Properties

Label 1520.2.d.j.609.3
Level $1520$
Weight $2$
Character 1520.609
Analytic conductor $12.137$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1520 = 2^{4} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1520.d (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.1372611072\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.5161984.1
Defining polynomial: \(x^{6} - 4 x^{3} + 25 x^{2} - 20 x + 8\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 190)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 609.3
Root \(-1.75233 - 1.75233i\) of defining polynomial
Character \(\chi\) \(=\) 1520.609
Dual form 1520.2.d.j.609.4

$q$-expansion

\(f(q)\) \(=\) \(q-1.36333i q^{3} +(1.38900 - 1.75233i) q^{5} +0.636672i q^{7} +1.14134 q^{9} +O(q^{10})\) \(q-1.36333i q^{3} +(1.38900 - 1.75233i) q^{5} +0.636672i q^{7} +1.14134 q^{9} -3.50466 q^{11} -0.141336i q^{13} +(-2.38900 - 1.89367i) q^{15} -2.14134i q^{17} +1.00000 q^{19} +0.867993 q^{21} -4.91934i q^{23} +(-1.14134 - 4.86799i) q^{25} -5.64600i q^{27} -7.15066 q^{29} +7.78734 q^{31} +4.77801i q^{33} +(1.11566 + 0.884340i) q^{35} -3.27334i q^{37} -0.192688 q^{39} -4.23132 q^{41} -2.49534i q^{43} +(1.58532 - 2.00000i) q^{45} -10.2827i q^{47} +6.59465 q^{49} -2.91934 q^{51} +8.14134i q^{53} +(-4.86799 + 6.14134i) q^{55} -1.36333i q^{57} -5.64600 q^{59} -6.49534 q^{61} +0.726656i q^{63} +(-0.247668 - 0.196316i) q^{65} +8.37266i q^{67} -6.70668 q^{69} +8.95798 q^{71} -3.69735i q^{73} +(-6.63667 + 1.55602i) q^{75} -2.23132i q^{77} -4.17997 q^{79} -4.27334 q^{81} +9.00933i q^{83} +(-3.75233 - 2.97432i) q^{85} +9.74870i q^{87} +6.77801 q^{89} +0.0899847 q^{91} -10.6167i q^{93} +(1.38900 - 1.75233i) q^{95} -14.5653i q^{97} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 2q^{5} - 10q^{9} + O(q^{10}) \) \( 6q + 2q^{5} - 10q^{9} - 8q^{15} + 6q^{19} - 20q^{21} + 10q^{25} + 16q^{29} - 8q^{31} - 8q^{35} + 20q^{39} + 4q^{41} + 18q^{45} + 6q^{49} + 12q^{51} - 4q^{55} + 4q^{59} - 60q^{61} - 12q^{65} + 44q^{69} + 16q^{71} - 44q^{75} - 34q^{81} - 12q^{85} + 28q^{89} - 12q^{91} + 2q^{95} - 24q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(401\) \(1141\) \(1217\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.36333i 0.787118i −0.919299 0.393559i \(-0.871244\pi\)
0.919299 0.393559i \(-0.128756\pi\)
\(4\) 0 0
