Properties

Label 630.2.g.c.379.1
Level $630$
Weight $2$
Character 630.379
Analytic conductor $5.031$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 630.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.03057532734\)
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 379.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 630.379
Dual form 630.2.g.c.379.2

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} -1.00000 q^{4} +(-1.00000 + 2.00000i) q^{5} -1.00000i q^{7} +1.00000i q^{8} +O(q^{10})\) \(q-1.00000i q^{2} -1.00000 q^{4} +(-1.00000 + 2.00000i) q^{5} -1.00000i q^{7} +1.00000i q^{8} +(2.00000 + 1.00000i) q^{10} -2.00000 q^{11} -6.00000i q^{13} -1.00000 q^{14} +1.00000 q^{16} -4.00000i q^{17} +6.00000 q^{19} +(1.00000 - 2.00000i) q^{20} +2.00000i q^{22} -8.00000i q^{23} +(-3.00000 - 4.00000i) q^{25} -6.00000 q^{26} +1.00000i q^{28} +6.00000 q^{29} -2.00000 q^{31} -1.00000i q^{32} -4.00000 q^{34} +(2.00000 + 1.00000i) q^{35} +4.00000i q^{37} -6.00000i q^{38} +(-2.00000 - 1.00000i) q^{40} -2.00000 q^{41} -4.00000i q^{43} +2.00000 q^{44} -8.00000 q^{46} -8.00000i q^{47} -1.00000 q^{49} +(-4.00000 + 3.00000i) q^{50} +6.00000i q^{52} +6.00000i q^{53} +(2.00000 - 4.00000i) q^{55} +1.00000 q^{56} -6.00000i q^{58} -8.00000 q^{59} -10.0000 q^{61} +2.00000i q^{62} -1.00000 q^{64} +(12.0000 + 6.00000i) q^{65} +8.00000i q^{67} +4.00000i q^{68} +(1.00000 - 2.00000i) q^{70} +6.00000 q^{71} +14.0000i q^{73} +4.00000 q^{74} -6.00000 q^{76} +2.00000i q^{77} +12.0000 q^{79} +(-1.00000 + 2.00000i) q^{80} +2.00000i q^{82} -8.00000i q^{83} +(8.00000 + 4.00000i) q^{85} -4.00000 q^{86} -2.00000i q^{88} -10.0000 q^{89} -6.00000 q^{91} +8.00000i q^{92} -8.00000 q^{94} +(-6.00000 + 12.0000i) q^{95} -10.0000i q^{97} +1.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{4} - 2q^{5} + O(q^{10}) \) \( 2q - 2q^{4} - 2q^{5} + 4q^{10} - 4q^{11} - 2q^{14} + 2q^{16} + 12q^{19} + 2q^{20} - 6q^{25} - 12q^{26} + 12q^{29} - 4q^{31} - 8q^{34} + 4q^{35} - 4q^{40} - 4q^{41} + 4q^{44} - 16q^{46} - 2q^{49} - 8q^{50} + 4q^{55} + 2q^{56} - 16q^{59} - 20q^{61} - 2q^{64} + 24q^{65} + 2q^{70} + 12q^{71} + 8q^{74} - 12q^{76} + 24q^{79} - 2q^{80} + 16q^{85} - 8q^{86} - 20q^{89} - 12q^{91} - 16q^{94} - 12q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(281\) \(451\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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
\(3\) 0 0
\(4\) −1.00000 −0.500000
\(5\) −1.00000 + 2.00000i −0.447214 + 0.894427i
\(6\) 0 0
\(7\) 1.00000i 0.377964i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 2.00000 + 1.00000i 0.632456 + 0.316228i
\(11\) −2.00000 −0.603023 −0.301511 0.953463i \(-0.597491\pi\)
−0.301511 + 0.953463i \(0.597491\pi\)
\(12\) 0 0
\(13\) 6.00000i 1.66410i −0.554700 0.832050i \(-0.687167\pi\)
0.554700 0.832050i \(-0.312833\pi\)
\(14\) −1.00000 −0.267261
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 4.00000i 0.970143i −0.874475 0.485071i \(-0.838794\pi\)
0.874475 0.485071i \(-0.161206\pi\)
\(18\) 0 0
\(19\) 6.00000 1.37649 0.688247 0.725476i \(-0.258380\pi\)
0.688247 + 0.725476i \(0.258380\pi\)
\(20\) 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 \(-0.313988\pi\)
\(24\) 0 0
\(25\) −3.00000 4.00000i −0.600000 0.800000i
\(26\) −6.00000 −1.17670
\(27\) 0 0
\(28\) 1.00000i 0.188982i
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) −2.00000 −0.359211 −0.179605 0.983739i \(-0.557482\pi\)
