Properties

Label 1470.2.g.b.589.1
Level $1470$
Weight $2$
Character 1470.589
Analytic conductor $11.738$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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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 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

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

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(-1.00000 - 2.00000i) q^{5} -1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(-1.00000 - 2.00000i) q^{5} -1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +(-2.00000 + 1.00000i) q^{10} +2.00000 q^{11} +1.00000i q^{12} -6.00000i q^{13} +(-2.00000 + 1.00000i) q^{15} +1.00000 q^{16} +4.00000i q^{17} +1.00000i q^{18} -6.00000 q^{19} +(1.00000 + 2.00000i) q^{20} -2.00000i q^{22} -8.00000i q^{23} +1.00000 q^{24} +(-3.00000 + 4.00000i) q^{25} -6.00000 q^{26} +1.00000i q^{27} -6.00000 q^{29} +(1.00000 + 2.00000i) q^{30} +2.00000 q^{31} -1.00000i q^{32} -2.00000i q^{33} +4.00000 q^{34} +1.00000 q^{36} -4.00000i q^{37} +6.00000i q^{38} -6.00000 q^{39} +(2.00000 - 1.00000i) q^{40} -2.00000 q^{41} +4.00000i q^{43} -2.00000 q^{44} +(1.00000 + 2.00000i) q^{45} -8.00000 q^{46} +8.00000i q^{47} -1.00000i q^{48} +(4.00000 + 3.00000i) q^{50} +4.00000 q^{51} +6.00000i q^{52} +6.00000i q^{53} +1.00000 q^{54} +(-2.00000 - 4.00000i) q^{55} +6.00000i q^{57} +6.00000i q^{58} -8.00000 q^{59} +(2.00000 - 1.00000i) q^{60} +10.0000 q^{61} -2.00000i q^{62} -1.00000 q^{64} +(-12.0000 + 6.00000i) q^{65} -2.00000 q^{66} -8.00000i q^{67} -4.00000i q^{68} -8.00000 q^{69} -6.00000 q^{71} -1.00000i q^{72} +14.0000i q^{73} -4.00000 q^{74} +(4.00000 + 3.00000i) q^{75} +6.00000 q^{76} +6.00000i q^{78} +12.0000 q^{79} +(-1.00000 - 2.00000i) q^{80} +1.00000 q^{81} +2.00000i q^{82} +8.00000i q^{83} +(8.00000 - 4.00000i) q^{85} +4.00000 q^{86} +6.00000i q^{87} +2.00000i q^{88} -10.0000 q^{89} +(2.00000 - 1.00000i) q^{90} +8.00000i q^{92} -2.00000i q^{93} +8.00000 q^{94} +(6.00000 + 12.0000i) q^{95} -1.00000 q^{96} -10.0000i q^{97} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{4} - 2q^{5} - 2q^{6} - 2q^{9} + O(q^{10}) \) \( 2q - 2q^{4} - 2q^{5} - 2q^{6} - 2q^{9} - 4q^{10} + 4q^{11} - 4q^{15} + 2q^{16} - 12q^{19} + 2q^{20} + 2q^{24} - 6q^{25} - 12q^{26} - 12q^{29} + 2q^{30} + 4q^{31} + 8q^{34} + 2q^{36} - 12q^{39} + 4q^{40} - 4q^{41} - 4q^{44} + 2q^{45} - 16q^{46} + 8q^{50} + 8q^{51} + 2q^{54} - 4q^{55} - 16q^{59} + 4q^{60} + 20q^{61} - 2q^{64} - 24q^{65} - 4q^{66} - 16q^{69} - 12q^{71} - 8q^{74} + 8q^{75} + 12q^{76} + 24q^{79} - 2q^{80} + 2q^{81} + 16q^{85} + 8q^{86} - 20q^{89} + 4q^{90} + 16q^{94} + 12q^{95} - 2q^{96} - 4q^{99} + O(q^{100}) \)

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
\(5\) −1.00000 2.00000i −0.447214 0.894427i
\(6\) −1.00000 −0.408248
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) −1.00000 −0.333333
\(10\) −2.00000 + 1.00000i −0.632456 + 0.316228i
\(11\) 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
\(15\) −2.00000 + 1.00000i −0.516398 + 0.258199i
\(16\) 1.00000 0.250000
\(17\) 4.00000i 0.970143i 0.874475 + 0.485071i \(0.161206\pi\)
−0.874475 + 0.485071i \(0.838794\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −6.00000 −1.37649 −0.688247 0.725476i \(-0.741620\pi\)
−0.688247 + 0.725476i \(0.741620\pi\)
\(20\) 1.00000 + 2.00000i 0.223607 + 0.447214i
\(21\) 0 0
\(22\) 2.00000i 0.426401i
\(23\) 8.00000i 1.66812i −0.551677 0.834058i \(-0.686012\pi\)
0.551677 0.834058i \(-0.313988\pi\)
\(24\) 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
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) 1.00000 + 2.00000i 0.182574 + 0.365148i
\(31\) 2.00000 0.359211 0.179605 0.983739i \(-0.442518\pi\)
0.179605 + 0.983739i \(0.442518\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 2.00000i 0.348155i
\(34\) 4.00000 0.685994
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 4.00000i 0.657596i −0.944400 0.328798i \(-0.893356\pi\)
0.944400 0.328798i \(-0.106644\pi\)
\(38\) 6.00000i 0.973329i
\(39\) −6.00000 −0.960769
\(40\) 2.00000 1.00000i 0.316228 0.158114i
\(41\) −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 \(0.0986555\pi\)
−0.952353 + 0.304997i \(0.901344\pi\)