\(5\) 1.38900 1.75233i 0.621181 0.783667i
\(6\) 0 0
\(7\) 0.636672i 0.240639i 0.992735 + 0.120320i \(0.0383920\pi\)
−0.992735 + 0.120320i \(0.961608\pi\)
\(8\) 0 0
\(9\) 1.14134 0.380445
\(10\) 0 0
\(11\) −3.50466 −1.05670 −0.528348 0.849028i \(-0.677188\pi\)
−0.528348 + 0.849028i \(0.677188\pi\)
\(12\) 0 0
\(13\) 0.141336i 0.0391996i −0.999808 0.0195998i \(-0.993761\pi\)
0.999808 0.0195998i \(-0.00623921\pi\)
\(14\) 0 0
\(15\) −2.38900 1.89367i −0.616838 0.488943i
\(16\) 0 0
\(17\) 2.14134i 0.519350i −0.965696 0.259675i \(-0.916385\pi\)
0.965696 0.259675i \(-0.0836155\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 0.867993 0.189412
\(22\) 0 0
\(23\) 4.91934i 1.02575i −0.858462 0.512877i \(-0.828580\pi\)
0.858462 0.512877i \(-0.171420\pi\)
\(24\) 0 0
\(25\) −1.14134 4.86799i −0.228267 0.973599i
\(26\) 0 0
\(27\) 5.64600i 1.08657i
\(28\) 0 0
\(29\) −7.15066 −1.32785 −0.663923 0.747801i \(-0.731110\pi\)
−0.663923 + 0.747801i \(0.731110\pi\)
\(30\) 0 0
\(31\) 7.78734 1.39865 0.699323 0.714805i \(-0.253485\pi\)
0.699323 + 0.714805i \(0.253485\pi\)
\(32\) 0 0
\(33\) 4.77801i 0.831744i
\(34\) 0 0
\(35\) 1.11566 + 0.884340i 0.188581 + 0.149481i
\(36\) 0 0
\(37\) 3.27334i 0.538134i −0.963121 0.269067i \(-0.913285\pi\)
0.963121 0.269067i \(-0.0867154\pi\)
\(38\) 0 0
\(39\) −0.192688 −0.0308547
\(40\) 0 0
\(41\) −4.23132 −0.660821 −0.330411 0.943837i \(-0.607187\pi\)
−0.330411 + 0.943837i \(0.607187\pi\)
\(42\) 0 0
\(43\) 2.49534i 0.380535i −0.981732 0.190268i \(-0.939064\pi\)
0.981732 0.190268i \(-0.0609356\pi\)
\(44\) 0 0
\(45\) 1.58532 2.00000i 0.236326 0.298142i
\(46\) 0 0
\(47\) 10.2827i 1.49988i −0.661505 0.749941i \(-0.730082\pi\)
0.661505 0.749941i \(-0.269918\pi\)
\(48\) 0 0
\(49\) 6.59465 0.942093
\(50\) 0 0
\(51\) −2.91934 −0.408790
\(52\) 0 0
\(53\) 8.14134i 1.11830i 0.829067 + 0.559149i \(0.188872\pi\)
−0.829067 + 0.559149i \(0.811128\pi\)
\(54\) 0 0
\(55\) −4.86799 + 6.14134i −0.656400 + 0.828098i
\(56\) 0 0
\(57\) 1.36333i 0.180577i
\(58\) 0 0
\(59\) −5.64600 −0.735047 −0.367523 0.930014i \(-0.619794\pi\)
−0.367523 + 0.930014i \(0.619794\pi\)
\(60\) 0 0
\(61\) −6.49534 −0.831643 −0.415821 0.909446i \(-0.636506\pi\)
−0.415821 + 0.909446i \(0.636506\pi\)
\(62\) 0 0
\(63\) 0.726656i 0.0915501i
\(64\) 0 0
\(65\) −0.247668 0.196316i −0.0307194 0.0243501i
\(66\) 0 0
\(67\) 8.37266i 1.02288i 0.859318 + 0.511441i \(0.170888\pi\)