−0.179605 + 0.983739i \(0.557482\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) −4.00000 −0.685994
\(35\) 2.00000 + 1.00000i 0.338062 + 0.169031i
\(36\) 0 0
\(37\) 4.00000i 0.657596i 0.944400 + 0.328798i \(0.106644\pi\)
−0.944400 + 0.328798i \(0.893356\pi\)
\(38\) 6.00000i 0.973329i
\(39\) 0 0
\(40\) −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 \(-0.901344\pi\)
0.952353 0.304997i \(-0.0986555\pi\)
\(44\) 2.00000 0.301511
\(45\) 0 0
\(46\) −8.00000 −1.17954
\(47\) 8.00000i 1.16692i −0.812142 0.583460i \(-0.801699\pi\)
0.812142 0.583460i \(-0.198301\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) −4.00000 + 3.00000i −0.565685 + 0.424264i
\(51\) 0 0
\(52\) 6.00000i 0.832050i
\(53\) 6.00000i 0.824163i 0.911147 + 0.412082i \(0.135198\pi\)
−0.911147 + 0.412082i \(0.864802\pi\)
\(54\) 0 0
\(55\) 2.00000 4.00000i 0.269680 0.539360i
\(56\) 1.00000 0.133631
\(57\) 0 0
\(58\) 6.00000i 0.787839i
\(59\) −8.00000 −1.04151 −0.520756 0.853706i \(-0.674350\pi\)
−0.520756 + 0.853706i \(0.674350\pi\)
\(60\) 0 0
\(61\) −10.0000 −1.28037 −0.640184 0.768221i \(-0.721142\pi\)
−0.640184 + 0.768221i \(0.721142\pi\)
\(62\) 2.00000i 0.254000i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 12.0000 + 6.00000i 1.48842 + 0.744208i
\(66\) 0 0
\(67\) 8.00000i 0.977356i 0.872464 + 0.488678i \(0.162521\pi\)
−0.872464 + 0.488678i \(0.837479\pi\)
\(68\) 4.00000i 0.485071i
\(69\) 0 0
\(70\) 1.00000 2.00000i 0.119523 0.239046i
\(71\) 6.00000 0.712069 0.356034 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) 0 0
\(73\) 14.0000i 1.63858i 0.573382 + 0.819288i \(0.305631\pi\)
−0.573382 + 0.819288i \(0.694369\pi\)
\(74\) 4.00000 0.464991
\(75\) 0 0
\(76\) −6.00000 −0.688247
\(77\) 2.00000i 0.227921i
\(78\) 0 0
\(79\) 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
\(81\) 0 0
\(82\) 2.00000i 0.220863i
\(83\) 8.00000i 0.878114i −0.898459 0.439057i \(-0.855313\pi\)
0.898459 0.439057i \(-0.144687\pi\)
\(84\) 0 0
\(85\) 8.00000 + 4.00000i 0.867722 + 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 \(0.677808\pi\)
\(90\) 0 0
\(91\) −6.00000 −0.628971
\(92\) 8.00000i 0.834058i
\(93\) 0 0
\(94\) −8.00000 −0.825137
\(95\) −6.00000 + 12.0000i −0.615587 + 1.23117i
\(96\) 0 0
\(97\) 10.0000i 1.01535i −0.861550 0.507673i \(-0.830506\pi\)
0.861550 0.507673i \(-0.169494\pi\)
\(98\) 1.00000i 0.101015i
\(99\) 0 0
\(100\) 3.00000 + 4.00000i 0.300000 + 0.400000i
\(101\) −10.0000 −0.995037 −0.497519 0.867453i \(-0.665755\pi\)
−0.497519 + 0.867453i \(0.665755\pi\)
\(102\) 0 0
\(103\) 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 \(-0.196964\pi\)
\(108\) 0 0
\(109\) 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
\(111\) 0 0
\(112\) 1.00000i 0.0944911i
\(113\) 6.00000i 0.564433i 0.959351 + 0.282216i \(0.0910696\pi\)
−0.959351 + 0.282216i \(0.908930\pi\)
\(114\) 0 0
\(115\) 16.0000 + 8.00000i 1.49201 + 0.746004i
\(116\) −6.00000 −0.557086
\(117\) 0 0
\(118\) 8.00000i 0.736460i
\(119\) −4.00000 −0.366679
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 10.0000i 0.905357i
\(123\) 0 0
\(124\) 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 \(0.0567917\pi\)
−0.984126 + 0.177471i \(0.943208\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0 0
\(130\) 6.00000 12.0000i 0.526235 1.05247i
\(131\) 12.0000 1.04844 0.524222 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) 0 0