\(44\) −2.00000 −0.301511
\(45\) 1.00000 + 2.00000i 0.149071 + 0.298142i
\(46\) −8.00000 −1.17954
\(47\) 8.00000i 1.16692i 0.812142 + 0.583460i \(0.198301\pi\)
−0.812142 + 0.583460i \(0.801699\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 0 0
\(50\) 4.00000 + 3.00000i 0.565685 + 0.424264i
\(51\) 4.00000 0.560112
\(52\) 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
\(55\) −2.00000 4.00000i −0.269680 0.539360i
\(56\) 0 0
\(57\) 6.00000i 0.794719i
\(58\) 6.00000i 0.787839i
\(59\) −8.00000 −1.04151 −0.520756 0.853706i \(-0.674350\pi\)
−0.520756 + 0.853706i \(0.674350\pi\)
\(60\) 2.00000 1.00000i 0.258199 0.129099i
\(61\) 10.0000 1.28037 0.640184 0.768221i \(-0.278858\pi\)
0.640184 + 0.768221i \(0.278858\pi\)
\(62\) 2.00000i 0.254000i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −12.0000 + 6.00000i −1.48842 + 0.744208i
\(66\) −2.00000 −0.246183
\(67\) 8.00000i 0.977356i −0.872464 0.488678i \(-0.837479\pi\)
0.872464 0.488678i \(-0.162521\pi\)
\(68\) 4.00000i 0.485071i
\(69\) −8.00000 −0.963087
\(70\) 0 0
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 14.0000i 1.63858i 0.573382 + 0.819288i \(0.305631\pi\)
−0.573382 + 0.819288i \(0.694369\pi\)
\(74\) −4.00000 −0.464991
\(75\) 4.00000 + 3.00000i 0.461880 + 0.346410i
\(76\) 6.00000 0.688247
\(77\) 0 0
\(78\) 6.00000i 0.679366i
\(79\) 12.0000 1.35011 0.675053 0.737769i \(-0.264121\pi\)
0.675053 + 0.737769i \(0.264121\pi\)
\(80\) −1.00000 2.00000i −0.111803 0.223607i
\(81\) 1.00000 0.111111
\(82\) 2.00000i 0.220863i
\(83\) 8.00000i 0.878114i 0.898459 + 0.439057i \(0.144687\pi\)
−0.898459 + 0.439057i \(0.855313\pi\)
\(84\) 0 0
\(85\) 8.00000 4.00000i 0.867722 0.433861i
\(86\) 4.00000 0.431331
\(87\) 6.00000i 0.643268i
\(88\) 2.00000i 0.213201i
\(89\) −10.0000 −1.06000 −0.529999 0.847998i \(-0.677808\pi\)
−0.529999 + 0.847998i \(0.677808\pi\)
\(90\) 2.00000 1.00000i 0.210819 0.105409i
\(91\) 0 0
\(92\) 8.00000i 0.834058i
\(93\) 2.00000i 0.207390i
\(94\) 8.00000 0.825137
\(95\) 6.00000 + 12.0000i 0.615587 + 1.23117i
\(96\) −1.00000 −0.102062
\(97\) 10.0000i 1.01535i −0.861550 0.507673i \(-0.830506\pi\)
0.861550 0.507673i \(-0.169494\pi\)
\(98\) 0 0
\(99\) −2.00000 −0.201008
\(100\) 3.00000 4.00000i 0.300000 0.400000i
\(101\) −10.0000 −0.995037 −0.497519 0.867453i \(-0.665755\pi\)
−0.497519 + 0.867453i \(0.665755\pi\)
\(102\) 4.00000i 0.396059i
\(103\) 8.00000i 0.788263i −0.919054 0.394132i \(-0.871045\pi\)
0.919054 0.394132i \(-0.128955\pi\)
\(104\) 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
\(109\) 14.0000 1.34096 0.670478 0.741929i \(-0.266089\pi\)
0.670478 + 0.741929i \(0.266089\pi\)
\(110\) −4.00000 + 2.00000i −0.381385 + 0.190693i
\(111\) −4.00000 −0.379663
\(112\) 0 0
\(113\) 6.00000i 0.564433i 0.959351 + 0.282216i \(0.0910696\pi\)
−0.959351 + 0.282216i \(0.908930\pi\)
\(114\) 6.00000 0.561951
\(115\) −16.0000 + 8.00000i −1.49201 + 0.746004i
\(116\) 6.00000 0.557086
\(117\) 6.00000i 0.554700i
\(118\) 8.00000i 0.736460i
\(119\) 0 0
\(120\) −1.00000 2.00000i −0.0912871 0.182574i
\(121\) −7.00000 −0.636364
\(122\) 10.0000i 0.905357i
\(123\) 2.00000i 0.180334i
\(124\) −2.00000 −0.179605
\(125\) 11.0000 + 2.00000i 0.983870 + 0.178885i
\(126\) 0 0
\(127\) 4.00000i 0.354943i −0.984126 0.177471i \(-0.943208\pi\)
0.984126 0.177471i \(-0.0567917\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 4.00000 0.352180
\(130\) 6.00000 + 12.0000i 0.526235 + 1.05247i
\(131\) 12.0000 1.04844 0.524222 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) 2.00000i 0.174078i
\(133\) 0 0
\(134\) −8.00000 −0.691095
\(135\) 2.00000 1.00000i 0.172133 0.0860663i
\(136\) −4.00000 −0.342997
\(137\) 6.00000i 0.512615i 0.966595 + 0.256307i \(0.0825059\pi\)
−0.966595 + 0.256307i \(0.917494\pi\)
\(138\) 8.00000i 0.681005i
\(139\) −14.0000 −1.18746 −0.593732 0.804663i \(-0.702346\pi\)
−0.593732 + 0.804663i \(0.702346\pi\)
\(140\) 0 0
\(141\) 8.00000 0.673722
\(142\) 6.00000i 0.503509i
\(143\) 12.0000i 1.00349i
\(144\) −1.00000 −0.0833333
\(145\) 6.00000 + 12.0000i 0.498273 + 0.996546i
\(146\) 14.0000 1.15865
\(147\) 0 0
\(148\) 4.00000i 0.328798i
\(149\) −10.0000 −0.819232 −0.409616 0.912258i \(-0.634337\pi\)
−0.409616 + 0.912258i \(0.634337\pi\)