−0.859318 + 0.511441i \(0.829112\pi\)
\(68\) 0 0
\(69\) −6.70668 −0.807389
\(70\) 0 0
\(71\) 8.95798 1.06312 0.531558 0.847022i \(-0.321607\pi\)
0.531558 + 0.847022i \(0.321607\pi\)
\(72\) 0 0
\(73\) 3.69735i 0.432742i −0.976311 0.216371i \(-0.930578\pi\)
0.976311 0.216371i \(-0.0694221\pi\)
\(74\) 0 0
\(75\) −6.63667 + 1.55602i −0.766337 + 0.179673i
\(76\) 0 0
\(77\) 2.23132i 0.254283i
\(78\) 0 0
\(79\) −4.17997 −0.470283 −0.235142 0.971961i \(-0.575555\pi\)
−0.235142 + 0.971961i \(0.575555\pi\)
\(80\) 0 0
\(81\) −4.27334 −0.474816
\(82\) 0 0
\(83\) 9.00933i 0.988902i 0.869205 + 0.494451i \(0.164631\pi\)
−0.869205 + 0.494451i \(0.835369\pi\)
\(84\) 0 0
\(85\) −3.75233 2.97432i −0.406998 0.322611i
\(86\) 0 0
\(87\) 9.74870i 1.04517i
\(88\) 0 0
\(89\) 6.77801 0.718467 0.359234 0.933248i \(-0.383038\pi\)
0.359234 + 0.933248i \(0.383038\pi\)
\(90\) 0 0
\(91\) 0.0899847 0.00943296
\(92\) 0 0
\(93\) 10.6167i 1.10090i
\(94\) 0 0
\(95\) 1.38900 1.75233i 0.142509 0.179785i
\(96\) 0 0
\(97\) 14.5653i 1.47889i −0.673219 0.739443i \(-0.735089\pi\)
0.673219 0.739443i \(-0.264911\pi\)
\(98\) 0 0
\(99\) −4.00000 −0.402015
\(100\) 0 0
\(101\) −16.6167 −1.65342 −0.826712 0.562626i \(-0.809791\pi\)
−0.826712 + 0.562626i \(0.809791\pi\)
\(102\) 0 0
\(103\) 9.06068i 0.892775i −0.894840 0.446388i \(-0.852710\pi\)
0.894840 0.446388i \(-0.147290\pi\)
\(104\) 0 0
\(105\) 1.20565 1.52101i 0.117659 0.148436i
\(106\) 0 0
\(107\) 0.0899847i 0.00869915i 0.999991 + 0.00434958i \(0.00138452\pi\)
−0.999991 + 0.00434958i \(0.998615\pi\)
\(108\) 0 0
\(109\) 13.5946 1.30213 0.651066 0.759021i \(-0.274322\pi\)
0.651066 + 0.759021i \(0.274322\pi\)
\(110\) 0 0
\(111\) −4.46264 −0.423575
\(112\) 0 0
\(113\) 11.5233i 1.08402i 0.840371 + 0.542011i \(0.182337\pi\)
−0.840371 + 0.542011i \(0.817663\pi\)
\(114\) 0 0
\(115\) −8.62032 6.83299i −0.803849 0.637179i
\(116\) 0 0
\(117\) 0.161312i 0.0149133i
\(118\) 0 0
\(119\) 1.36333 0.124976
\(120\) 0 0
\(121\) 1.28267 0.116607
\(122\) 0 0
\(123\) 5.76868i 0.520144i
\(124\) 0 0
\(125\) −10.1157 4.76166i −0.904772 0.425896i
\(126\) 0 0
\(127\) 3.29200i 0.292118i −0.989276 0.146059i \(-0.953341\pi\)
0.989276 0.146059i \(-0.0466589\pi\)
\(128\) 0 0
\(129\) −3.40196 −0.299526
\(130\) 0 0
\(131\) −18.0187 −1.57430 −0.787149 0.616763i \(-0.788444\pi\)