\(133\) 6.00000i 0.520266i
\(134\) 8.00000 0.691095
\(135\) 0 0
\(136\) 4.00000 0.342997
\(137\) 6.00000i 0.512615i 0.966595 + 0.256307i \(0.0825059\pi\)
−0.966595 + 0.256307i \(0.917494\pi\)
\(138\) 0 0
\(139\) 14.0000 1.18746 0.593732 0.804663i \(-0.297654\pi\)
0.593732 + 0.804663i \(0.297654\pi\)
\(140\) −2.00000 1.00000i −0.169031 0.0845154i
\(141\) 0 0
\(142\) 6.00000i 0.503509i
\(143\) 12.0000i 1.00349i
\(144\) 0 0
\(145\) −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 \(-0.365663\pi\)
0.409616 + 0.912258i \(0.365663\pi\)
\(150\) 0 0
\(151\) −8.00000 −0.651031 −0.325515 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) 6.00000i 0.486664i
\(153\) 0 0
\(154\) 2.00000 0.161165
\(155\) 2.00000 4.00000i 0.160644 0.321288i
\(156\) 0 0
\(157\) 22.0000i 1.75579i −0.478852 0.877896i \(-0.658947\pi\)
0.478852 0.877896i \(-0.341053\pi\)
\(158\) 12.0000i 0.954669i
\(159\) 0 0
\(160\) 2.00000 + 1.00000i 0.158114 + 0.0790569i
\(161\) −8.00000 −0.630488
\(162\) 0 0
\(163\) 4.00000i 0.313304i 0.987654 + 0.156652i \(0.0500701\pi\)
−0.987654 + 0.156652i \(0.949930\pi\)
\(164\) 2.00000 0.156174
\(165\) 0 0
\(166\) −8.00000 −0.620920
\(167\) 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 8.00000i 0.306786 0.613572i
\(171\) 0 0
\(172\) 4.00000i 0.304997i
\(173\) 8.00000i 0.608229i 0.952636 + 0.304114i \(0.0983605\pi\)
−0.952636 + 0.304114i \(0.901639\pi\)
\(174\) 0 0
\(175\) −4.00000 + 3.00000i −0.302372 + 0.226779i
\(176\) −2.00000 −0.150756
\(177\) 0 0
\(178\) 10.0000i 0.749532i
\(179\) 10.0000 0.747435 0.373718 0.927543i \(-0.378083\pi\)
0.373718 + 0.927543i \(0.378083\pi\)
\(180\) 0 0
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 6.00000i 0.444750i
\(183\) 0 0
\(184\) 8.00000 0.589768
\(185\) −8.00000 4.00000i −0.588172 0.294086i
\(186\) 0 0
\(187\) 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 \(-0.274259\pi\)
0.651217 + 0.758891i \(0.274259\pi\)
\(192\) 0 0
\(193\) 8.00000i 0.575853i 0.957653 + 0.287926i \(0.0929658\pi\)
−0.957653 + 0.287926i \(0.907034\pi\)
\(194\) −10.0000 −0.717958
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) 2.00000i 0.142494i −0.997459 0.0712470i \(-0.977302\pi\)
0.997459 0.0712470i \(-0.0226979\pi\)
\(198\) 0 0
\(199\) −6.00000 −0.425329 −0.212664 0.977125i \(-0.568214\pi\)
−0.212664 + 0.977125i \(0.568214\pi\)
\(200\) 4.00000 3.00000i 0.282843 0.212132i
\(201\) 0 0
\(202\) 10.0000i 0.703598i
\(203\) 6.00000i 0.421117i
\(204\) 0 0
\(205\) 2.00000 4.00000i 0.139686 0.279372i
\(206\) −8.00000 −0.557386
\(207\) 0 0
\(208\) 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
\(213\) 0 0
\(214\) −12.0000 −0.820303
\(215\) 8.00000 + 4.00000i 0.545595 + 0.272798i
\(216\) 0 0
\(217\) 2.00000i 0.135769i
\(218\) 14.0000i 0.948200i
\(219\) 0 0
\(220\) −2.00000 + 4.00000i −0.134840 + 0.269680i
\(221\) −24.0000 −1.61441
\(222\) 0 0
\(223\) 8.00000i 0.535720i 0.963458 + 0.267860i \(0.0863164\pi\)
−0.963458 + 0.267860i \(0.913684\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 0 0
\(226\) 6.00000 0.399114
\(227\) 8.00000i 0.530979i 0.964114 + 0.265489i \(0.0855335\pi\)
−0.964114 + 0.265489i \(0.914466\pi\)
\(228\) 0 0
\(229\) −14.0000 −0.925146 −0.462573 0.886581i \(-0.653074\pi\)
−0.462573 + 0.886581i \(0.653074\pi\)
\(230\) 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 \(-0.106227\pi\)
\(234\) 0 0
\(235\) 16.0000 + 8.00000i 1.04372 + 0.521862i