\(150\) 3.00000 4.00000i 0.244949 0.326599i
\(151\) −8.00000 −0.651031 −0.325515 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) 6.00000i 0.486664i
\(153\) 4.00000i 0.323381i
\(154\) 0 0
\(155\) −2.00000 4.00000i −0.160644 0.321288i
\(156\) 6.00000 0.480384
\(157\) 22.0000i 1.75579i −0.478852 0.877896i \(-0.658947\pi\)
0.478852 0.877896i \(-0.341053\pi\)
\(158\) 12.0000i 0.954669i
\(159\) 6.00000 0.475831
\(160\) −2.00000 + 1.00000i −0.158114 + 0.0790569i
\(161\) 0 0
\(162\) 1.00000i 0.0785674i
\(163\) 4.00000i 0.313304i −0.987654 0.156652i \(-0.949930\pi\)
0.987654 0.156652i \(-0.0500701\pi\)
\(164\) 2.00000 0.156174
\(165\) −4.00000 + 2.00000i −0.311400 + 0.155700i
\(166\) 8.00000 0.620920
\(167\) 12.0000i 0.928588i −0.885681 0.464294i \(-0.846308\pi\)
0.885681 0.464294i \(-0.153692\pi\)
\(168\) 0 0
\(169\) −23.0000 −1.76923
\(170\) −4.00000 8.00000i −0.306786 0.613572i
\(171\) 6.00000 0.458831
\(172\) 4.00000i 0.304997i
\(173\) 8.00000i 0.608229i −0.952636 0.304114i \(-0.901639\pi\)
0.952636 0.304114i \(-0.0983605\pi\)
\(174\) 6.00000 0.454859
\(175\) 0 0
\(176\) 2.00000 0.150756
\(177\) 8.00000i 0.601317i
\(178\) 10.0000i 0.749532i
\(179\) −10.0000 −0.747435 −0.373718 0.927543i \(-0.621917\pi\)
−0.373718 + 0.927543i \(0.621917\pi\)
\(180\) −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
\(183\) 10.0000i 0.739221i
\(184\) 8.00000 0.589768
\(185\) −8.00000 + 4.00000i −0.588172 + 0.294086i
\(186\) −2.00000 −0.146647
\(187\) 8.00000i 0.585018i
\(188\) 8.00000i 0.583460i
\(189\) 0 0
\(190\) 12.0000 6.00000i 0.870572 0.435286i
\(191\) −18.0000 −1.30243 −0.651217 0.758891i \(-0.725741\pi\)
−0.651217 + 0.758891i \(0.725741\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) 8.00000i 0.575853i −0.957653 0.287926i \(-0.907034\pi\)
0.957653 0.287926i \(-0.0929658\pi\)
\(194\) −10.0000 −0.717958
\(195\) 6.00000 + 12.0000i 0.429669 + 0.859338i
\(196\) 0 0
\(197\) 2.00000i 0.142494i −0.997459 0.0712470i \(-0.977302\pi\)
0.997459 0.0712470i \(-0.0226979\pi\)
\(198\) 2.00000i 0.142134i
\(199\) 6.00000 0.425329 0.212664 0.977125i \(-0.431786\pi\)
0.212664 + 0.977125i \(0.431786\pi\)
\(200\) −4.00000 3.00000i −0.282843 0.212132i
\(201\) −8.00000 −0.564276
\(202\) 10.0000i 0.703598i
\(203\) 0 0
\(204\) −4.00000 −0.280056
\(205\) 2.00000 + 4.00000i 0.139686 + 0.279372i
\(206\) −8.00000 −0.557386
\(207\) 8.00000i 0.556038i
\(208\) 6.00000i 0.416025i
\(209\) −12.0000 −0.830057
\(210\) 0 0
\(211\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(212\) 6.00000i 0.412082i
\(213\) 6.00000i 0.411113i
\(214\) −12.0000 −0.820303
\(215\) 8.00000 4.00000i 0.545595 0.272798i
\(216\) −1.00000 −0.0680414
\(217\) 0 0
\(218\) 14.0000i 0.948200i
\(219\) 14.0000 0.946032
\(220\) 2.00000 + 4.00000i 0.134840 + 0.269680i
\(221\) 24.0000 1.61441
\(222\) 4.00000i 0.268462i
\(223\) 8.00000i 0.535720i 0.963458 + 0.267860i \(0.0863164\pi\)
−0.963458 + 0.267860i \(0.913684\pi\)
\(224\) 0 0
\(225\) 3.00000 4.00000i 0.200000 0.266667i
\(226\) 6.00000 0.399114
\(227\) 8.00000i 0.530979i −0.964114 0.265489i \(-0.914466\pi\)
0.964114 0.265489i \(-0.0855335\pi\)
\(228\) 6.00000i 0.397360i
\(229\) 14.0000 0.925146 0.462573 0.886581i \(-0.346926\pi\)
0.462573 + 0.886581i \(0.346926\pi\)
\(230\) 8.00000 + 16.0000i 0.527504 + 1.05501i
\(231\) 0 0
\(232\) 6.00000i 0.393919i
\(233\) 10.0000i 0.655122i −0.944830 0.327561i \(-0.893773\pi\)
0.944830 0.327561i \(-0.106227\pi\)
\(234\) 6.00000 0.392232
\(235\) 16.0000 8.00000i 1.04372 0.521862i
\(236\) 8.00000 0.520756
\(237\) 12.0000i 0.779484i
\(238\) 0 0
\(239\) −26.0000 −1.68180 −0.840900 0.541190i \(-0.817974\pi\)
−0.840900 + 0.541190i \(0.817974\pi\)
\(240\) −2.00000 + 1.00000i −0.129099 + 0.0645497i
\(241\) 26.0000 1.67481 0.837404 0.546585i \(-0.184072\pi\)
0.837404 + 0.546585i \(0.184072\pi\)
\(242\) 7.00000i 0.449977i
\(243\) 1.00000i 0.0641500i
\(244\) −10.0000 −0.640184
\(245\) 0 0
\(246\) 2.00000 0.127515
\(247\) 36.0000i 2.29063i
\(248\) 2.00000i 0.127000i
\(249\) 8.00000 0.506979
\(250\) 2.00000 11.0000i 0.126491 0.695701i
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 16.0000i 1.00591i
\(254\) −4.00000 −0.250982
\(255\) −4.00000 8.00000i −0.250490 0.500979i
\(256\) 1.00000 0.0625000
