Properties

Label 1470.2.g.g.589.2
Level $1470$
Weight $2$
Character 1470.589
Analytic conductor $11.738$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1470.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.7380090971\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \(x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 30)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 589.2
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 1470.589
Dual form 1470.2.g.g.589.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(2.00000 - 1.00000i) q^{5} -1.00000 q^{6} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(2.00000 - 1.00000i) q^{5} -1.00000 q^{6} -1.00000i q^{8} -1.00000 q^{9} +(1.00000 + 2.00000i) q^{10} +2.00000 q^{11} -1.00000i q^{12} -6.00000i q^{13} +(1.00000 + 2.00000i) q^{15} +1.00000 q^{16} +2.00000i q^{17} -1.00000i q^{18} +(-2.00000 + 1.00000i) q^{20} +2.00000i q^{22} -4.00000i q^{23} +1.00000 q^{24} +(3.00000 - 4.00000i) q^{25} +6.00000 q^{26} -1.00000i q^{27} +(-2.00000 + 1.00000i) q^{30} +8.00000 q^{31} +1.00000i q^{32} +2.00000i q^{33} -2.00000 q^{34} +1.00000 q^{36} -2.00000i q^{37} +6.00000 q^{39} +(-1.00000 - 2.00000i) q^{40} -2.00000 q^{41} -4.00000i q^{43} -2.00000 q^{44} +(-2.00000 + 1.00000i) q^{45} +4.00000 q^{46} -8.00000i q^{47} +1.00000i q^{48} +(4.00000 + 3.00000i) q^{50} -2.00000 q^{51} +6.00000i q^{52} +6.00000i q^{53} +1.00000 q^{54} +(4.00000 - 2.00000i) q^{55} +10.0000 q^{59} +(-1.00000 - 2.00000i) q^{60} -2.00000 q^{61} +8.00000i q^{62} -1.00000 q^{64} +(-6.00000 - 12.0000i) q^{65} -2.00000 q^{66} +8.00000i q^{67} -2.00000i q^{68} +4.00000 q^{69} +12.0000 q^{71} +1.00000i q^{72} +4.00000i q^{73} +2.00000 q^{74} +(4.00000 + 3.00000i) q^{75} +6.00000i q^{78} +(2.00000 - 1.00000i) q^{80} +1.00000 q^{81} -2.00000i q^{82} +4.00000i q^{83} +(2.00000 + 4.00000i) q^{85} +4.00000 q^{86} -2.00000i q^{88} -10.0000 q^{89} +(-1.00000 - 2.00000i) q^{90} +4.00000i q^{92} +8.00000i q^{93} +8.00000 q^{94} -1.00000 q^{96} -8.00000i q^{97} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{4} + 4q^{5} - 2q^{6} - 2q^{9} + O(q^{10}) \) \( 2q - 2q^{4} + 4q^{5} - 2q^{6} - 2q^{9} + 2q^{10} + 4q^{11} + 2q^{15} + 2q^{16} - 4q^{20} + 2q^{24} + 6q^{25} + 12q^{26} - 4q^{30} + 16q^{31} - 4q^{34} + 2q^{36} + 12q^{39} - 2q^{40} - 4q^{41} - 4q^{44} - 4q^{45} + 8q^{46} + 8q^{50} - 4q^{51} + 2q^{54} + 8q^{55} + 20q^{59} - 2q^{60} - 4q^{61} - 2q^{64} - 12q^{65} - 4q^{66} + 8q^{69} + 24q^{71} + 4q^{74} + 8q^{75} + 4q^{80} + 2q^{81} + 4q^{85} + 8q^{86} - 20q^{89} - 2q^{90} + 16q^{94} - 2q^{96} - 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).

\(n\) \(491\) \(1081\) \(1177\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 1.00000i 0.577350i
\(4\) −1.00000 −0.500000
\(5\) 2.00000 1.00000i 0.894427 0.447214i
\(6\) −1.00000 −0.408248
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) −1.00000 −0.333333
\(10\) 1.00000 + 2.00000i 0.316228 + 0.632456i
\(11\) 2.00000 0.603023 0.301511 0.953463i \(-0.402509\pi\)
0.301511 + 0.953463i \(0.402509\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 6.00000i 1.66410i −0.554700 0.832050i \(-0.687167\pi\)
0.554700 0.832050i \(-0.312833\pi\)
\(14\) 0 0
\(15\) 1.00000 + 2.00000i 0.258199 + 0.516398i
\(16\) 1.00000 0.250000
\(17\) 2.00000i 0.485071i 0.970143 + 0.242536i \(0.0779791\pi\)
−0.970143 + 0.242536i \(0.922021\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) −2.00000 + 1.00000i −0.447214 + 0.223607i
\(21\) 0 0
\(22\) 2.00000i 0.426401i
\(23\) 4.00000i 0.834058i −0.908893 0.417029i \(-0.863071\pi\)
0.908893 0.417029i \(-0.136929\pi\)
\(24\) 1.00000 0.204124
\(25\) 3.00000 4.00000i 0.600000 0.800000i
\(26\) 6.00000 1.17670
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) −2.00000 + 1.00000i −0.365148 + 0.182574i
\(31\) 8.00000 1.43684 0.718421 0.695608i \(-0.244865\pi\)
0.718421 + 0.695608i \(0.244865\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 2.00000i 0.348155i
\(34\) −2.00000 −0.342997
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 2.00000i 0.328798i −0.986394 0.164399i \(-0.947432\pi\)
0.986394 0.164399i \(-0.0525685\pi\)