−0.787149 + 0.616763i \(0.788444\pi\)
\(132\) 0 0
\(133\) 0.636672i 0.0552064i
\(134\) 0 0
\(135\) −9.89367 7.84232i −0.851511 0.674959i
\(136\) 0 0
\(137\) 14.4240i 1.23233i 0.787619 + 0.616163i \(0.211314\pi\)
−0.787619 + 0.616163i \(0.788686\pi\)
\(138\) 0 0
\(139\) 15.4720 1.31232 0.656158 0.754624i \(-0.272181\pi\)
0.656158 + 0.754624i \(0.272181\pi\)
\(140\) 0 0
\(141\) −14.0187 −1.18058
\(142\) 0 0
\(143\) 0.495336i 0.0414220i
\(144\) 0 0
\(145\) −9.93230 + 12.5303i −0.824833 + 1.04059i
\(146\) 0 0
\(147\) 8.99067i 0.741538i
\(148\) 0 0
\(149\) 17.1893 1.40820 0.704101 0.710100i \(-0.251350\pi\)
0.704101 + 0.710100i \(0.251350\pi\)
\(150\) 0 0
\(151\) −3.29200 −0.267899 −0.133950 0.990988i \(-0.542766\pi\)
−0.133950 + 0.990988i \(0.542766\pi\)
\(152\) 0 0
\(153\) 2.44398i 0.197584i
\(154\) 0 0
\(155\) 10.8166 13.6460i 0.868814 1.09607i
\(156\) 0 0
\(157\) 15.1893i 1.21224i −0.795374 0.606119i \(-0.792726\pi\)
0.795374 0.606119i \(-0.207274\pi\)
\(158\) 0 0
\(159\) 11.0993 0.880233
\(160\) 0 0
\(161\) 3.13201 0.246837
\(162\) 0 0
\(163\) 14.0700i 1.10205i 0.834489 + 0.551024i \(0.185763\pi\)
−0.834489 + 0.551024i \(0.814237\pi\)
\(164\) 0 0
\(165\) 8.37266 + 6.63667i 0.651810 + 0.516664i
\(166\) 0 0
\(167\) 14.7967i 1.14500i −0.819905 0.572500i \(-0.805974\pi\)
0.819905 0.572500i \(-0.194026\pi\)
\(168\) 0 0
\(169\) 12.9800 0.998463
\(170\) 0 0
\(171\) 1.14134 0.0872802
\(172\) 0 0
\(173\) 17.2920i 1.31469i −0.753591 0.657343i \(-0.771680\pi\)
0.753591 0.657343i \(-0.228320\pi\)
\(174\) 0 0
\(175\) 3.09931 0.726656i 0.234286 0.0549301i
\(176\) 0 0
\(177\) 7.69735i 0.578568i
\(178\) 0 0
\(179\) 17.7360 1.32565 0.662825 0.748774i \(-0.269357\pi\)
0.662825 + 0.748774i \(0.269357\pi\)
\(180\) 0 0
\(181\) 6.17997 0.459354 0.229677 0.973267i \(-0.426233\pi\)
0.229677 + 0.973267i \(0.426233\pi\)
\(182\) 0 0
\(183\) 8.85527i 0.654601i
\(184\) 0 0
\(185\) −5.73599 4.54669i −0.421718 0.334279i
\(186\) 0 0
\(187\) 7.50466i 0.548795i
\(188\) 0 0
\(189\) 3.59465 0.261472
\(190\) 0 0
\(191\) −14.6367 −1.05907 −0.529536 0.848287i \(-0.677634\pi\)
−0.529536 + 0.848287i \(0.677634\pi\)
\(192\) 0 0
\(193\) 20.0187i 1.44097i 0.693468 + 0.720487i \(0.256082\pi\)
−0.693468 + 0.720487i \(0.743918\pi\)
\(194\) 0 0
\(195\) −0.267644 + 0.337653i −0.0191664 + 0.0241798i
\(196\) 0 0
\(197\) 9.94865i 0.708812i 0.935092 + 0.354406i \(0.115317\pi\)