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 4.00000i 0.249029i
\(259\) 0 0
\(260\) 12.0000 6.00000i 0.744208 0.372104i
\(261\) 6.00000 0.371391
\(262\) 12.0000i 0.741362i
\(263\) 16.0000i 0.986602i 0.869859 + 0.493301i \(0.164210\pi\)
−0.869859 + 0.493301i \(0.835790\pi\)
\(264\) 2.00000 0.123091
\(265\) 12.0000 6.00000i 0.737154 0.368577i
\(266\) 0 0
\(267\) 10.0000i 0.611990i
\(268\) 8.00000i 0.488678i
\(269\) 18.0000 1.09748 0.548740 0.835993i \(-0.315108\pi\)
0.548740 + 0.835993i \(0.315108\pi\)
\(270\) −1.00000 2.00000i −0.0608581 0.121716i
\(271\) −10.0000 −0.607457 −0.303728 0.952759i \(-0.598232\pi\)
−0.303728 + 0.952759i \(0.598232\pi\)
\(272\) 4.00000i 0.242536i
\(273\) 0 0
\(274\) 6.00000 0.362473
\(275\) −6.00000 + 8.00000i −0.361814 + 0.482418i
\(276\) 8.00000 0.481543
\(277\) 28.0000i 1.68236i −0.540758 0.841178i \(-0.681862\pi\)
0.540758 0.841178i \(-0.318138\pi\)
\(278\) 14.0000i 0.839664i
\(279\) −2.00000 −0.119737
\(280\) 0 0
\(281\) 30.0000 1.78965 0.894825 0.446417i \(-0.147300\pi\)
0.894825 + 0.446417i \(0.147300\pi\)
\(282\) 8.00000i 0.476393i
\(283\) 20.0000i 1.18888i −0.804141 0.594438i \(-0.797374\pi\)
0.804141 0.594438i \(-0.202626\pi\)
\(284\) 6.00000 0.356034
\(285\) 12.0000 6.00000i 0.710819 0.355409i
\(286\) −12.0000 −0.709575
\(287\) 0 0
\(288\) 1.00000i 0.0589256i
\(289\) 1.00000 0.0588235
\(290\) 12.0000 6.00000i 0.704664 0.352332i
\(291\) −10.0000 −0.586210
\(292\) 14.0000i 0.819288i
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 0 0
\(295\) 8.00000 + 16.0000i 0.465778 + 0.931556i
\(296\) 4.00000 0.232495
\(297\) 2.00000i 0.116052i
\(298\) 10.0000i 0.579284i
\(299\) −48.0000 −2.77591
\(300\) −4.00000 3.00000i −0.230940 0.173205i
\(301\) 0 0
\(302\) 8.00000i 0.460348i
\(303\) 10.0000i 0.574485i
\(304\) −6.00000 −0.344124
\(305\) −10.0000 20.0000i −0.572598 1.14520i
\(306\) −4.00000 −0.228665
\(307\) 12.0000i 0.684876i −0.939540 0.342438i \(-0.888747\pi\)
0.939540 0.342438i \(-0.111253\pi\)
\(308\) 0 0
\(309\) −8.00000 −0.455104
\(310\) −4.00000 + 2.00000i −0.227185 + 0.113592i
\(311\) −24.0000 −1.36092 −0.680458 0.732787i \(-0.738219\pi\)
−0.680458 + 0.732787i \(0.738219\pi\)
\(312\) 6.00000i 0.339683i
\(313\) 2.00000i 0.113047i 0.998401 + 0.0565233i \(0.0180015\pi\)
−0.998401 + 0.0565233i \(0.981998\pi\)
\(314\) −22.0000 −1.24153
\(315\) 0 0
\(316\) −12.0000 −0.675053
\(317\) 2.00000i 0.112331i 0.998421 + 0.0561656i \(0.0178875\pi\)
−0.998421 + 0.0561656i \(0.982113\pi\)
\(318\) 6.00000i 0.336463i
\(319\) −12.0000 −0.671871
\(320\) 1.00000 + 2.00000i 0.0559017 + 0.111803i
\(321\) −12.0000 −0.669775
\(322\) 0 0
\(323\) 24.0000i 1.33540i
\(324\) −1.00000 −0.0555556
\(325\) 24.0000 + 18.0000i 1.33128 + 0.998460i
\(326\) −4.00000 −0.221540
\(327\) 14.0000i 0.774202i
\(328\) 2.00000i 0.110432i
\(329\) 0 0
\(330\) 2.00000 + 4.00000i 0.110096 + 0.220193i
\(331\) −8.00000 −0.439720 −0.219860 0.975531i \(-0.570560\pi\)
−0.219860 + 0.975531i \(0.570560\pi\)
\(332\) 8.00000i 0.439057i
\(333\) 4.00000i 0.219199i
\(334\) −12.0000 −0.656611
\(335\) −16.0000 + 8.00000i −0.874173 + 0.437087i
\(336\) 0 0
\(337\) 8.00000i 0.435788i 0.975972 + 0.217894i \(0.0699187\pi\)
−0.975972 + 0.217894i \(0.930081\pi\)
\(338\) 23.0000i 1.25104i
\(339\) 6.00000 0.325875
\(340\) −8.00000 + 4.00000i −0.433861 + 0.216930i
\(341\) 4.00000 0.216612
\(342\) 6.00000i 0.324443i
\(343\) 0 0
\(344\) −4.00000 −0.215666
\(345\) 8.00000 + 16.0000i 0.430706 + 0.861411i
\(346\) −8.00000 −0.430083
\(347\) 36.0000i 1.93258i −0.257454 0.966291i \(-0.582883\pi\)
0.257454 0.966291i \(-0.417117\pi\)
\(348\) 6.00000i 0.321634i
\(349\) −26.0000 −1.39175 −0.695874 0.718164i \(-0.744983\pi\)
−0.695874 + 0.718164i \(0.744983\pi\)
\(350\) 0 0
\(351\) 6.00000 0.320256
\(352\) 2.00000i 0.106600i
\(353\) 20.0000i 1.06449i −0.846590 0.532246i \(-0.821348\pi\)
0.846590 0.532246i \(-0.178652\pi\)
\(354\) 8.00000 0.425195
\(355\) 6.00000 + 12.0000i 0.318447 + 0.636894i
\(356\) 10.0000 0.529999
\(357\) 0 0
\(358\) 10.0000i 0.528516i
\(359\) −6.00000 −0.316668 −0.158334 0.987386i \(-0.550612\pi\)
−0.158334 + 0.987386i \(0.550612\pi\)
\(360\) −2.00000 + 1.00000i −0.105409 + 0.0527046i
\(361\) 17.0000 0.894737
\(362\) 2.00000i 0.105118i