\(236\) 8.00000 0.520756
\(237\) 0 0
\(238\) 4.00000i 0.259281i
\(239\) 26.0000 1.68180 0.840900 0.541190i \(-0.182026\pi\)
0.840900 + 0.541190i \(0.182026\pi\)
\(240\) 0 0
\(241\) −26.0000 −1.67481 −0.837404 0.546585i \(-0.815928\pi\)
−0.837404 + 0.546585i \(0.815928\pi\)
\(242\) 7.00000i 0.449977i
\(243\) 0 0
\(244\) 10.0000 0.640184
\(245\) 1.00000 2.00000i 0.0638877 0.127775i
\(246\) 0 0
\(247\) 36.0000i 2.29063i
\(248\) 2.00000i 0.127000i
\(249\) 0 0
\(250\) −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
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) 4.00000 0.248548
\(260\) −12.0000 6.00000i −0.744208 0.372104i
\(261\) 0 0
\(262\) 12.0000i 0.741362i
\(263\) 16.0000i 0.986602i 0.869859 + 0.493301i \(0.164210\pi\)
−0.869859 + 0.493301i \(0.835790\pi\)
\(264\) 0 0
\(265\) −12.0000 6.00000i −0.737154 0.368577i
\(266\) −6.00000 −0.367884
\(267\) 0 0
\(268\) 8.00000i 0.488678i
\(269\) 18.0000 1.09748 0.548740 0.835993i \(-0.315108\pi\)
0.548740 + 0.835993i \(0.315108\pi\)
\(270\) 0 0
\(271\) 10.0000 0.607457 0.303728 0.952759i \(-0.401768\pi\)
0.303728 + 0.952759i \(0.401768\pi\)
\(272\) 4.00000i 0.242536i
\(273\) 0 0
\(274\) 6.00000 0.362473
\(275\) 6.00000 + 8.00000i 0.361814 + 0.482418i
\(276\) 0 0
\(277\) 28.0000i 1.68236i 0.540758 + 0.841178i \(0.318138\pi\)
−0.540758 + 0.841178i \(0.681862\pi\)
\(278\) 14.0000i 0.839664i
\(279\) 0 0
\(280\) −1.00000 + 2.00000i −0.0597614 + 0.119523i
\(281\) −30.0000 −1.78965 −0.894825 0.446417i \(-0.852700\pi\)
−0.894825 + 0.446417i \(0.852700\pi\)
\(282\) 0 0
\(283\) 20.0000i 1.18888i −0.804141 0.594438i \(-0.797374\pi\)
0.804141 0.594438i \(-0.202626\pi\)
\(284\) −6.00000 −0.356034
\(285\) 0 0
\(286\) 12.0000 0.709575
\(287\) 2.00000i 0.118056i
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 12.0000 + 6.00000i 0.704664 + 0.352332i
\(291\) 0 0
\(292\) 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
\(297\) 0 0
\(298\) 10.0000i 0.579284i
\(299\) −48.0000 −2.77591
\(300\) 0 0
\(301\) −4.00000 −0.230556
\(302\) 8.00000i 0.460348i
\(303\) 0 0
\(304\) 6.00000 0.344124
\(305\) 10.0000 20.0000i 0.572598 1.14520i
\(306\) 0 0
\(307\) 12.0000i 0.684876i −0.939540 0.342438i \(-0.888747\pi\)
0.939540 0.342438i \(-0.111253\pi\)
\(308\) 2.00000i 0.113961i
\(309\) 0 0
\(310\) −4.00000 2.00000i −0.227185 0.113592i
\(311\) −24.0000 −1.36092 −0.680458 0.732787i \(-0.738219\pi\)
−0.680458 + 0.732787i \(0.738219\pi\)
\(312\) 0 0
\(313\) 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 \(0.982113\pi\)
\(318\) 0 0
\(319\) −12.0000 −0.671871
\(320\) 1.00000 2.00000i 0.0559017 0.111803i
\(321\) 0 0
\(322\) 8.00000i 0.445823i
\(323\) 24.0000i 1.33540i
\(324\) 0 0
\(325\) −24.0000 + 18.0000i −1.33128 + 0.998460i
\(326\) 4.00000 0.221540
\(327\) 0 0
\(328\) 2.00000i 0.110432i
\(329\) −8.00000 −0.441054
\(330\) 0 0
\(331\) −8.00000 −0.439720 −0.219860 0.975531i \(-0.570560\pi\)
−0.219860 + 0.975531i \(0.570560\pi\)
\(332\) 8.00000i 0.439057i
\(333\) 0 0
\(334\) 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 \(-0.930081\pi\)
0.975972 0.217894i \(-0.0699187\pi\)
\(338\) 23.0000i 1.25104i
\(339\) 0 0
\(340\) −8.00000 4.00000i −0.433861 0.216930i
\(341\) 4.00000 0.216612
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 4.00000 0.215666
\(345\) 0 0
\(346\) 8.00000 0.430083
\(347\) 36.0000i 1.93258i −0.257454 0.966291i \(-0.582883\pi\)
0.257454 0.966291i \(-0.417117\pi\)