−0.935092 + 0.354406i \(0.884683\pi\)
\(198\) 0 0
\(199\) 9.74870 0.691067 0.345534 0.938406i \(-0.387698\pi\)
0.345534 + 0.938406i \(0.387698\pi\)
\(200\) 0 0
\(201\) 11.4147 0.805129
\(202\) 0 0
\(203\) 4.55263i 0.319532i
\(204\) 0 0
\(205\) −5.87732 + 7.41468i −0.410490 + 0.517864i
\(206\) 0 0
\(207\) 5.61462i 0.390243i
\(208\) 0 0
\(209\) −3.50466 −0.242423
\(210\) 0 0
\(211\) 20.7580 1.42904 0.714521 0.699614i \(-0.246645\pi\)
0.714521 + 0.699614i \(0.246645\pi\)
\(212\) 0 0
\(213\) 12.2127i 0.836798i
\(214\) 0 0
\(215\) −4.37266 3.46603i −0.298213 0.236381i
\(216\) 0 0
\(217\) 4.95798i 0.336569i
\(218\) 0 0
\(219\) −5.04070 −0.340619
\(220\) 0 0
\(221\) −0.302648 −0.0203583
\(222\) 0 0
\(223\) 10.7267i 0.718310i 0.933278 + 0.359155i \(0.116935\pi\)
−0.933278 + 0.359155i \(0.883065\pi\)
\(224\) 0 0
\(225\) −1.30265 5.55602i −0.0868432 0.370401i
\(226\) 0 0
\(227\) 12.5526i 0.833147i 0.909102 + 0.416574i \(0.136769\pi\)
−0.909102 + 0.416574i \(0.863231\pi\)
\(228\) 0 0
\(229\) −25.4720 −1.68324 −0.841618 0.540074i \(-0.818396\pi\)
−0.841618 + 0.540074i \(0.818396\pi\)
\(230\) 0 0
\(231\) −3.04202 −0.200150
\(232\) 0 0
\(233\) 3.11203i 0.203876i −0.994791 0.101938i \(-0.967496\pi\)
0.994791 0.101938i \(-0.0325043\pi\)
\(234\) 0 0
\(235\) −18.0187 14.2827i −1.17541 0.931699i
\(236\) 0 0
\(237\) 5.69867i 0.370168i
\(238\) 0 0
\(239\) −1.54330 −0.0998276 −0.0499138 0.998754i \(-0.515895\pi\)
−0.0499138 + 0.998754i \(0.515895\pi\)
\(240\) 0 0
\(241\) 10.2827 0.662365 0.331183 0.943567i \(-0.392552\pi\)
0.331183 + 0.943567i \(0.392552\pi\)
\(242\) 0 0
\(243\) 11.1120i 0.712837i
\(244\) 0 0
\(245\) 9.15999 11.5560i 0.585211 0.738287i
\(246\) 0 0
\(247\) 0.141336i 0.00899300i
\(248\) 0 0
\(249\) 12.2827 0.778383
\(250\) 0 0
\(251\) 2.51399 0.158682 0.0793409 0.996848i \(-0.474718\pi\)
0.0793409 + 0.996848i \(0.474718\pi\)
\(252\) 0 0
\(253\) 17.2406i 1.08391i
\(254\) 0 0
\(255\) −4.05498 + 5.11566i −0.253933 + 0.320355i
\(256\) 0 0
\(257\) 24.7967i 1.54677i 0.633934 + 0.773387i \(0.281439\pi\)
−0.633934 + 0.773387i \(0.718561\pi\)
\(258\) 0 0
\(259\) 2.08405 0.129496
\(260\) 0 0
\(261\) −8.16131 −0.505173
\(262\) 0 0
\(263\) 22.5653i 1.39144i 0.718314 + 0.695719i \(0.244914\pi\)
−0.718314 + 0.695719i \(0.755086\pi\)
\(264\) 0 0
\(265\) 14.2663 + 11.3083i 0.876373 + 0.694666i