\(363\) 7.00000i 0.367405i
\(364\) 0 0
\(365\) 28.0000 14.0000i 1.46559 0.732793i
\(366\) −10.0000 −0.522708
\(367\) 32.0000i 1.67039i −0.549957 0.835193i \(-0.685356\pi\)
0.549957 0.835193i \(-0.314644\pi\)
\(368\) 8.00000i 0.417029i
\(369\) 2.00000 0.104116
\(370\) 4.00000 + 8.00000i 0.207950 + 0.415900i
\(371\) 0 0
\(372\) 2.00000i 0.103695i
\(373\) 24.0000i 1.24267i −0.783544 0.621336i \(-0.786590\pi\)
0.783544 0.621336i \(-0.213410\pi\)
\(374\) 8.00000 0.413670
\(375\) 2.00000 11.0000i 0.103280 0.568038i
\(376\) −8.00000 −0.412568
\(377\) 36.0000i 1.85409i
\(378\) 0 0
\(379\) −20.0000 −1.02733 −0.513665 0.857991i \(-0.671713\pi\)
−0.513665 + 0.857991i \(0.671713\pi\)
\(380\) −6.00000 12.0000i −0.307794 0.615587i
\(381\) −4.00000 −0.204926
\(382\) 18.0000i 0.920960i
\(383\) 20.0000i 1.02195i −0.859595 0.510976i \(-0.829284\pi\)
0.859595 0.510976i \(-0.170716\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) −8.00000 −0.407189
\(387\) 4.00000i 0.203331i
\(388\) 10.0000i 0.507673i
\(389\) −2.00000 −0.101404 −0.0507020 0.998714i \(-0.516146\pi\)
−0.0507020 + 0.998714i \(0.516146\pi\)
\(390\) 12.0000 6.00000i 0.607644 0.303822i
\(391\) 32.0000 1.61831
\(392\) 0 0
\(393\) 12.0000i 0.605320i
\(394\) −2.00000 −0.100759
\(395\) −12.0000 24.0000i −0.603786 1.20757i
\(396\) 2.00000 0.100504
\(397\) 2.00000i 0.100377i −0.998740 0.0501886i \(-0.984018\pi\)
0.998740 0.0501886i \(-0.0159822\pi\)
\(398\) 6.00000i 0.300753i
\(399\) 0 0
\(400\) −3.00000 + 4.00000i −0.150000 + 0.200000i
\(401\) −14.0000 −0.699127 −0.349563 0.936913i \(-0.613670\pi\)
−0.349563 + 0.936913i \(0.613670\pi\)
\(402\) 8.00000i 0.399004i
\(403\) 12.0000i 0.597763i
\(404\) 10.0000 0.497519
\(405\) −1.00000 2.00000i −0.0496904 0.0993808i
\(406\) 0 0
\(407\) 8.00000i 0.396545i
\(408\) 4.00000i 0.198030i
\(409\) 26.0000 1.28562 0.642809 0.766027i \(-0.277769\pi\)
0.642809 + 0.766027i \(0.277769\pi\)
\(410\) 4.00000 2.00000i 0.197546 0.0987730i
\(411\) 6.00000 0.295958
\(412\) 8.00000i 0.394132i
\(413\) 0 0
\(414\) 8.00000 0.393179
\(415\) 16.0000 8.00000i 0.785409 0.392705i
\(416\) −6.00000 −0.294174
\(417\) 14.0000i 0.685583i
\(418\) 12.0000i 0.586939i
\(419\) 20.0000 0.977064 0.488532 0.872546i \(-0.337533\pi\)
0.488532 + 0.872546i \(0.337533\pi\)
\(420\) 0 0
\(421\) 34.0000 1.65706 0.828529 0.559946i \(-0.189178\pi\)
0.828529 + 0.559946i \(0.189178\pi\)
\(422\) 0 0
\(423\) 8.00000i 0.388973i
\(424\) −6.00000 −0.291386
\(425\) −16.0000 12.0000i −0.776114 0.582086i
\(426\) 6.00000 0.290701
\(427\) 0 0
\(428\) 12.0000i 0.580042i
\(429\) −12.0000 −0.579365
\(430\) −4.00000 8.00000i −0.192897 0.385794i
\(431\) 2.00000 0.0963366 0.0481683 0.998839i \(-0.484662\pi\)
0.0481683 + 0.998839i \(0.484662\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 26.0000i 1.24948i 0.780833 + 0.624740i \(0.214795\pi\)
−0.780833 + 0.624740i \(0.785205\pi\)
\(434\) 0 0
\(435\) 12.0000 6.00000i 0.575356 0.287678i
\(436\) −14.0000 −0.670478
\(437\) 48.0000i 2.29615i
\(438\) 14.0000i 0.668946i
\(439\) −18.0000 −0.859093 −0.429547 0.903045i \(-0.641327\pi\)
−0.429547 + 0.903045i \(0.641327\pi\)
\(440\) 4.00000 2.00000i 0.190693 0.0953463i
\(441\) 0 0
\(442\) 24.0000i 1.14156i
\(443\) 12.0000i 0.570137i −0.958507 0.285069i \(-0.907984\pi\)
0.958507 0.285069i \(-0.0920164\pi\)
\(444\) 4.00000 0.189832
\(445\) 10.0000 + 20.0000i 0.474045 + 0.948091i
\(446\) 8.00000 0.378811
\(447\) 10.0000i 0.472984i
\(448\) 0 0
\(449\) 6.00000 0.283158 0.141579 0.989927i \(-0.454782\pi\)
0.141579 + 0.989927i \(0.454782\pi\)
\(450\) −4.00000 3.00000i −0.188562 0.141421i
\(451\) −4.00000 −0.188353
\(452\) 6.00000i 0.282216i
\(453\) 8.00000i 0.375873i
\(454\) −8.00000 −0.375459
\(455\) 0 0
\(456\) −6.00000 −0.280976
\(457\) 28.0000i 1.30978i −0.755722 0.654892i \(-0.772714\pi\)
0.755722 0.654892i \(-0.227286\pi\)
\(458\) 14.0000i 0.654177i
\(459\) −4.00000 −0.186704
\(460\) 16.0000 8.00000i 0.746004 0.373002i
\(461\) 18.0000 0.838344 0.419172 0.907907i \(-0.362320\pi\)
0.419172 + 0.907907i \(0.362320\pi\)
\(462\) 0 0
\(463\) 36.0000i 1.67306i 0.547920 + 0.836531i \(0.315420\pi\)
−0.547920 + 0.836531i \(0.684580\pi\)
\(464\) −6.00000 −0.278543
\(465\) −4.00000 + 2.00000i −0.185496 + 0.0927478i