\(38\) 0 0
\(39\) 6.00000 0.960769
\(40\) −1.00000 2.00000i −0.158114 0.316228i
\(41\) −2.00000 −0.312348 −0.156174 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) 0 0
\(43\) 4.00000i 0.609994i −0.952353 0.304997i \(-0.901344\pi\)
0.952353 0.304997i \(-0.0986555\pi\)
\(44\) −2.00000 −0.301511
\(45\) −2.00000 + 1.00000i −0.298142 + 0.149071i
\(46\) 4.00000 0.589768
\(47\) 8.00000i 1.16692i −0.812142 0.583460i \(-0.801699\pi\)
0.812142 0.583460i \(-0.198301\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 0 0
\(50\) 4.00000 + 3.00000i 0.565685 + 0.424264i
\(51\) −2.00000 −0.280056
\(52\) 6.00000i 0.832050i
\(53\) 6.00000i 0.824163i 0.911147 + 0.412082i \(0.135198\pi\)
−0.911147 + 0.412082i \(0.864802\pi\)
\(54\) 1.00000 0.136083
\(55\) 4.00000 2.00000i 0.539360 0.269680i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 10.0000 1.30189 0.650945 0.759125i \(-0.274373\pi\)
0.650945 + 0.759125i \(0.274373\pi\)
\(60\) −1.00000 2.00000i −0.129099 0.258199i
\(61\) −2.00000 −0.256074 −0.128037 0.991769i \(-0.540868\pi\)
−0.128037 + 0.991769i \(0.540868\pi\)
\(62\) 8.00000i 1.01600i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −6.00000 12.0000i −0.744208 1.48842i
\(66\) −2.00000 −0.246183
\(67\) 8.00000i 0.977356i 0.872464 + 0.488678i \(0.162521\pi\)
−0.872464 + 0.488678i \(0.837479\pi\)
\(68\) 2.00000i 0.242536i
\(69\) 4.00000 0.481543
\(70\) 0 0
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 4.00000i 0.468165i 0.972217 + 0.234082i \(0.0752085\pi\)
−0.972217 + 0.234082i \(0.924791\pi\)
\(74\) 2.00000 0.232495
\(75\) 4.00000 + 3.00000i 0.461880 + 0.346410i
\(76\) 0 0
\(77\) 0 0
\(78\) 6.00000i 0.679366i
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 2.00000 1.00000i 0.223607 0.111803i
\(81\) 1.00000 0.111111
\(82\) 2.00000i 0.220863i
\(83\) 4.00000i 0.439057i 0.975606 + 0.219529i \(0.0704519\pi\)
−0.975606 + 0.219529i \(0.929548\pi\)
\(84\) 0 0
\(85\) 2.00000 + 4.00000i 0.216930 + 0.433861i
\(86\) 4.00000 0.431331
\(87\) 0 0
\(88\) 2.00000i 0.213201i
\(89\) −10.0000 −1.06000 −0.529999 0.847998i \(-0.677808\pi\)
−0.529999 + 0.847998i \(0.677808\pi\)
\(90\) −1.00000 2.00000i −0.105409 0.210819i
\(91\) 0 0
\(92\) 4.00000i 0.417029i
\(93\) 8.00000i 0.829561i
\(94\) 8.00000 0.825137
\(95\) 0 0
\(96\) −1.00000 −0.102062
\(97\) 8.00000i 0.812277i −0.913812 0.406138i \(-0.866875\pi\)
0.913812 0.406138i \(-0.133125\pi\)
\(98\) 0 0
\(99\) −2.00000 −0.201008
\(100\) −3.00000 + 4.00000i −0.300000 + 0.400000i
\(101\) 8.00000 0.796030 0.398015 0.917379i \(-0.369699\pi\)
0.398015 + 0.917379i \(0.369699\pi\)
\(102\) 2.00000i 0.198030i
\(103\) 14.0000i 1.37946i 0.724066 + 0.689730i \(0.242271\pi\)
−0.724066 + 0.689730i \(0.757729\pi\)
\(104\) −6.00000 −0.588348
\(105\) 0 0
\(106\) −6.00000 −0.582772
\(107\) 12.0000i 1.16008i −0.814587 0.580042i \(-0.803036\pi\)
0.814587 0.580042i \(-0.196964\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) −10.0000 −0.957826 −0.478913 0.877862i \(-0.658969\pi\)
−0.478913 + 0.877862i \(0.658969\pi\)
\(110\) 2.00000 + 4.00000i 0.190693 + 0.381385i
\(111\) 2.00000 0.189832
\(112\) 0 0
\(113\) 6.00000i 0.564433i 0.959351 + 0.282216i \(0.0910696\pi\)
−0.959351 + 0.282216i \(0.908930\pi\)
\(114\) 0 0
\(115\) −4.00000 8.00000i −0.373002 0.746004i
\(116\) 0 0
\(117\) 6.00000i 0.554700i
\(118\) 10.0000i 0.920575i
\(119\) 0 0
\(120\) 2.00000 1.00000i 0.182574 0.0912871i
\(121\) −7.00000 −0.636364
\(122\) 2.00000i 0.181071i
\(123\) 2.00000i 0.180334i
\(124\) −8.00000 −0.718421
\(125\) 2.00000 11.0000i 0.178885 0.983870i
\(126\) 0 0
\(127\) 2.00000i 0.177471i −0.996055 0.0887357i \(-0.971717\pi\)
0.996055 0.0887357i \(-0.0282826\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 4.00000 0.352180
\(130\) 12.0000 6.00000i 1.05247 0.526235i
\(131\) 18.0000 1.57267 0.786334 0.617802i \(-0.211977\pi\)
0.786334 + 0.617802i \(0.211977\pi\)
\(132\) 2.00000i 0.174078i
\(133\) 0 0
\(134\) −8.00000 −0.691095
\(135\) −1.00000 2.00000i −0.0860663 0.172133i
\(136\) 2.00000 0.171499
\(137\) 18.0000i 1.53784i 0.639343 + 0.768922i \(0.279207\pi\)
−0.639343 + 0.768922i \(0.720793\pi\)
\(138\) 4.00000i 0.340503i