\(348\) 0 0
\(349\) 26.0000 1.39175 0.695874 0.718164i \(-0.255017\pi\)
0.695874 + 0.718164i \(0.255017\pi\)
\(350\) 3.00000 + 4.00000i 0.160357 + 0.213809i
\(351\) 0 0
\(352\) 2.00000i 0.106600i
\(353\) 20.0000i 1.06449i 0.846590 + 0.532246i \(0.178652\pi\)
−0.846590 + 0.532246i \(0.821348\pi\)
\(354\) 0 0
\(355\) −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 \(-0.449388\pi\)
0.158334 + 0.987386i \(0.449388\pi\)
\(360\) 0 0
\(361\) 17.0000 0.894737
\(362\) 2.00000i 0.105118i
\(363\) 0 0
\(364\) 6.00000 0.314485
\(365\) −28.0000 14.0000i −1.46559 0.732793i
\(366\) 0 0
\(367\) 32.0000i 1.67039i −0.549957 0.835193i \(-0.685356\pi\)
0.549957 0.835193i \(-0.314644\pi\)
\(368\) 8.00000i 0.417029i
\(369\) 0 0
\(370\) −4.00000 + 8.00000i −0.207950 + 0.415900i
\(371\) 6.00000 0.311504
\(372\) 0 0
\(373\) 24.0000i 1.24267i 0.783544 + 0.621336i \(0.213410\pi\)
−0.783544 + 0.621336i \(0.786590\pi\)
\(374\) 8.00000 0.413670
\(375\) 0 0
\(376\) 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
\(381\) 0 0
\(382\) 18.0000i 0.920960i
\(383\) 20.0000i 1.02195i 0.859595 + 0.510976i \(0.170716\pi\)
−0.859595 + 0.510976i \(0.829284\pi\)
\(384\) 0 0
\(385\) −4.00000 2.00000i −0.203859 0.101929i
\(386\) 8.00000 0.407189
\(387\) 0 0
\(388\) 10.0000i 0.507673i
\(389\) 2.00000 0.101404 0.0507020 0.998714i \(-0.483854\pi\)
0.0507020 + 0.998714i \(0.483854\pi\)
\(390\) 0 0
\(391\) −32.0000 −1.61831
\(392\) 1.00000i 0.0505076i
\(393\) 0 0
\(394\) −2.00000 −0.100759
\(395\) −12.0000 + 24.0000i −0.603786 + 1.20757i
\(396\) 0 0
\(397\) 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 \(-0.386330\pi\)
0.349563 + 0.936913i \(0.386330\pi\)
\(402\) 0 0
\(403\) 12.0000i 0.597763i
\(404\) 10.0000 0.497519
\(405\) 0 0
\(406\) −6.00000 −0.297775
\(407\) 8.00000i 0.396545i
\(408\) 0 0
\(409\) −26.0000 −1.28562 −0.642809 0.766027i \(-0.722231\pi\)
−0.642809 + 0.766027i \(0.722231\pi\)
\(410\) −4.00000 2.00000i −0.197546 0.0987730i
\(411\) 0 0
\(412\) 8.00000i 0.394132i
\(413\) 8.00000i 0.393654i
\(414\) 0 0
\(415\) 16.0000 + 8.00000i 0.785409 + 0.392705i
\(416\) −6.00000 −0.294174
\(417\) 0 0
\(418\) 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
\(423\) 0 0
\(424\) −6.00000 −0.291386
\(425\) −16.0000 + 12.0000i −0.776114 + 0.582086i
\(426\) 0 0
\(427\) 10.0000i 0.483934i
\(428\) 12.0000i 0.580042i
\(429\) 0 0
\(430\) 4.00000 8.00000i 0.192897 0.385794i
\(431\) −2.00000 −0.0963366 −0.0481683 0.998839i \(-0.515338\pi\)
−0.0481683 + 0.998839i \(0.515338\pi\)
\(432\) 0 0
\(433\) 26.0000i 1.24948i 0.780833 + 0.624740i \(0.214795\pi\)
−0.780833 + 0.624740i \(0.785205\pi\)
\(434\) 2.00000 0.0960031
\(435\) 0 0
\(436\) −14.0000 −0.670478
\(437\) 48.0000i 2.29615i
\(438\) 0 0
\(439\) 18.0000 0.859093 0.429547 0.903045i \(-0.358673\pi\)
0.429547 + 0.903045i \(0.358673\pi\)
\(440\) 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 \(-0.0920164\pi\)
\(444\) 0 0
\(445\) 10.0000 20.0000i 0.474045 0.948091i
\(446\) 8.00000 0.378811
\(447\) 0 0
\(448\) 1.00000i 0.0472456i
\(449\) −6.00000 −0.283158 −0.141579 0.989927i \(-0.545218\pi\)
−0.141579 + 0.989927i \(0.545218\pi\)
\(450\) 0 0
\(451\) 4.00000 0.188353
\(452\) 6.00000i 0.282216i
\(453\) 0 0
\(454\) 8.00000 0.375459
\(455\) 6.00000 12.0000i 0.281284 0.562569i
\(456\) 0 0
\(457\) 28.0000i 1.30978i 0.755722 + 0.654892i \(0.227286\pi\)
−0.755722 + 0.654892i \(0.772714\pi\)