\(466\) −10.0000 −0.463241
\(467\) 24.0000i 1.11059i −0.831654 0.555294i \(-0.812606\pi\)
0.831654 0.555294i \(-0.187394\pi\)
\(468\) 6.00000i 0.277350i
\(469\) 0 0
\(470\) −8.00000 16.0000i −0.369012 0.738025i
\(471\) −22.0000 −1.01371
\(472\) 8.00000i 0.368230i
\(473\) 8.00000i 0.367840i
\(474\) −12.0000 −0.551178
\(475\) 18.0000 24.0000i 0.825897 1.10120i
\(476\) 0 0
\(477\) 6.00000i 0.274721i
\(478\) 26.0000i 1.18921i
\(479\) 8.00000 0.365529 0.182765 0.983157i \(-0.441495\pi\)
0.182765 + 0.983157i \(0.441495\pi\)
\(480\) 1.00000 + 2.00000i 0.0456435 + 0.0912871i
\(481\) −24.0000 −1.09431
\(482\) 26.0000i 1.18427i
\(483\) 0 0
\(484\) 7.00000 0.318182
\(485\) −20.0000 + 10.0000i −0.908153 + 0.454077i
\(486\) −1.00000 −0.0453609
\(487\) 12.0000i 0.543772i −0.962329 0.271886i \(-0.912353\pi\)
0.962329 0.271886i \(-0.0876473\pi\)
\(488\) 10.0000i 0.452679i
\(489\) −4.00000 −0.180886
\(490\) 0 0
\(491\) −30.0000 −1.35388 −0.676941 0.736038i \(-0.736695\pi\)
−0.676941 + 0.736038i \(0.736695\pi\)
\(492\) 2.00000i 0.0901670i
\(493\) 24.0000i 1.08091i
\(494\) 36.0000 1.61972
\(495\) 2.00000 + 4.00000i 0.0898933 + 0.179787i
\(496\) 2.00000 0.0898027
\(497\) 0 0
\(498\) 8.00000i 0.358489i
\(499\) 12.0000 0.537194 0.268597 0.963253i \(-0.413440\pi\)
0.268597 + 0.963253i \(0.413440\pi\)
\(500\) −11.0000 2.00000i −0.491935 0.0894427i
\(501\) −12.0000 −0.536120
\(502\) 0 0
\(503\) 12.0000i 0.535054i 0.963550 + 0.267527i \(0.0862064\pi\)
−0.963550 + 0.267527i \(0.913794\pi\)
\(504\) 0 0
\(505\) 10.0000 + 20.0000i 0.444994 + 0.889988i
\(506\) −16.0000 −0.711287
\(507\) 23.0000i 1.02147i
\(508\) 4.00000i 0.177471i
\(509\) 30.0000 1.32973 0.664863 0.746965i \(-0.268490\pi\)
0.664863 + 0.746965i \(0.268490\pi\)
\(510\) −8.00000 + 4.00000i −0.354246 + 0.177123i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 6.00000i 0.264906i
\(514\) 0 0
\(515\) −16.0000 + 8.00000i −0.705044 + 0.352522i
\(516\) −4.00000 −0.176090
\(517\) 16.0000i 0.703679i
\(518\) 0 0
\(519\) −8.00000 −0.351161
\(520\) −6.00000 12.0000i −0.263117 0.526235i
\(521\) 26.0000 1.13908 0.569540 0.821963i \(-0.307121\pi\)
0.569540 + 0.821963i \(0.307121\pi\)
\(522\) 6.00000i 0.262613i
\(523\) 28.0000i 1.22435i 0.790721 + 0.612177i \(0.209706\pi\)
−0.790721 + 0.612177i \(0.790294\pi\)
\(524\) −12.0000 −0.524222
\(525\) 0 0
\(526\) 16.0000 0.697633
\(527\) 8.00000i 0.348485i
\(528\) 2.00000i 0.0870388i
\(529\) −41.0000 −1.78261
\(530\) −6.00000 12.0000i −0.260623 0.521247i
\(531\) 8.00000 0.347170
\(532\) 0 0
\(533\) 12.0000i 0.519778i
\(534\) 10.0000 0.432742
\(535\) −24.0000 + 12.0000i −1.03761 + 0.518805i
\(536\) 8.00000 0.345547
\(537\) 10.0000i 0.431532i
\(538\) 18.0000i 0.776035i
\(539\) 0 0
\(540\) −2.00000 + 1.00000i −0.0860663 + 0.0430331i
\(541\) 22.0000 0.945854 0.472927 0.881102i \(-0.343197\pi\)
0.472927 + 0.881102i \(0.343197\pi\)
\(542\) 10.0000i 0.429537i
\(543\) 2.00000i 0.0858282i
\(544\) 4.00000 0.171499
\(545\) −14.0000 28.0000i −0.599694 1.19939i
\(546\) 0 0
\(547\) 40.0000i 1.71028i −0.518400 0.855138i \(-0.673472\pi\)
0.518400 0.855138i \(-0.326528\pi\)
\(548\) 6.00000i 0.256307i
\(549\) −10.0000 −0.426790
\(550\) 8.00000 + 6.00000i 0.341121 + 0.255841i
\(551\) 36.0000 1.53365
\(552\) 8.00000i 0.340503i
\(553\) 0 0
\(554\) −28.0000 −1.18961
\(555\) 4.00000 + 8.00000i 0.169791 + 0.339581i
\(556\) 14.0000 0.593732
\(557\) 42.0000i 1.77960i 0.456354 + 0.889799i \(0.349155\pi\)
−0.456354 + 0.889799i \(0.650845\pi\)
\(558\) 2.00000i 0.0846668i
\(559\) 24.0000 1.01509
\(560\) 0 0
\(561\) 8.00000 0.337760
\(562\) 30.0000i 1.26547i
\(563\) 4.00000i 0.168580i 0.996441 + 0.0842900i \(0.0268622\pi\)
−0.996441 + 0.0842900i \(0.973138\pi\)
\(564\) −8.00000 −0.336861
\(565\) 12.0000 6.00000i 0.504844 0.252422i
\(566\) −20.0000 −0.840663
\(567\) 0 0
\(568\) 6.00000i 0.251754i
\(569\) 46.0000 1.92842 0.964210 0.265139i \(-0.0854179\pi\)
0.964210 + 0.265139i \(0.0854179\pi\)
\(570\) −6.00000 12.0000i −0.251312 0.502625i
\(571\) 4.00000 0.167395 0.0836974 0.996491i \(-0.473327\pi\)
0.0836974 + 0.996491i \(0.473327\pi\)
\(572\) 12.0000i 0.501745i
\(573\) 18.0000i 0.751961i
\(574\) 0 0
\(575\) 32.0000 + 24.0000i 1.33449 + 1.00087i
\(576\) 1.00000 0.0416667