\(139\) −20.0000 −1.69638 −0.848189 0.529694i \(-0.822307\pi\)
−0.848189 + 0.529694i \(0.822307\pi\)
\(140\) 0 0
\(141\) 8.00000 0.673722
\(142\) 12.0000i 1.00702i
\(143\) 12.0000i 1.00349i
\(144\) −1.00000 −0.0833333
\(145\) 0 0
\(146\) −4.00000 −0.331042
\(147\) 0 0
\(148\) 2.00000i 0.164399i
\(149\) 20.0000 1.63846 0.819232 0.573462i \(-0.194400\pi\)
0.819232 + 0.573462i \(0.194400\pi\)
\(150\) −3.00000 + 4.00000i −0.244949 + 0.326599i
\(151\) −8.00000 −0.651031 −0.325515 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) 0 0
\(153\) 2.00000i 0.161690i
\(154\) 0 0
\(155\) 16.0000 8.00000i 1.28515 0.642575i
\(156\) −6.00000 −0.480384
\(157\) 22.0000i 1.75579i 0.478852 + 0.877896i \(0.341053\pi\)
−0.478852 + 0.877896i \(0.658947\pi\)
\(158\) 0 0
\(159\) −6.00000 −0.475831
\(160\) 1.00000 + 2.00000i 0.0790569 + 0.158114i
\(161\) 0 0
\(162\) 1.00000i 0.0785674i
\(163\) 16.0000i 1.25322i 0.779334 + 0.626608i \(0.215557\pi\)
−0.779334 + 0.626608i \(0.784443\pi\)
\(164\) 2.00000 0.156174
\(165\) 2.00000 + 4.00000i 0.155700 + 0.311400i
\(166\) −4.00000 −0.310460
\(167\) 12.0000i 0.928588i 0.885681 + 0.464294i \(0.153692\pi\)
−0.885681 + 0.464294i \(0.846308\pi\)
\(168\) 0 0
\(169\) −23.0000 −1.76923
\(170\) −4.00000 + 2.00000i −0.306786 + 0.153393i
\(171\) 0 0
\(172\) 4.00000i 0.304997i
\(173\) 14.0000i 1.06440i 0.846619 + 0.532200i \(0.178635\pi\)
−0.846619 + 0.532200i \(0.821365\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 2.00000 0.150756
\(177\) 10.0000i 0.751646i
\(178\) 10.0000i 0.749532i
\(179\) −10.0000 −0.747435 −0.373718 0.927543i \(-0.621917\pi\)
−0.373718 + 0.927543i \(0.621917\pi\)
\(180\) 2.00000 1.00000i 0.149071 0.0745356i
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) 0 0
\(183\) 2.00000i 0.147844i
\(184\) −4.00000 −0.294884
\(185\) −2.00000 4.00000i −0.147043 0.294086i
\(186\) −8.00000 −0.586588
\(187\) 4.00000i 0.292509i
\(188\) 8.00000i 0.583460i
\(189\) 0 0
\(190\) 0 0
\(191\) 12.0000 0.868290 0.434145 0.900843i \(-0.357051\pi\)
0.434145 + 0.900843i \(0.357051\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) 4.00000i 0.287926i −0.989583 0.143963i \(-0.954015\pi\)
0.989583 0.143963i \(-0.0459847\pi\)
\(194\) 8.00000 0.574367
\(195\) 12.0000 6.00000i 0.859338 0.429669i
\(196\) 0 0
\(197\) 22.0000i 1.56744i −0.621117 0.783718i \(-0.713321\pi\)
0.621117 0.783718i \(-0.286679\pi\)
\(198\) 2.00000i 0.142134i
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) −4.00000 3.00000i −0.282843 0.212132i
\(201\) −8.00000 −0.564276
\(202\) 8.00000i 0.562878i
\(203\) 0 0
\(204\) 2.00000 0.140028
\(205\) −4.00000 + 2.00000i −0.279372 + 0.139686i
\(206\) −14.0000 −0.975426
\(207\) 4.00000i 0.278019i
\(208\) 6.00000i 0.416025i
\(209\) 0 0
\(210\) 0 0
\(211\) 12.0000 0.826114 0.413057 0.910705i \(-0.364461\pi\)
0.413057 + 0.910705i \(0.364461\pi\)
\(212\) 6.00000i 0.412082i
\(213\) 12.0000i 0.822226i
\(214\) 12.0000 0.820303
\(215\) −4.00000 8.00000i −0.272798 0.545595i
\(216\) −1.00000 −0.0680414
\(217\) 0 0
\(218\) 10.0000i 0.677285i
\(219\) −4.00000 −0.270295
\(220\) −4.00000 + 2.00000i −0.269680 + 0.134840i
\(221\) 12.0000 0.807207
\(222\) 2.00000i 0.134231i
\(223\) 26.0000i 1.74109i −0.492090 0.870544i \(-0.663767\pi\)
0.492090 0.870544i \(-0.336233\pi\)
\(224\) 0 0
\(225\) −3.00000 + 4.00000i −0.200000 + 0.266667i
\(226\) −6.00000 −0.399114
\(227\) 28.0000i 1.85843i −0.369546 0.929213i \(-0.620487\pi\)
0.369546 0.929213i \(-0.379513\pi\)
\(228\) 0 0
\(229\) −10.0000 −0.660819 −0.330409 0.943838i \(-0.607187\pi\)
−0.330409 + 0.943838i \(0.607187\pi\)
\(230\) 8.00000 4.00000i 0.527504 0.263752i
\(231\) 0 0
\(232\) 0 0
\(233\) 14.0000i 0.917170i −0.888650 0.458585i \(-0.848356\pi\)
0.888650 0.458585i \(-0.151644\pi\)
\(234\) −6.00000 −0.392232
\(235\) −8.00000 16.0000i −0.521862 1.04372i
\(236\) −10.0000 −0.650945
\(237\) 0 0
\(238\) 0 0
\(239\) −20.0000 −1.29369 −0.646846 0.762620i \(-0.723912\pi\)
−0.646846 + 0.762620i \(0.723912\pi\)
\(240\) 1.00000 + 2.00000i 0.0645497 + 0.129099i
\(241\) −22.0000 −1.41714 −0.708572 0.705638i \(-0.750660\pi\)
−0.708572 + 0.705638i \(0.750660\pi\)
\(242\) 7.00000i 0.449977i
