
\(701\) 30.0000 1.13308 0.566542 0.824033i \(-0.308281\pi\)
0.566542 + 0.824033i \(0.308281\pi\)
\(702\) 8.00000 12.0000i 0.301941 0.452911i
\(703\) 36.0000i 1.35777i
\(704\) 14.0000i 0.527645i
\(705\) 32.0000 + 16.0000i 1.20519 + 0.602595i
\(706\) 14.0000 0.526897
\(707\) 0 0
\(708\) −4.00000 −0.150329
\(709\) 12.0000i 0.450669i 0.974281 + 0.225335i \(0.0723476\pi\)
−0.974281 + 0.225335i \(0.927652\pi\)
\(710\) 4.00000 + 2.00000i 0.150117 + 0.0750587i
\(711\) 0 0
\(712\) 24.0000i 0.899438i
\(713\) 36.0000 1.34821
\(714\) 0 0
\(715\) 8.00000 + 14.0000i 0.299183 + 0.523570i
\(716\) 12.0000 0.448461
\(717\) −20.0000 −0.746914
\(718\) 2.00000i 0.0746393i
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 1.00000 2.00000i 0.0372678 0.0745356i
\(721\) 0 0
\(722\) −17.0000 −0.632674
\(723\) 0 0
\(724\) 2.00000 0.0743294
\(725\) −18.0000 24.0000i −0.668503 0.891338i
\(726\) 14.0000i 0.519589i
\(727\) 26.0000i 0.964287i −0.876092 0.482143i \(-0.839858\pi\)
0.876092 0.482143i \(-0.160142\pi\)
\(728\) 0 0
\(729\) −13.0000 −0.481481
\(730\) 6.00000 12.0000i 0.222070 0.444140i
\(731\) 0 0
\(732\) 12.0000i 0.443533i
\(733\) 42.0000 1.55131 0.775653 0.631160i \(-0.217421\pi\)
0.775653 + 0.631160i \(0.217421\pi\)
\(734\) 18.0000i 0.664392i
\(735\) −28.0000 14.0000i −1.03280 0.516398i
\(736\) 30.0000i 1.10581i
\(737\) 24.0000i 0.884051i
\(738\) 8.00000i 0.294484i
\(739\) 6.00000i 0.220714i 0.993892 + 0.110357i \(0.0351994\pi\)
−0.993892 + 0.110357i \(0.964801\pi\)
\(740\) 6.00000 12.0000i 0.220564 0.441129i
\(741\) 36.0000 + 24.0000i 1.32249 + 0.881662i
\(742\) 0 0
\(743\) 16.0000 0.586983 0.293492 0.955962i \(-0.405183\pi\)
0.293492 + 0.955962i \(0.405183\pi\)
\(744\) −36.0000 −1.31982
\(745\) −40.0000 20.0000i −1.46549 0.732743i
\(746\) 4.00000i 0.146450i
\(747\) −4.00000 −0.146352
\(748\) 0 0
\(749\) 0 0
\(750\) −4.00000 22.0000i −0.146059 0.803326i
\(751\) −32.0000 −1.16770 −0.583848 0.811863i \(-0.698454\pi\)
−0.583848 + 0.811863i \(0.698454\pi\)
\(752\) −8.00000 −0.291730
\(753\) 24.0000i 0.874609i
\(754\) −18.0000 12.0000i −0.655521 0.437014i
\(755\) 36.0000 + 18.0000i 1.31017 + 0.655087i
\(756\) 0 0
\(757\) 20.0000i 0.726912i 0.931611 + 0.363456i \(0.118403\pi\)
−0.931611 + 0.363456i \(0.881597\pi\)
\(758\) 18.0000i 0.653789i
\(759\) 24.0000i 0.871145i
\(760\) −36.0000 18.0000i −1.30586 0.652929i
\(761\) 40.0000i 1.45000i 0.688749 + 0.724999i \(0.258160\pi\)
−0.688749 + 0.724999i \(0.741840\pi\)
\(762\) 4.00000 0.144905
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) −8.00000 −0.289052
\(767\) −4.00000 + 6.00000i −0.144432 + 0.216647i
\(768\) 34.0000i 1.22687i
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −6.00000 −0.215945
\(773\) −38.0000 −1.36677 −0.683383 0.730061i \(-0.739492\pi\)
−0.683383 + 0.730061i \(0.739492\pi\)
\(774\) 6.00000i 0.215666i
\(775\) −24.0000 + 18.0000i −0.862105 + 0.646579i
\(776\) −18.0000 −0.646162
\(777\) 0 0
\(778\) 6.00000 0.215110
\(779\) −48.0000 −1.71978
\(780\) 8.00000 + 14.0000i 0.286446 + 0.501280i
\(781\) 4.00000 0.143131
\(782\) 0 0
\(783\) 24.0000i 0.857690i
\(784\) 7.00000 0.250000
\(785\) 24.0000 + 12.0000i 0.856597 + 0.428298i
\(786\) 24.0000i 0.856052i
\(787\) −12.0000 −0.427754 −0.213877 0.976861i \(-0.568609\pi\)
−0.213877 + 0.976861i \(0.568609\pi\)
\(788\) −2.00000 −0.0712470
\(789\) −12.0000 −0.427211
\(790\) 0 0
\(791\) 0 0
\(792\) 6.00000i 0.213201i
\(793\) −18.0000 12.0000i −0.639199 0.426132i
\(794\) 18.0000 0.638796
\(795\) 24.0000 48.0000i 0.851192 1.70238i
\(796\) 24.0000 0.850657
\(797\) 12.0000i 0.425062i 0.977154 + 0.212531i \(0.0681706\pi\)
−0.977154 + 0.212531i \(0.931829\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −15.0000 20.0000i −0.530330 0.707107i
\(801\) 8.00000i 0.282666i
\(802\) 16.0000i 0.564980i
\(803\) 12.0000i 0.423471i
\(804\) 24.0000i 0.846415i
\(805\) 0 0
\(806\) −12.0000 + 18.0000i −0.422682 + 0.634023i