\(458\) 14.0000i 0.654177i
\(459\) 0 0
\(460\) −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 \(-0.684580\pi\)
0.547920 0.836531i \(-0.315420\pi\)
\(464\) 6.00000 0.278543
\(465\) 0 0
\(466\) −10.0000 −0.463241
\(467\) 24.0000i 1.11059i 0.831654 + 0.555294i \(0.187394\pi\)
−0.831654 + 0.555294i \(0.812606\pi\)
\(468\) 0 0
\(469\) 8.00000 0.369406
\(470\) 8.00000 16.0000i 0.369012 0.738025i
\(471\) 0 0
\(472\) 8.00000i 0.368230i
\(473\) 8.00000i 0.367840i
\(474\) 0 0
\(475\) −18.0000 24.0000i −0.825897 1.10120i
\(476\) 4.00000 0.183340
\(477\) 0 0
\(478\) 26.0000i 1.18921i
\(479\) 8.00000 0.365529 0.182765 0.983157i \(-0.441495\pi\)
0.182765 + 0.983157i \(0.441495\pi\)
\(480\) 0 0
\(481\) 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
\(486\) 0 0
\(487\) 12.0000i 0.543772i 0.962329 + 0.271886i \(0.0876473\pi\)
−0.962329 + 0.271886i \(0.912353\pi\)
\(488\) 10.0000i 0.452679i
\(489\) 0 0
\(490\) −2.00000 1.00000i −0.0903508 0.0451754i
\(491\) 30.0000 1.35388 0.676941 0.736038i \(-0.263305\pi\)
0.676941 + 0.736038i \(0.263305\pi\)
\(492\) 0 0
\(493\) 24.0000i 1.08091i
\(494\) −36.0000 −1.61972
\(495\) 0 0
\(496\) −2.00000 −0.0898027
\(497\) 6.00000i 0.269137i
\(498\) 0 0
\(499\) 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
\(501\) 0 0
\(502\) 0 0
\(503\) 12.0000i 0.535054i −0.963550 0.267527i \(-0.913794\pi\)
0.963550 0.267527i \(-0.0862064\pi\)
\(504\) 0 0
\(505\) 10.0000 20.0000i 0.444994 0.889988i
\(506\) 16.0000 0.711287
\(507\) 0 0
\(508\) 4.00000i 0.177471i
\(509\) 30.0000 1.32973 0.664863 0.746965i \(-0.268490\pi\)
0.664863 + 0.746965i \(0.268490\pi\)
\(510\) 0 0
\(511\) 14.0000 0.619324
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 0 0
\(515\) 16.0000 + 8.00000i 0.705044 + 0.352522i
\(516\) 0 0
\(517\) 16.0000i 0.703679i
\(518\) 4.00000i 0.175750i
\(519\) 0 0
\(520\) −6.00000 + 12.0000i −0.263117 + 0.526235i
\(521\) 26.0000 1.13908 0.569540 0.821963i \(-0.307121\pi\)
0.569540 + 0.821963i \(0.307121\pi\)
\(522\) 0 0
\(523\) 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
\(528\) 0 0
\(529\) −41.0000 −1.78261
\(530\) −6.00000 + 12.0000i −0.260623 + 0.521247i
\(531\) 0 0
\(532\) 6.00000i 0.260133i
\(533\) 12.0000i 0.519778i
\(534\) 0 0
\(535\) 24.0000 + 12.0000i 1.03761 + 0.518805i
\(536\) −8.00000 −0.345547
\(537\) 0 0
\(538\) 18.0000i 0.776035i
\(539\) 2.00000 0.0861461
\(540\) 0 0
\(541\) 22.0000 0.945854 0.472927 0.881102i \(-0.343197\pi\)
0.472927 + 0.881102i \(0.343197\pi\)
\(542\) 10.0000i 0.429537i
\(543\) 0 0
\(544\) −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 \(0.326528\pi\)
−0.518400 + 0.855138i \(0.673472\pi\)
\(548\) 6.00000i 0.256307i
\(549\) 0 0
\(550\) 8.00000 6.00000i 0.341121 0.255841i
\(551\) 36.0000 1.53365
\(552\) 0 0
\(553\) 12.0000i 0.510292i
\(554\) 28.0000 1.18961
\(555\) 0 0
\(556\) −14.0000 −0.593732
\(557\) 42.0000i 1.77960i 0.456354 + 0.889799i \(0.349155\pi\)
−0.456354 + 0.889799i \(0.650845\pi\)
\(558\) 0 0
\(559\) −24.0000 −1.01509
\(560\) 2.00000 + 1.00000i 0.0845154 + 0.0422577i
\(561\) 0 0
\(562\) 30.0000i 1.26547i
\(563\) 4.00000i 0.168580i −0.996441 0.0842900i \(-0.973138\pi\)
0.996441 0.0842900i \(-0.0268622\pi\)
\(564\) 0 0
\(565\) −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 \(-0.914582\pi\)
−0.964210 + 0.265139i \(0.914582\pi\)
\(570\) 0 0
\(571\) 4.00000 0.167395 0.0836974 0.996491i \(-0.473327\pi\)