\(266\) 0 0
\(267\) 9.24065i 0.565519i
\(268\) 0 0
\(269\) 26.5653 1.61972 0.809859 0.586625i \(-0.199544\pi\)
0.809859 + 0.586625i \(0.199544\pi\)
\(270\) 0 0
\(271\) 24.9380 1.51488 0.757438 0.652907i \(-0.226451\pi\)
0.757438 + 0.652907i \(0.226451\pi\)
\(272\) 0 0
\(273\) 0.122679i 0.00742485i
\(274\) 0 0
\(275\) 4.00000 + 17.0607i 0.241209 + 1.02880i
\(276\) 0 0
\(277\) 18.5467i 1.11436i −0.830391 0.557181i \(-0.811883\pi\)
0.830391 0.557181i \(-0.188117\pi\)
\(278\) 0 0
\(279\) 8.88797 0.532109
\(280\) 0 0
\(281\) 24.7967 1.47925 0.739623 0.673022i \(-0.235004\pi\)
0.739623 + 0.673022i \(0.235004\pi\)
\(282\) 0 0
\(283\) 13.5747i 0.806931i −0.914995 0.403465i \(-0.867806\pi\)
0.914995 0.403465i \(-0.132194\pi\)
\(284\) 0 0
\(285\) −2.38900 1.89367i −0.141512 0.112171i
\(286\) 0 0
\(287\) 2.69396i 0.159020i
\(288\) 0 0
\(289\) 12.4147 0.730275
\(290\) 0 0
\(291\) −19.8573 −1.16406
\(292\) 0 0
\(293\) 15.6133i 0.912139i −0.889944 0.456070i \(-0.849257\pi\)
0.889944 0.456070i \(-0.150743\pi\)
\(294\) 0 0
\(295\) −7.84232 + 9.89367i −0.456597 + 0.576032i
\(296\) 0 0
\(297\) 19.7873i 1.14818i
\(298\) 0 0
\(299\) −0.695281 −0.0402091
\(300\) 0 0
\(301\) 1.58871 0.0915717
\(302\) 0 0
\(303\) 22.6540i 1.30144i
\(304\) 0 0
\(305\) −9.02205 + 11.3820i −0.516601 + 0.651731i
\(306\) 0 0
\(307\) 34.0187i 1.94155i 0.239997 + 0.970774i \(0.422854\pi\)
−0.239997 + 0.970774i \(0.577146\pi\)
\(308\) 0 0
\(309\) −12.3527 −0.702719
\(310\) 0 0
\(311\) −8.93800 −0.506828 −0.253414 0.967358i \(-0.581553\pi\)
−0.253414 + 0.967358i \(0.581553\pi\)
\(312\) 0 0
\(313\) 18.4240i 1.04139i −0.853744 0.520693i \(-0.825674\pi\)
0.853744 0.520693i \(-0.174326\pi\)
\(314\) 0 0
\(315\) 1.27334 + 1.00933i 0.0717448 + 0.0568692i
\(316\) 0 0
\(317\) 33.5547i 1.88462i −0.334742 0.942310i \(-0.608649\pi\)
0.334742 0.942310i \(-0.391351\pi\)
\(318\) 0 0
\(319\) 25.0607 1.40313
\(320\) 0 0
\(321\) 0.122679 0.00684726
\(322\) 0 0
\(323\) 2.14134i 0.119147i
\(324\) 0 0
\(325\) −0.688023 + 0.161312i −0.0381647 + 0.00894798i
\(326\) 0 0
\(327\) 18.5340i 1.02493i
\(328\) 0 0
\(329\) 6.54669 0.360931
\(330\) 0 0
\(331\) −2.25130 −0.123742 −0.0618712 0.998084i \(-0.519707\pi\)
−0.0618712 + 0.998084i \(0.519707\pi\)
\(332\) 0 0
\(333\) 3.73599i 0.204731i
\(334\) 0 0
\(335\) 14.6717 + 11.6297i 0.801599 + 0.635396i
\(336\) 0 0