\(577\) 26.0000i 1.08239i −0.840896 0.541197i \(-0.817971\pi\)
0.840896 0.541197i \(-0.182029\pi\)
\(578\) 1.00000i 0.0415945i
\(579\) −8.00000 −0.332469
\(580\) −6.00000 12.0000i −0.249136 0.498273i
\(581\) 0 0
\(582\) 10.0000i 0.414513i
\(583\) 12.0000i 0.496989i
\(584\) −14.0000 −0.579324
\(585\) 12.0000 6.00000i 0.496139 0.248069i
\(586\) 0 0
\(587\) 12.0000i 0.495293i −0.968850 0.247647i \(-0.920343\pi\)
0.968850 0.247647i \(-0.0796572\pi\)
\(588\) 0 0
\(589\) −12.0000 −0.494451
\(590\) 16.0000 8.00000i 0.658710 0.329355i
\(591\) −2.00000 −0.0822690
\(592\) 4.00000i 0.164399i
\(593\) 12.0000i 0.492781i −0.969171 0.246390i \(-0.920755\pi\)
0.969171 0.246390i \(-0.0792446\pi\)
\(594\) 2.00000 0.0820610
\(595\) 0 0
\(596\) 10.0000 0.409616
\(597\) 6.00000i 0.245564i
\(598\) 48.0000i 1.96287i
\(599\) −30.0000 −1.22577 −0.612883 0.790173i \(-0.709990\pi\)
−0.612883 + 0.790173i \(0.709990\pi\)
\(600\) −3.00000 + 4.00000i −0.122474 + 0.163299i
\(601\) −38.0000 −1.55005 −0.775026 0.631929i \(-0.782263\pi\)
−0.775026 + 0.631929i \(0.782263\pi\)
\(602\) 0 0
\(603\) 8.00000i 0.325785i
\(604\) 8.00000 0.325515
\(605\) 7.00000 + 14.0000i 0.284590 + 0.569181i
\(606\) 10.0000 0.406222
\(607\) 8.00000i 0.324710i 0.986732 + 0.162355i \(0.0519090\pi\)
−0.986732 + 0.162355i \(0.948091\pi\)
\(608\) 6.00000i 0.243332i
\(609\) 0 0
\(610\) −20.0000 + 10.0000i −0.809776 + 0.404888i
\(611\) 48.0000 1.94187
\(612\) 4.00000i 0.161690i
\(613\) 28.0000i 1.13091i 0.824779 + 0.565455i \(0.191299\pi\)
−0.824779 + 0.565455i \(0.808701\pi\)
\(614\) −12.0000 −0.484281
\(615\) 4.00000 2.00000i 0.161296 0.0806478i
\(616\) 0 0
\(617\) 26.0000i 1.04672i 0.852111 + 0.523360i \(0.175322\pi\)
−0.852111 + 0.523360i \(0.824678\pi\)
\(618\) 8.00000i 0.321807i
\(619\) −22.0000 −0.884255 −0.442127 0.896952i \(-0.645776\pi\)
−0.442127 + 0.896952i \(0.645776\pi\)
\(620\) 2.00000 + 4.00000i 0.0803219 + 0.160644i
\(621\) 8.00000 0.321029
\(622\) 24.0000i 0.962312i
\(623\) 0 0
\(624\) −6.00000 −0.240192
\(625\) −7.00000 24.0000i −0.280000 0.960000i
\(626\) 2.00000 0.0799361
\(627\) 12.0000i 0.479234i
\(628\) 22.0000i 0.877896i
\(629\) 16.0000 0.637962
\(630\) 0 0
\(631\) −4.00000 −0.159237 −0.0796187 0.996825i \(-0.525370\pi\)
−0.0796187 + 0.996825i \(0.525370\pi\)
\(632\) 12.0000i 0.477334i
\(633\) 0 0
\(634\) 2.00000 0.0794301
\(635\) −8.00000 + 4.00000i −0.317470 + 0.158735i
\(636\) −6.00000 −0.237915
\(637\) 0 0
\(638\) 12.0000i 0.475085i
\(639\) 6.00000 0.237356
\(640\) 2.00000 1.00000i 0.0790569 0.0395285i
\(641\) 14.0000 0.552967 0.276483 0.961019i \(-0.410831\pi\)
0.276483 + 0.961019i \(0.410831\pi\)
\(642\) 12.0000i 0.473602i
\(643\) 12.0000i 0.473234i −0.971603 0.236617i \(-0.923961\pi\)
0.971603 0.236617i \(-0.0760386\pi\)
\(644\) 0 0
\(645\) −4.00000 8.00000i −0.157500 0.315000i
\(646\) −24.0000 −0.944267
\(647\) 36.0000i 1.41531i 0.706560 + 0.707653i \(0.250246\pi\)
−0.706560 + 0.707653i \(0.749754\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) −16.0000 −0.628055
\(650\) 18.0000 24.0000i 0.706018 0.941357i
\(651\) 0 0
\(652\) 4.00000i 0.156652i
\(653\) 34.0000i 1.33052i 0.746611 + 0.665261i \(0.231680\pi\)
−0.746611 + 0.665261i \(0.768320\pi\)
\(654\) −14.0000 −0.547443
\(655\) −12.0000 24.0000i −0.468879 0.937758i
\(656\) −2.00000 −0.0780869
\(657\) 14.0000i 0.546192i
\(658\) 0 0
\(659\) 26.0000 1.01282 0.506408 0.862294i \(-0.330973\pi\)
0.506408 + 0.862294i \(0.330973\pi\)
\(660\) 4.00000 2.00000i 0.155700 0.0778499i
\(661\) −38.0000 −1.47803 −0.739014 0.673690i \(-0.764708\pi\)
−0.739014 + 0.673690i \(0.764708\pi\)
\(662\) 8.00000i 0.310929i
\(663\) 24.0000i 0.932083i
\(664\) −8.00000 −0.310460
\(665\) 0 0
\(666\) 4.00000 0.154997
\(667\) 48.0000i 1.85857i
\(668\) 12.0000i 0.464294i
\(669\) 8.00000 0.309298
\(670\) 8.00000 + 16.0000i 0.309067 + 0.618134i
\(671\) 20.0000 0.772091
\(672\) 0 0
\(673\) 12.0000i 0.462566i 0.972887 + 0.231283i \(0.0742923\pi\)
−0.972887 + 0.231283i \(0.925708\pi\)
\(674\) 8.00000 0.308148
\(675\) −4.00000 3.00000i −0.153960 0.115470i
\(676\) 23.0000 0.884615
\(677\) 40.0000i 1.53732i 0.639655 + 0.768662i \(0.279077\pi\)
−0.639655 + 0.768662i \(0.720923\pi\)
\(678\) 6.00000i 0.230429i
\(679\) 0 0
\(680\) 4.00000 + 8.00000i 0.153393 + 0.306786i