0.0836974 + 0.996491i \(0.473327\pi\)
\(572\) 12.0000i 0.501745i
\(573\) 0 0
\(574\) 2.00000 0.0834784
\(575\) −32.0000 + 24.0000i −1.33449 + 1.00087i
\(576\) 0 0
\(577\) 26.0000i 1.08239i −0.840896 0.541197i \(-0.817971\pi\)
0.840896 0.541197i \(-0.182029\pi\)
\(578\) 1.00000i 0.0415945i
\(579\) 0 0
\(580\) 6.00000 12.0000i 0.249136 0.498273i
\(581\) −8.00000 −0.331896
\(582\) 0 0
\(583\) 12.0000i 0.496989i
\(584\) −14.0000 −0.579324
\(585\) 0 0
\(586\) 0 0
\(587\) 12.0000i 0.495293i 0.968850 + 0.247647i \(0.0796572\pi\)
−0.968850 + 0.247647i \(0.920343\pi\)
\(588\) 0 0
\(589\) −12.0000 −0.494451
\(590\) −16.0000 8.00000i −0.658710 0.329355i
\(591\) 0 0
\(592\) 4.00000i 0.164399i
\(593\) 12.0000i 0.492781i 0.969171 + 0.246390i \(0.0792446\pi\)
−0.969171 + 0.246390i \(0.920755\pi\)
\(594\) 0 0
\(595\) 4.00000 8.00000i 0.163984 0.327968i
\(596\) −10.0000 −0.409616
\(597\) 0 0
\(598\) 48.0000i 1.96287i
\(599\) 30.0000 1.22577 0.612883 0.790173i \(-0.290010\pi\)
0.612883 + 0.790173i \(0.290010\pi\)
\(600\) 0 0
\(601\) 38.0000 1.55005 0.775026 0.631929i \(-0.217737\pi\)
0.775026 + 0.631929i \(0.217737\pi\)
\(602\) 4.00000i 0.163028i
\(603\) 0 0
\(604\) 8.00000 0.325515
\(605\) 7.00000 14.0000i 0.284590 0.569181i
\(606\) 0 0
\(607\) 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
\(612\) 0 0
\(613\) 28.0000i 1.13091i −0.824779 0.565455i \(-0.808701\pi\)
0.824779 0.565455i \(-0.191299\pi\)
\(614\) −12.0000 −0.484281
\(615\) 0 0
\(616\) −2.00000 −0.0805823
\(617\) 26.0000i 1.04672i 0.852111 + 0.523360i \(0.175322\pi\)
−0.852111 + 0.523360i \(0.824678\pi\)
\(618\) 0 0
\(619\) 22.0000 0.884255 0.442127 0.896952i \(-0.354224\pi\)
0.442127 + 0.896952i \(0.354224\pi\)
\(620\) −2.00000 + 4.00000i −0.0803219 + 0.160644i
\(621\) 0 0
\(622\) 24.0000i 0.962312i
\(623\) 10.0000i 0.400642i
\(624\) 0 0
\(625\) −7.00000 + 24.0000i −0.280000 + 0.960000i
\(626\) 2.00000 0.0799361
\(627\) 0 0
\(628\) 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
\(636\) 0 0
\(637\) 6.00000i 0.237729i
\(638\) 12.0000i 0.475085i
\(639\) 0 0
\(640\) −2.00000 1.00000i −0.0790569 0.0395285i
\(641\) −14.0000 −0.552967 −0.276483 0.961019i \(-0.589169\pi\)
−0.276483 + 0.961019i \(0.589169\pi\)
\(642\) 0 0
\(643\) 12.0000i 0.473234i −0.971603 0.236617i \(-0.923961\pi\)
0.971603 0.236617i \(-0.0760386\pi\)
\(644\) 8.00000 0.315244
\(645\) 0 0
\(646\) −24.0000 −0.944267
\(647\) 36.0000i 1.41531i −0.706560 0.707653i \(-0.749754\pi\)
0.706560 0.707653i \(-0.250246\pi\)
\(648\) 0 0
\(649\) 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 \(0.768320\pi\)
\(654\) 0 0
\(655\) −12.0000 + 24.0000i −0.468879 + 0.937758i
\(656\) −2.00000 −0.0780869
\(657\) 0 0
\(658\) 8.00000i 0.311872i
\(659\) −26.0000 −1.01282 −0.506408 0.862294i \(-0.669027\pi\)
−0.506408 + 0.862294i \(0.669027\pi\)
\(660\) 0 0
\(661\) 38.0000 1.47803 0.739014 0.673690i \(-0.235292\pi\)
0.739014 + 0.673690i \(0.235292\pi\)
\(662\) 8.00000i 0.310929i
\(663\) 0 0
\(664\) 8.00000 0.310460
\(665\) 12.0000 + 6.00000i 0.465340 + 0.232670i
\(666\) 0 0
\(667\) 48.0000i 1.85857i
\(668\) 12.0000i 0.464294i
\(669\) 0 0
\(670\) −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 \(-0.925708\pi\)
0.972887 0.231283i \(-0.0742923\pi\)
\(674\) −8.00000 −0.308148
\(675\) 0 0
\(676\) 23.0000 0.884615
\(677\) 40.0000i 1.53732i −0.639655 0.768662i \(-0.720923\pi\)
0.639655 0.768662i \(-0.279077\pi\)
\(678\) 0 0