\(243\) 1.00000i 0.0641500i
\(244\) 2.00000 0.128037
\(245\) 0 0
\(246\) 2.00000 0.127515
\(247\) 0 0
\(248\) 8.00000i 0.508001i
\(249\) −4.00000 −0.253490
\(250\) 11.0000 + 2.00000i 0.695701 + 0.126491i
\(251\) 18.0000 1.13615 0.568075 0.822977i \(-0.307688\pi\)
0.568075 + 0.822977i \(0.307688\pi\)
\(252\) 0 0
\(253\) 8.00000i 0.502956i
\(254\) 2.00000 0.125491
\(255\) −4.00000 + 2.00000i −0.250490 + 0.125245i
\(256\) 1.00000 0.0625000
\(257\) 18.0000i 1.12281i −0.827541 0.561405i \(-0.810261\pi\)
0.827541 0.561405i \(-0.189739\pi\)
\(258\) 4.00000i 0.249029i
\(259\) 0 0
\(260\) 6.00000 + 12.0000i 0.372104 + 0.744208i
\(261\) 0 0
\(262\) 18.0000i 1.11204i
\(263\) 4.00000i 0.246651i −0.992366 0.123325i \(-0.960644\pi\)
0.992366 0.123325i \(-0.0393559\pi\)
\(264\) 2.00000 0.123091
\(265\) 6.00000 + 12.0000i 0.368577 + 0.737154i
\(266\) 0 0
\(267\) 10.0000i 0.611990i
\(268\) 8.00000i 0.488678i
\(269\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) 2.00000 1.00000i 0.121716 0.0608581i
\(271\) 8.00000 0.485965 0.242983 0.970031i \(-0.421874\pi\)
0.242983 + 0.970031i \(0.421874\pi\)
\(272\) 2.00000i 0.121268i
\(273\) 0 0
\(274\) −18.0000 −1.08742
\(275\) 6.00000 8.00000i 0.361814 0.482418i
\(276\) −4.00000 −0.240772
\(277\) 2.00000i 0.120168i −0.998193 0.0600842i \(-0.980863\pi\)
0.998193 0.0600842i \(-0.0191369\pi\)
\(278\) 20.0000i 1.19952i
\(279\) −8.00000 −0.478947
\(280\) 0 0
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) 8.00000i 0.476393i
\(283\) 16.0000i 0.951101i −0.879688 0.475551i \(-0.842249\pi\)
0.879688 0.475551i \(-0.157751\pi\)
\(284\) −12.0000 −0.712069
\(285\) 0 0
\(286\) 12.0000 0.709575
\(287\) 0 0
\(288\) 1.00000i 0.0589256i
\(289\) 13.0000 0.764706
\(290\) 0 0
\(291\) 8.00000 0.468968
\(292\) 4.00000i 0.234082i
\(293\) 6.00000i 0.350524i −0.984522 0.175262i \(-0.943923\pi\)
0.984522 0.175262i \(-0.0560772\pi\)
\(294\) 0 0
\(295\) 20.0000 10.0000i 1.16445 0.582223i
\(296\) −2.00000 −0.116248
\(297\) 2.00000i 0.116052i
\(298\) 20.0000i 1.15857i
\(299\) −24.0000 −1.38796
\(300\) −4.00000 3.00000i −0.230940 0.173205i
\(301\) 0 0
\(302\) 8.00000i 0.460348i
\(303\) 8.00000i 0.459588i
\(304\) 0 0
\(305\) −4.00000 + 2.00000i −0.229039 + 0.114520i
\(306\) 2.00000 0.114332
\(307\) 12.0000i 0.684876i 0.939540 + 0.342438i \(0.111253\pi\)
−0.939540 + 0.342438i \(0.888747\pi\)
\(308\) 0 0
\(309\) −14.0000 −0.796432
\(310\) 8.00000 + 16.0000i 0.454369 + 0.908739i
\(311\) −12.0000 −0.680458 −0.340229 0.940343i \(-0.610505\pi\)
−0.340229 + 0.940343i \(0.610505\pi\)
\(312\) 6.00000i 0.339683i
\(313\) 4.00000i 0.226093i 0.993590 + 0.113047i \(0.0360610\pi\)
−0.993590 + 0.113047i \(0.963939\pi\)
\(314\) −22.0000 −1.24153
\(315\) 0 0
\(316\) 0 0
\(317\) 2.00000i 0.112331i −0.998421 0.0561656i \(-0.982113\pi\)
0.998421 0.0561656i \(-0.0178875\pi\)
\(318\) 6.00000i 0.336463i
\(319\) 0 0
\(320\) −2.00000 + 1.00000i −0.111803 + 0.0559017i
\(321\) 12.0000 0.669775
\(322\) 0 0
\(323\) 0 0
\(324\) −1.00000 −0.0555556
\(325\) −24.0000 18.0000i −1.33128 0.998460i
\(326\) −16.0000 −0.886158
\(327\) 10.0000i 0.553001i
\(328\) 2.00000i 0.110432i
\(329\) 0 0
\(330\) −4.00000 + 2.00000i −0.220193 + 0.110096i
\(331\) −8.00000 −0.439720 −0.219860 0.975531i \(-0.570560\pi\)
−0.219860 + 0.975531i \(0.570560\pi\)
\(332\) 4.00000i 0.219529i
\(333\) 2.00000i 0.109599i
\(334\) −12.0000 −0.656611
\(335\) 8.00000 + 16.0000i 0.437087 + 0.874173i
\(336\) 0 0
\(337\) 28.0000i 1.52526i 0.646837 + 0.762629i \(0.276092\pi\)
−0.646837 + 0.762629i \(0.723908\pi\)
\(338\) 23.0000i 1.25104i
\(339\) −6.00000 −0.325875
\(340\) −2.00000 4.00000i −0.108465 0.216930i
\(341\) 16.0000 0.866449
\(342\) 0 0
\(343\) 0 0
\(344\) −4.00000 −0.215666
\(345\) 8.00000 4.00000i 0.430706 0.215353i
\(346\) −14.0000 −0.752645
\(347\) 12.0000i 0.644194i −0.946707 0.322097i \(-0.895612\pi\)
0.946707 0.322097i \(-0.104388\pi\)
\(348\) 0 0
\(349\) 10.0000 0.535288 0.267644 0.963518i \(-0.413755\pi\)
0.267644 + 0.963518i \(0.413755\pi\)
\(350\) 0 0
\(351\) −6.00000 −0.320256
\(352\) 2.00000i 0.106600i
\(353\) 14.0000i 0.745145i 0.928003 + 0.372572i \(0.121524\pi\)