\(337\) 21.3620i 1.16366i 0.813309 + 0.581831i \(0.197664\pi\)
−0.813309 + 0.581831i \(0.802336\pi\)
\(338\) 0 0
\(339\) 15.7101 0.853254
\(340\) 0 0
\(341\) −27.2920 −1.47794
\(342\) 0 0
\(343\) 8.65533i 0.467344i
\(344\) 0 0
\(345\) −9.31561 + 11.7523i −0.501535 + 0.632724i
\(346\) 0 0
\(347\) 11.5560i 0.620359i 0.950678 + 0.310180i \(0.100389\pi\)
−0.950678 + 0.310180i \(0.899611\pi\)
\(348\) 0 0
\(349\) 17.1120 0.915986 0.457993 0.888956i \(-0.348568\pi\)
0.457993 + 0.888956i \(0.348568\pi\)
\(350\) 0 0
\(351\) −0.797984 −0.0425932
\(352\) 0 0
\(353\) 11.6974i 0.622587i 0.950314 + 0.311294i \(0.100762\pi\)
−0.950314 + 0.311294i \(0.899238\pi\)
\(354\) 0 0
\(355\) 12.4427 15.6974i 0.660388 0.833129i
\(356\) 0 0
\(357\) 1.85866i 0.0983709i
\(358\) 0 0
\(359\) −4.47536 −0.236200 −0.118100 0.993002i \(-0.537680\pi\)
−0.118100 + 0.993002i \(0.537680\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 1.74870i 0.0917831i
\(364\) 0 0
\(365\) −6.47899 5.13564i −0.339126 0.268811i
\(366\) 0 0
\(367\) 18.7453i 0.978497i 0.872144 + 0.489249i \(0.162729\pi\)
−0.872144 + 0.489249i \(0.837271\pi\)
\(368\) 0 0
\(369\) −4.82936 −0.251406
\(370\) 0 0
\(371\) −5.18336 −0.269107
\(372\) 0 0
\(373\) 1.69735i 0.0878855i 0.999034 + 0.0439428i \(0.0139919\pi\)
−0.999034 + 0.0439428i \(0.986008\pi\)
\(374\) 0 0
\(375\) −6.49171 + 13.7910i −0.335230 + 0.712162i
\(376\) 0 0
\(377\) 1.01065i 0.0520510i
\(378\) 0 0
\(379\) 2.63667 0.135437 0.0677184 0.997704i \(-0.478428\pi\)
0.0677184 + 0.997704i \(0.478428\pi\)
\(380\) 0 0
\(381\) −4.48808 −0.229931
\(382\) 0 0
\(383\) 12.4953i 0.638482i −0.947674 0.319241i \(-0.896572\pi\)
0.947674 0.319241i \(-0.103428\pi\)
\(384\) 0 0
\(385\) −3.91002 3.09931i −0.199273 0.157956i
\(386\) 0 0
\(387\) 2.84802i 0.144773i
\(388\) 0 0
\(389\) 4.51399 0.228869 0.114434 0.993431i \(-0.463494\pi\)
0.114434 + 0.993431i \(0.463494\pi\)
\(390\) 0 0
\(391\) −10.5340 −0.532726
\(392\) 0 0
\(393\) 24.5653i 1.23916i
\(394\) 0 0
\(395\) −5.80599 + 7.32469i −0.292131 + 0.368545i
\(396\) 0 0
\(397\) 35.6774i 1.79060i 0.445468 + 0.895298i \(0.353037\pi\)
−0.445468 + 0.895298i \(0.646963\pi\)
\(398\) 0 0
\(399\) 0.867993 0.0434540
\(400\) 0 0
\(401\) 15.3434 0.766210 0.383105 0.923705i \(-0.374855\pi\)
0.383105 + 0.923705i \(0.374855\pi\)
\(402\) 0 0
\(403\) 1.10063i 0.0548264i
\(404\) 0 0