\(679\) −10.0000 −0.383765
\(680\) −4.00000 + 8.00000i −0.153393 + 0.306786i
\(681\) 0 0
\(682\) 4.00000i 0.153168i
\(683\) 4.00000i 0.153056i 0.997067 + 0.0765279i \(0.0243834\pi\)
−0.997067 + 0.0765279i \(0.975617\pi\)
\(684\) 0 0
\(685\) −12.0000 6.00000i −0.458496 0.229248i
\(686\) 1.00000 0.0381802
\(687\) 0 0
\(688\) 4.00000i 0.152499i
\(689\) 36.0000 1.37149
\(690\) 0 0
\(691\) −2.00000 −0.0760836 −0.0380418 0.999276i \(-0.512112\pi\)
−0.0380418 + 0.999276i \(0.512112\pi\)
\(692\) 8.00000i 0.304114i
\(693\) 0 0
\(694\) −36.0000 −1.36654
\(695\) −14.0000 + 28.0000i −0.531050 + 1.06210i
\(696\) 0 0
\(697\) 8.00000i 0.303022i
\(698\) 26.0000i 0.984115i
\(699\) 0 0
\(700\) 4.00000 3.00000i 0.151186 0.113389i
\(701\) 34.0000 1.28416 0.642081 0.766637i \(-0.278071\pi\)
0.642081 + 0.766637i \(0.278071\pi\)
\(702\) 0 0
\(703\) 24.0000i 0.905177i
\(704\) 2.00000 0.0753778
\(705\) 0 0
\(706\) 20.0000 0.752710
\(707\) 10.0000i 0.376089i
\(708\) 0 0
\(709\) 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
\(711\) 0 0
\(712\) 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
\(717\) 0 0
\(718\) 6.00000i 0.223918i
\(719\) −4.00000 −0.149175 −0.0745874 0.997214i \(-0.523764\pi\)
−0.0745874 + 0.997214i \(0.523764\pi\)
\(720\) 0 0
\(721\) −8.00000 −0.297936
\(722\) 17.0000i 0.632674i
\(723\) 0 0
\(724\) −2.00000 −0.0743294
\(725\) −18.0000 24.0000i −0.668503 0.891338i
\(726\) 0 0
\(727\) 24.0000i 0.890111i 0.895503 + 0.445055i \(0.146816\pi\)
−0.895503 + 0.445055i \(0.853184\pi\)
\(728\) 6.00000i 0.222375i
\(729\) 0 0
\(730\) −14.0000 + 28.0000i −0.518163 + 1.03633i
\(731\) −16.0000 −0.591781
\(732\) 0 0
\(733\) 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
\(738\) 0 0
\(739\) 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
\(741\) 0 0
\(742\) 6.00000i 0.220267i
\(743\) 48.0000i 1.76095i −0.474093 0.880475i \(-0.657224\pi\)
0.474093 0.880475i \(-0.342776\pi\)
\(744\) 0 0
\(745\) −10.0000 + 20.0000i −0.366372 + 0.732743i
\(746\) 24.0000 0.878702
\(747\) 0 0
\(748\) 8.00000i 0.292509i
\(749\) −12.0000 −0.438470
\(750\) 0 0
\(751\) 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 \(-0.802454\pi\)
0.813525 0.581530i \(-0.197546\pi\)
\(758\) 20.0000i 0.726433i
\(759\) 0 0
\(760\) −12.0000 6.00000i −0.435286 0.217643i
\(761\) 6.00000 0.217500 0.108750 0.994069i \(-0.465315\pi\)
0.108750 + 0.994069i \(0.465315\pi\)
\(762\) 0 0
\(763\) 14.0000i 0.506834i
\(764\) −18.0000 −0.651217
\(765\) 0 0
\(766\) 20.0000 0.722629
\(767\) 48.0000i 1.73318i
\(768\) 0 0
\(769\) −30.0000 −1.08183 −0.540914 0.841078i \(-0.681921\pi\)
−0.540914 + 0.841078i \(0.681921\pi\)
\(770\) −2.00000 + 4.00000i −0.0720750 + 0.144150i
\(771\) 0 0
\(772\) 8.00000i 0.287926i
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 0 0
\(775\) 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
\(780\) 0 0
\(781\) −12.0000 −0.429394
\(782\) 32.0000i 1.14432i
\(783\) 0 0
\(784\) −1.00000 −0.0357143
\(785\) 44.0000 + 22.0000i 1.57043 + 0.785214i
\(786\) 0 0
\(787\) 28.0000i 0.998092i 0.866575 + 0.499046i \(0.166316\pi\)
−0.866575 + 0.499046i \(0.833684\pi\)
\(788\) 2.00000i 0.0712470i
\(789\) 0 0
\(790\) 24.0000 + 12.0000i 0.853882 + 0.426941i
\(791\) 6.00000 0.213335
\(792\) 0 0
\(793\) 60.0000i 2.13066i
\(794\) −2.00000 −0.0709773
\(795\) 0 0
\(796\) 6.00000 0.212664
\(797\) 8.00000i 0.283375i 0.989911 + 0.141687i \(0.0452527\pi\)
−0.989911 +