−0.928003 + 0.372572i \(0.878476\pi\)
\(354\) −10.0000 −0.531494
\(355\) 24.0000 12.0000i 1.27379 0.636894i
\(356\) 10.0000 0.529999
\(357\) 0 0
\(358\) 10.0000i 0.528516i
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 1.00000 + 2.00000i 0.0527046 + 0.105409i
\(361\) −19.0000 −1.00000
\(362\) 2.00000i 0.105118i
\(363\) 7.00000i 0.367405i
\(364\) 0 0
\(365\) 4.00000 + 8.00000i 0.209370 + 0.418739i
\(366\) 2.00000 0.104542
\(367\) 2.00000i 0.104399i 0.998637 + 0.0521996i \(0.0166232\pi\)
−0.998637 + 0.0521996i \(0.983377\pi\)
\(368\) 4.00000i 0.208514i
\(369\) 2.00000 0.104116
\(370\) 4.00000 2.00000i 0.207950 0.103975i
\(371\) 0 0
\(372\) 8.00000i 0.414781i
\(373\) 6.00000i 0.310668i 0.987862 + 0.155334i \(0.0496454\pi\)
−0.987862 + 0.155334i \(0.950355\pi\)
\(374\) −4.00000 −0.206835
\(375\) 11.0000 + 2.00000i 0.568038 + 0.103280i
\(376\) −8.00000 −0.412568
\(377\) 0 0
\(378\) 0 0
\(379\) −20.0000 −1.02733 −0.513665 0.857991i \(-0.671713\pi\)
−0.513665 + 0.857991i \(0.671713\pi\)
\(380\) 0 0
\(381\) 2.00000 0.102463
\(382\) 12.0000i 0.613973i
\(383\) 16.0000i 0.817562i −0.912633 0.408781i \(-0.865954\pi\)
0.912633 0.408781i \(-0.134046\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) 4.00000 0.203595
\(387\) 4.00000i 0.203331i
\(388\) 8.00000i 0.406138i
\(389\) −20.0000 −1.01404 −0.507020 0.861934i \(-0.669253\pi\)
−0.507020 + 0.861934i \(0.669253\pi\)
\(390\) 6.00000 + 12.0000i 0.303822 + 0.607644i
\(391\) 8.00000 0.404577
\(392\) 0 0
\(393\) 18.0000i 0.907980i
\(394\) 22.0000 1.10834
\(395\) 0 0
\(396\) 2.00000 0.100504
\(397\) 2.00000i 0.100377i 0.998740 + 0.0501886i \(0.0159822\pi\)
−0.998740 + 0.0501886i \(0.984018\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 3.00000 4.00000i 0.150000 0.200000i
\(401\) 22.0000 1.09863 0.549314 0.835616i \(-0.314889\pi\)
0.549314 + 0.835616i \(0.314889\pi\)
\(402\) 8.00000i 0.399004i
\(403\) 48.0000i 2.39105i
\(404\) −8.00000 −0.398015
\(405\) 2.00000 1.00000i 0.0993808 0.0496904i
\(406\) 0 0
\(407\) 4.00000i 0.198273i
\(408\) 2.00000i 0.0990148i
\(409\) −10.0000 −0.494468 −0.247234 0.968956i \(-0.579522\pi\)
−0.247234 + 0.968956i \(0.579522\pi\)
\(410\) −2.00000 4.00000i −0.0987730 0.197546i
\(411\) −18.0000 −0.887875
\(412\) 14.0000i 0.689730i
\(413\) 0 0
\(414\) −4.00000 −0.196589
\(415\) 4.00000 + 8.00000i 0.196352 + 0.392705i
\(416\) 6.00000 0.294174
\(417\) 20.0000i 0.979404i
\(418\) 0 0
\(419\) −10.0000 −0.488532 −0.244266 0.969708i \(-0.578547\pi\)
−0.244266 + 0.969708i \(0.578547\pi\)
\(420\) 0 0
\(421\) 22.0000 1.07221 0.536107 0.844150i \(-0.319894\pi\)
0.536107 + 0.844150i \(0.319894\pi\)
\(422\) 12.0000i 0.584151i
\(423\) 8.00000i 0.388973i
\(424\) 6.00000 0.291386
\(425\) 8.00000 + 6.00000i 0.388057 + 0.291043i
\(426\) −12.0000 −0.581402
\(427\) 0 0
\(428\) 12.0000i 0.580042i
\(429\) 12.0000 0.579365
\(430\) 8.00000 4.00000i 0.385794 0.192897i
\(431\) 32.0000 1.54139 0.770693 0.637207i \(-0.219910\pi\)
0.770693 + 0.637207i \(0.219910\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 4.00000i 0.192228i 0.995370 + 0.0961139i \(0.0306413\pi\)
−0.995370 + 0.0961139i \(0.969359\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 10.0000 0.478913
\(437\) 0 0
\(438\) 4.00000i 0.191127i
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) −2.00000 4.00000i −0.0953463 0.190693i
\(441\) 0 0
\(442\) 12.0000i 0.570782i
\(443\) 36.0000i 1.71041i 0.518289 + 0.855206i \(0.326569\pi\)
−0.518289 + 0.855206i \(0.673431\pi\)
\(444\) −2.00000 −0.0949158
\(445\) −20.0000 + 10.0000i −0.948091 + 0.474045i
\(446\) 26.0000 1.23114
\(447\) 20.0000i 0.945968i
\(448\) 0 0
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) −4.00000 3.00000i −0.188562 0.141421i
\(451\) −4.00000 −0.188353
\(452\) 6.00000i 0.282216i
\(453\) 8.00000i 0.375873i
\(454\) 28.0000 1.31411
\(455\) 0 0
\(456\) 0 0
\(457\) 32.0000i 1.49690i −0.663193 0.748448i \(-0.730799\pi\)
0.663193 0.748448i \(-0.269201\pi\)
\(458\) 10.0000i 0.467269i
\(459\) 2.00000 0.0933520
\(460\) 4.00000 + 8.00000i 0.186501 + 0.373002i
\(461\) −12.0000 −0.558896 −0.279448 0.960161i \(-0.590151\pi\)
−0.279448 + 0.960161i \(0.590151\pi\)
\(462\) 0 0