\(681\) −8.00000 −0.306561
\(682\) 4.00000i 0.153168i
\(683\) 4.00000i 0.153056i 0.997067 + 0.0765279i \(0.0243834\pi\)
−0.997067 + 0.0765279i \(0.975617\pi\)
\(684\) −6.00000 −0.229416
\(685\) 12.0000 6.00000i 0.458496 0.229248i
\(686\) 0 0
\(687\) 14.0000i 0.534133i
\(688\) 4.00000i 0.152499i
\(689\) 36.0000 1.37149
\(690\) 16.0000 8.00000i 0.609110 0.304555i
\(691\) 2.00000 0.0760836 0.0380418 0.999276i \(-0.487888\pi\)
0.0380418 + 0.999276i \(0.487888\pi\)
\(692\) 8.00000i 0.304114i
\(693\) 0 0
\(694\) −36.0000 −1.36654
\(695\) 14.0000 + 28.0000i 0.531050 + 1.06210i
\(696\) −6.00000 −0.227429
\(697\) 8.00000i 0.303022i
\(698\) 26.0000i 0.984115i
\(699\) −10.0000 −0.378235
\(700\) 0 0
\(701\) −34.0000 −1.28416 −0.642081 0.766637i \(-0.721929\pi\)
−0.642081 + 0.766637i \(0.721929\pi\)
\(702\) 6.00000i 0.226455i
\(703\) 24.0000i 0.905177i
\(704\) −2.00000 −0.0753778
\(705\) −8.00000 16.0000i −0.301297 0.602595i
\(706\) −20.0000 −0.752710
\(707\) 0 0
\(708\) 8.00000i 0.300658i
\(709\) 6.00000 0.225335 0.112667 0.993633i \(-0.464061\pi\)
0.112667 + 0.993633i \(0.464061\pi\)
\(710\) 12.0000 6.00000i 0.450352 0.225176i
\(711\) −12.0000 −0.450035
\(712\) 10.0000i 0.374766i
\(713\) 16.0000i 0.599205i
\(714\) 0 0
\(715\) −24.0000 + 12.0000i −0.897549 + 0.448775i
\(716\) 10.0000 0.373718
\(717\) 26.0000i 0.970988i
\(718\) 6.00000i 0.223918i
\(719\) −4.00000 −0.149175 −0.0745874 0.997214i \(-0.523764\pi\)
−0.0745874 + 0.997214i \(0.523764\pi\)
\(720\) 1.00000 + 2.00000i 0.0372678 + 0.0745356i
\(721\) 0 0
\(722\) 17.0000i 0.632674i
\(723\) 26.0000i 0.966950i
\(724\) 2.00000 0.0743294
\(725\) 18.0000 24.0000i 0.668503 0.891338i
\(726\) 7.00000 0.259794
\(727\) 24.0000i 0.890111i 0.895503 + 0.445055i \(0.146816\pi\)
−0.895503 + 0.445055i \(0.853184\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) −14.0000 28.0000i −0.518163 1.03633i
\(731\) −16.0000 −0.591781
\(732\) 10.0000i 0.369611i
\(733\) 14.0000i 0.517102i −0.965998 0.258551i \(-0.916755\pi\)
0.965998 0.258551i \(-0.0832450\pi\)
\(734\) −32.0000 −1.18114
\(735\) 0 0
\(736\) −8.00000 −0.294884
\(737\) 16.0000i 0.589368i
\(738\) 2.00000i 0.0736210i
\(739\) 44.0000 1.61857 0.809283 0.587419i \(-0.199856\pi\)
0.809283 + 0.587419i \(0.199856\pi\)
\(740\) 8.00000 4.00000i 0.294086 0.147043i
\(741\) 36.0000 1.32249
\(742\) 0 0
\(743\) 48.0000i 1.76095i −0.474093 0.880475i \(-0.657224\pi\)
0.474093 0.880475i \(-0.342776\pi\)
\(744\) 2.00000 0.0733236
\(745\) 10.0000 + 20.0000i 0.366372 + 0.732743i
\(746\) −24.0000 −0.878702
\(747\) 8.00000i 0.292705i
\(748\) 8.00000i 0.292509i
\(749\) 0 0
\(750\) −11.0000 2.00000i −0.401663 0.0730297i
\(751\) 20.0000 0.729810 0.364905 0.931045i \(-0.381101\pi\)
0.364905 + 0.931045i \(0.381101\pi\)
\(752\) 8.00000i 0.291730i
\(753\) 0 0
\(754\) 36.0000 1.31104
\(755\) 8.00000 + 16.0000i 0.291150 + 0.582300i
\(756\) 0 0
\(757\) 32.0000i 1.16306i 0.813525 + 0.581530i \(0.197546\pi\)
−0.813525 + 0.581530i \(0.802454\pi\)
\(758\) 20.0000i 0.726433i
\(759\) −16.0000 −0.580763
\(760\) −12.0000 + 6.00000i −0.435286 + 0.217643i
\(761\) 6.00000 0.217500 0.108750 0.994069i \(-0.465315\pi\)
0.108750 + 0.994069i \(0.465315\pi\)
\(762\) 4.00000i 0.144905i
\(763\) 0 0
\(764\) 18.0000 0.651217
\(765\) −8.00000 + 4.00000i −0.289241 + 0.144620i
\(766\) −20.0000 −0.722629
\(767\) 48.0000i 1.73318i
\(768\) 1.00000i 0.0360844i
\(769\) 30.0000 1.08183 0.540914 0.841078i \(-0.318079\pi\)
0.540914 + 0.841078i \(0.318079\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 8.00000i 0.287926i
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) −4.00000 −0.143777
\(775\) −6.00000 + 8.00000i −0.215526 + 0.287368i
\(776\) 10.0000 0.358979
\(777\) 0 0
\(778\) 2.00000i 0.0717035i
\(779\) 12.0000 0.429945
\(780\) −6.00000 12.0000i −0.214834 0.429669i
\(781\) −12.0000 −0.429394
\(782\) 32.0000i 1.14432i
\(783\) 6.00000i 0.214423i
\(784\) 0 0
\(785\) −44.0000 + 22.0000i −1.57043 + 0.785214i
\(786\) −12.0000 −0.428026
\(787\) 28.0000i 0.998092i 0.866575 + 0.499046i \(0.166316\pi\)
−0.866575 + 0.499046i \(0.833684\pi\)
\(788\) 2.00000i 0.0712470i
\(789\) 16.0000 0.569615
\(790\) −24.0000 + 12.0000i −0.853882 + 0.426941i
\(791\) 0 0
\(792\) 2.00000i