\(463\) 6.00000i 0.278844i 0.990233 + 0.139422i \(0.0445244\pi\)
−0.990233 + 0.139422i \(0.955476\pi\)
\(464\) 0 0
\(465\) 8.00000 + 16.0000i 0.370991 + 0.741982i
\(466\) 14.0000 0.648537
\(467\) 12.0000i 0.555294i 0.960683 + 0.277647i \(0.0895545\pi\)
−0.960683 + 0.277647i \(0.910445\pi\)
\(468\) 6.00000i 0.277350i
\(469\) 0 0
\(470\) 16.0000 8.00000i 0.738025 0.369012i
\(471\) −22.0000 −1.01371
\(472\) 10.0000i 0.460287i
\(473\) 8.00000i 0.367840i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 6.00000i 0.274721i
\(478\) 20.0000i 0.914779i
\(479\) 20.0000 0.913823 0.456912 0.889512i \(-0.348956\pi\)
0.456912 + 0.889512i \(0.348956\pi\)
\(480\) −2.00000 + 1.00000i −0.0912871 + 0.0456435i
\(481\) −12.0000 −0.547153
\(482\) 22.0000i 1.00207i
\(483\) 0 0
\(484\) 7.00000 0.318182
\(485\) −8.00000 16.0000i −0.363261 0.726523i
\(486\) −1.00000 −0.0453609
\(487\) 18.0000i 0.815658i 0.913058 + 0.407829i \(0.133714\pi\)
−0.913058 + 0.407829i \(0.866286\pi\)
\(488\) 2.00000i 0.0905357i
\(489\) −16.0000 −0.723545
\(490\) 0 0
\(491\) −18.0000 −0.812329 −0.406164 0.913800i \(-0.633134\pi\)
−0.406164 + 0.913800i \(0.633134\pi\)
\(492\) 2.00000i 0.0901670i
\(493\) 0 0
\(494\) 0 0
\(495\) −4.00000 + 2.00000i −0.179787 + 0.0898933i
\(496\) 8.00000 0.359211
\(497\) 0 0
\(498\) 4.00000i 0.179244i
\(499\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(500\) −2.00000 + 11.0000i −0.0894427 + 0.491935i
\(501\) −12.0000 −0.536120
\(502\) 18.0000i 0.803379i
\(503\) 24.0000i 1.07011i 0.844818 + 0.535054i \(0.179709\pi\)
−0.844818 + 0.535054i \(0.820291\pi\)
\(504\) 0 0
\(505\) 16.0000 8.00000i 0.711991 0.355995i
\(506\) 8.00000 0.355643
\(507\) 23.0000i 1.02147i
\(508\) 2.00000i 0.0887357i
\(509\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(510\) −2.00000 4.00000i −0.0885615 0.177123i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 18.0000 0.793946
\(515\) 14.0000 + 28.0000i 0.616914 + 1.23383i
\(516\) −4.00000 −0.176090
\(517\) 16.0000i 0.703679i
\(518\) 0 0
\(519\) −14.0000 −0.614532
\(520\) −12.0000 + 6.00000i −0.526235 + 0.263117i
\(521\) −22.0000 −0.963837 −0.481919 0.876216i \(-0.660060\pi\)
−0.481919 + 0.876216i \(0.660060\pi\)
\(522\) 0 0
\(523\) 16.0000i 0.699631i −0.936819 0.349816i \(-0.886244\pi\)
0.936819 0.349816i \(-0.113756\pi\)
\(524\) −18.0000 −0.786334
\(525\) 0 0
\(526\) 4.00000 0.174408
\(527\) 16.0000i 0.696971i
\(528\) 2.00000i 0.0870388i
\(529\) 7.00000 0.304348
\(530\) −12.0000 + 6.00000i −0.521247 + 0.260623i
\(531\) −10.0000 −0.433963
\(532\) 0 0
\(533\) 12.0000i 0.519778i
\(534\) 10.0000 0.432742
\(535\) −12.0000 24.0000i −0.518805 1.03761i
\(536\) 8.00000 0.345547
\(537\) 10.0000i 0.431532i
\(538\) 0 0
\(539\) 0 0
\(540\) 1.00000 + 2.00000i 0.0430331 + 0.0860663i
\(541\) −38.0000 −1.63375 −0.816874 0.576816i \(-0.804295\pi\)
−0.816874 + 0.576816i \(0.804295\pi\)
\(542\) 8.00000i 0.343629i
\(543\) 2.00000i 0.0858282i
\(544\) −2.00000 −0.0857493
\(545\) −20.0000 + 10.0000i −0.856706 + 0.428353i
\(546\) 0 0
\(547\) 28.0000i 1.19719i 0.801050 + 0.598597i \(0.204275\pi\)
−0.801050 + 0.598597i \(0.795725\pi\)
\(548\) 18.0000i 0.768922i
\(549\) 2.00000 0.0853579
\(550\) 8.00000 + 6.00000i 0.341121 + 0.255841i
\(551\) 0 0
\(552\) 4.00000i 0.170251i
\(553\) 0 0
\(554\) 2.00000 0.0849719
\(555\) 4.00000 2.00000i 0.169791 0.0848953i
\(556\) 20.0000 0.848189
\(557\) 18.0000i 0.762684i 0.924434 + 0.381342i \(0.124538\pi\)
−0.924434 + 0.381342i \(0.875462\pi\)
\(558\) 8.00000i 0.338667i
\(559\) −24.0000 −1.01509
\(560\) 0 0
\(561\) −4.00000 −0.168880
\(562\) 18.0000i 0.759284i
\(563\) 44.0000i 1.85438i 0.374593 + 0.927189i \(0.377783\pi\)
−0.374593 + 0.927189i \(0.622217\pi\)
\(564\) −8.00000 −0.336861
\(565\) 6.00000 + 12.0000i 0.252422 + 0.504844i
\(566\) 16.0000 0.672530
\(567\) 0 0
\(568\) 12.0000i 0.503509i
\(569\) 10.0000 0.419222 0.209611 0.977785i \(-0.432780\pi\)
0.209611 + 0.977785i \(0.432780\pi\)
\(570\) 0 0
\(571\) −8.00000 −0.334790 −0.167395 0.985890i \(-0.553535\pi\)
−0.167395 + 0.985890i \(0.553535\pi\)
\(572\) 12.0000i 0.501745i
\(573\) 12.0000i 0.501307i
\(574\) 0 0
\(575\) −16.0000 12.0000i −0.667246 0.500435i
\(576\) 1.00000 0.0416667
\(577\) 32.0000i 1.33218i 0.745873 + 0.666089i \(0.232033\pi\)
−0.745873 + 0.666089i \(0.767967\pi\)
\(578\) 13.0000i 0.540729i
\(579\) 4.00000 0.166234
\(580\) 0 0
\(581\) 0 0
\(582\) 8.00000i 0.331611i
\(583\) 12.0000i 0.496989i
\(584\) 4.00000 0.165521
\(585\) 6.00000 + 12.0000i 0.248069 + 0.496139i
\(586\) 6.00000 0.247858
\(587\) 12.0000i 0.495293i 0.968850 + 0.247647i \(0.0796572\pi\)
−0.968850 + 0.247647i \(0.920343\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 10.0000 + 20.0000i 0.411693 + 0.823387i
\(591\) 22.0000 0.904959
\(592\) 2.00000i 0.0821995i
\(593\) 6.00000i 0.246390i −0.992382 0.123195i \(-0.960686\pi\)
0.992382 0.123195i \(-0.0393141\pi\)
\(594\) 2.00000 0.0820610
\(595\) 0 0
\(596\) −20.0000 −0.819232
\(597\) 0 0
\(598\) 24.0000i 0.981433i
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 3.00000 4.00000i 0.122474 0.163299i
\(601\) −2.00000 −0.0815817 −0.0407909 0.999168i \(-0.512988\pi\)
−0.0407909 + 0.999168i \(0.512988\pi\)
\(602\) 0 0
\(603\) 8.00000i 0.325785i
\(604\) 8.00000 0.325515
\(605\) −14.0000 + 7.00000i −0.569181 + 0.284590i
\(606\) −8.00000 −0.324978
\(607\) 22.0000i 0.892952i 0.894795 + 0.446476i \(0.147321\pi\)
−0.894795 + 0.446476i \(0.852679\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) −2.00000 4.00000i −0.0809776 0.161955i
\(611\) −48.0000 −1.94187
\(612\) 2.00000i 0.0808452i
\(613\) 26.0000i 1.05013i 0.851062 + 0.525065i \(0.175959\pi\)
−0.851062 + 0.525065i \(0.824041\pi\)
\(614\) −12.0000 −0.484281
\(615\) −2.00000 4.00000i −0.0806478 0.161296i
\(616\) 0 0
\(617\) 2.00000i 0.0805170i −0.999189 0.0402585i \(-0.987182\pi\)
0.999189 0.0402585i \(-0.0128181\pi\)
\(618\) 14.0000i 0.563163i
\(619\) 20.0000 0.803868 0.401934 0.915669i \(-0.368338\pi\)
0.401934 + 0.915669i \(0.368338\pi\)
\(620\) −16.0000 + 8.00000i −0.642575 + 0.321288i
\(621\) −4.00000 −0.160514
\(622\) 12.0000i 0.481156i
\(623\) 0 0
\(624\) 6.00000 0.240192
\(625\) −7.00000 24.0000i −0.280000 0.960000i
\(626\) −4.00000 −0.159872
\(627\) 0 0
\(628\) 22.0000i 0.877896i
\(629\) 4.00000 0.159490
\(630\) 0 0
\(631\) 32.0000 1.27390 0.636950 0.770905i \(-0.280196\pi\)
0.636950 + 0.770905i \(0.280196\pi\)
\(632\) 0 0
\(633\) 12.0000i 0.476957i
\(634\) 2.00000 0.0794301
\(635\) −2.00000 4.00000i −0.0793676 0.158735i
\(636\) 6.00000 0.237915
\(637\) 0 0
\(638\) 0 0
\(639\) −12.0000 −0.474713
\(640\) −1.00000 2.00000i −0.0395285 0.0790569i
\(641\) 2.00000 0.0789953 0.0394976 0.999220i \(-0.487424\pi\)
0.0394976 + 0.999220i \(0.487424\pi\)
\(642\) 12.0000i 0.473602i
\(643\) 24.0000i 0.946468i 0.880937 + 0.473234i \(0.156913\pi\)
−0.880937 + 0.473234i \(0.843087\pi\)
\(644\) 0 0
\(645\) 8.00000 4.00000i 0.315000 0.157500i
\(646\) 0 0
\(647\) 48.0000i 1.88707i −0.331266 0.943537i \(-0.607476\pi\)
0.331266 0.943537i \(-0.392524\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) 20.0000 0.785069
\(650\) 18.0000 24.0000i 0.706018 0.941357i
\(651\) 0 0
\(652\) 16.0000i 0.626608i
\(653\) 26.0000i 1.01746i 0.860927 + 0.508729i \(0.169885\pi\)
−0.860927 + 0.508729i \(0.830115\pi\)
\(654\) 10.0000 0.391031
\(655\) 36.0000 18.0000i 1.40664 0.703318i
\(656\) −2.00000 −0.0780869
\(657\) 4.00000i 0.156055i
\(658\) 0 0
\(659\) 50.0000 1.94772 0.973862 0.227142i \(-0.0729380\pi\)
0.973862 + 0.227142i \(0.0729380\pi\)
\(660\) −2.00000 4.00000i −0.0778499 0.155700i
\(661\) −2.00000 −0.0777910 −0.0388955 0.999243i \(-0.512384\pi\)
−0.0388955 + 0.999243i \(0.512384\pi\)
\(662\) 8.00000i 0.310929i
\(663\) 12.0000i 0.466041i
\(664\) 4.00000 0.155230
\(665\) 0 0
\(666\) −2.00000 −0.0774984
\(667\) 0 0
\(668\) 12.0000i 0.464294i
\(669\) 26.0000 1.00522
\(670\) −16.0000 + 8.00000i −0.618134 + 0.309067i
\(671\) −4.00000 −0.154418
\(672\) 0 0
\(673\) 36.0000i 1.38770i 0.720121 + 0.693849i \(0.244086\pi\)
−0.720121 + 0.693849i \(0.755914\pi\)
\(674\) −28.0000 −1.07852
\(675\) −4.00000 3.00000i −0.153960 0.115470i
\(676\) 23.0000 0.884615
\(677\) 2.00000i 0.0768662i 0.999261 + 0.0384331i \(0.0122367\pi\)
−0.999261 + 0.0384331i \(0.987763\pi\)
\(678\) 6.00000i 0.230429i
\(679\) 0 0
\(680\) 4.00000 2.00000i 0.153393 0.0766965i
\(681\) 28.0000 1.07296
\(682\) 16.0000i 0.612672i
\(683\) 4.00000i 0.153056i −0.997067 0.0765279i \(-0.975617\pi\)
0.997067 0.0765279i \(-0.0243834\pi\)
\(684\) 0 0
\(685\) 18.0000 + 36.0000i 0.687745 + 1.37549i
\(686\) 0 0
\(687\) 10.0000i 0.381524i
\(688\) 4.00000i 0.152499i
\(689\) 36.0000 1.37149
\(690\) 4.00000 + 8.00000i 0.152277 + 0.304555i
\(691\) 8.00000 0.304334 0.152167 0.988355i \(-0.451375\pi\)
0.152167 + 0.988355i \(0.451375\pi\)
\(692\) 14.0000i 0.532200i
\(693\) 0 0
\(694\) 12.0000 0.455514
\(695\) −40.0000 + 20.0000i −1.51729 + 0.758643i
\(696\) 0 0
\(697\) 4.00000i 0.151511i
\(698\) 10.0000i 0.378506i
\(699\) 14.0000 0.529529
\(700\) 0 0
\(701\) 32.0000 1.20862 0.604312 0.796748i \(-0.293448\pi\)
0.604312 + 0.796748i \(0.293448\pi\)
\(702\) 6.00000i 0.226455i
\(703\) 0 0
\(704\) −2.00000 −0.0753778
\(705\) 16.0000 8.00000i 0.602595 0.301297i
\(706\) −14.0000 −0.526897
\(707\) 0 0
\(708\) 10.0000i 0.375823i
\(709\) −30.0000 −1.12667 −0.563337 0.826227i \(-0.690483\pi\)
−0.563337 + 0.826227i \(0.690483\pi\)
\(710\) 12.0000 + 24.0000i 0.450352 + 0.900704i
\(711\) 0 0
\(712\) 10.0000i 0.374766i
\(713\) 32.0000i 1.19841i
\(714\) 0 0
\(715\) −12.0000 24.0000i −0.448775 0.897549i
\(716\) 10.0000 0.373718
\(717\) 20.0000i 0.746914i
\(718\) 0 0
\(719\) −40.0000 −1.49175 −0.745874 0.666087i \(-0.767968\pi\)
−0.745874 + 0.666087i \(0.767968\pi\)
\(720\) −2.00000 + 1.00000i −0.0745356 + 0.0372678i
\(721\) 0 0
\(722\) 19.0000i 0.707107i
\(723\) 22.0000i 0.818189i
\(724\) 2.00000 0.0743294
\(725\) 0 0
\(726\) 7.00000 0.259794
\(727\) 18.0000i 0.667583i −0.942647 0.333792i \(-0.891672\pi\)
0.942647 0.333792i \(-0.108328\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) −8.00000 + 4.00000i −0.296093 + 0.148047i
\(731\) 8.00000 0.295891
\(732\) 2.00000i 0.0739221i
\(733\) 14.0000i 0.517102i 0.965998 + 0.258551i \(0.0832450\pi\)
−0.965998 + 0.258551i \(0.916755\pi\)
\(734\) −2.00000 −0.0738213
\(735\) 0 0
\(736\) 4.00000 0.147442
\(737\) 16.0000i 0.589368i
\(738\) 2.00000i 0.0736210i
\(739\) −40.0000 −1.47142 −0.735712 0.677295i \(-0.763152\pi\)
−0.735712 + 0.677295i \(0.763152\pi\)
\(740\) 2.00000 + 4.00000i 0.0735215 + 0.147043i
\(741\) 0 0
\(742\) 0 0
\(743\) 24.0000i 0.880475i −0.897881 0.440237i \(-0.854894\pi\)
0.897881 0.440237i \(-0.145106\pi\)
\(744\) 8.00000 0.293294
\(745\) 40.0000 20.0000i 1.46549 0.732743i
\(746\) −6.00000 −0.219676
\(747\) 4.00000i 0.146352i
\(748\) 4.00000i 0.146254i
\(749\) 0 0
\(750\) −2.00000 + 11.0000i −0.0730297 + 0.401663i
\(751\) 32.0000 1.16770 0.583848 0.811863i \(-0.301546\pi\)
0.583848 + 0.811863i \(0.301546\pi\)
\(752\) 8.00000i 0.291730i
\(753\) 18.0000i 0.655956i
\(754\) 0 0
\(755\) −16.0000 + 8.00000i −0.582300 + 0.291150i
\(756\) 0 0
\(757\) 2.00000i 0.0726912i −0.999339 0.0363456i \(-0.988428\pi\)
0.999339 0.0363456i \(-0.0115717\pi\)
\(758\) 20.0000i 0.726433i
\(759\) 8.00000 0.290382
\(760\) 0 0
\(761\) 18.0000 0.652499 0.326250 0.945284i \(-0.394215\pi\)
0.326250 + 0.945284i \(0.394215\pi\)
\(762\) 2.00000i 0.0724524i
\(763\) 0 0
\(764\) −12.0000 −0.434145
\(765\) −2.00000 4.00000i −0.0723102 0.144620i
\(766\) 16.0000 0.578103
\(767\) 60.0000i 2.16647i
\(768\) 1.00000i 0.0360844i
\(769\) −30.0000 −1.08183 −0.540914 0.841078i \(-0.681921\pi\)
−0.540914 + 0.841078i \(0.681921\pi\)
\(770\) 0 0
\(771\) 18.0000 0.648254
\(772\) 4.00000i 0.143963i
\(773\) 54.0000i 1.94225i 0.238581 + 0.971123i \(0.423318\pi\)
−0.238581 + 0.971123i \(0.576682\pi\)
\(774\) −4.00000 −0.143777
\(775\) 24.0000 32.0000i 0.862105 1.14947i
\(776\) −8.00000 −0.287183
\(777\) 0 0
\(778\) 20.0000i 0.717035i
\(779\) 0 0
\(780\) −12.0000 + 6.00000i −0.429669 + 0.214834i
\(781\) 24.0000 0.858788
\(782\) 8.00000i 0.286079i
\(783\) 0 0
\(784\) 0 0
\(785\) 22.0000 + 44.0000i 0.785214 + 1.57043i
\(786\) −18.0000 −0.642039
\(787\) 32.0000i 1.14068i 0.821410 + 0.570338i \(0.193188\pi\)
−0.821410 + 0.570338i \(0.806812\pi\)
\(788\) 22.0000i 0.783718i
\(789\) 4.00000 0.142404
\(790\) 0 0
\(791\) 0 0
\(792\) 2.00000i 0.0710669i
\(793\) 12.0000i 0.426132i
\(794\) −2.00000 −0.0709773
\(795\) −12.0000