\(405\) −5.93569 + 7.48832i −0.294947 + 0.372097i
\(406\) 0 0
\(407\) 11.4720i 0.568644i
\(408\) 0 0
\(409\) −29.3620 −1.45186 −0.725929 0.687770i \(-0.758590\pi\)
−0.725929 + 0.687770i \(0.758590\pi\)
\(410\) 0 0
\(411\) 19.6647 0.969986
\(412\) 0 0
\(413\) 3.59465i 0.176881i
\(414\) 0 0
\(415\) 15.7873 + 12.5140i 0.774970 + 0.614288i
\(416\) 0 0
\(417\) 21.0934i 1.03295i
\(418\) 0 0
\(419\) 25.1379 1.22807 0.614035 0.789279i \(-0.289546\pi\)
0.614035 + 0.789279i \(0.289546\pi\)
\(420\) 0 0
\(421\) 14.5454 0.708898 0.354449 0.935075i \(-0.384668\pi\)
0.354449 + 0.935075i \(0.384668\pi\)
\(422\) 0 0
\(423\) 11.7360i 0.570623i
\(424\) 0 0
\(425\) −10.4240 + 2.44398i −0.505639 + 0.118551i
\(426\) 0 0
\(427\) 4.13540i 0.200126i
\(428\) 0 0
\(429\) 0.675305 0.0326040
\(430\) 0 0
\(431\) −19.4020 −0.934560 −0.467280 0.884109i \(-0.654766\pi\)
−0.467280 + 0.884109i \(0.654766\pi\)
\(432\) 0 0
\(433\) 5.50466i 0.264537i 0.991214 + 0.132269i \(0.0422262\pi\)
−0.991214 + 0.132269i \(0.957774\pi\)
\(434\) 0 0
\(435\) 17.0830 + 13.5410i 0.819066 + 0.649241i
\(436\) 0 0
\(437\) 4.91934i 0.235324i
\(438\) 0 0
\(439\) 12.2500 0.584660 0.292330 0.956318i \(-0.405570\pi\)
0.292330 + 0.956318i \(0.405570\pi\)
\(440\) 0 0
\(441\) 7.52671 0.358415
\(442\) 0 0
\(443\) 31.6006i 1.50139i −0.660649 0.750695i \(-0.729719\pi\)
0.660649 0.750695i \(-0.270281\pi\)
\(444\) 0 0
\(445\) 9.41468 11.8773i 0.446299 0.563039i
\(446\) 0 0
\(447\) 23.4347i 1.10842i
\(448\) 0 0
\(449\) 36.0187 1.69983 0.849913 0.526923i \(-0.176655\pi\)
0.849913 + 0.526923i \(0.176655\pi\)
\(450\) 0 0
\(451\) 14.8294 0.698287
\(452\) 0 0
\(453\) 4.48808i 0.210868i
\(454\) 0 0
\(455\) 0.124989 0.157683i 0.00585958 0.00739230i
\(456\) 0 0
\(457\) 22.1413i 1.03573i −0.855463 0.517864i \(-0.826727\pi\)
0.855463 0.517864i \(-0.173273\pi\)
\(458\) 0 0
\(459\) −12.0900 −0.564312
\(460\) 0 0
\(461\) −2.31537 −0.107837 −0.0539187 0.998545i \(-0.517171\pi\)
−0.0539187 + 0.998545i \(0.517171\pi\)
\(462\) 0 0
\(463\) 15.8387i 0.736086i −0.929809 0.368043i \(-0.880028\pi\)
0.929809 0.368043i \(-0.119972\pi\)
\(464\) 0 0
\(465\) −18.6040 14.7466i −0.862739 0.683859i
\(466\) 0 0
\(467\) 23.1379i 1.07070i 0.844631 + 0.535348i \(0.179820\pi\)
−0.844631 + 0.535348i \(0.820180\pi\)
\(468\) 0 0
\(469\) −5.33063 −0.246146
\(470\) 0 0
\(471\) −20.7080 −0.954174
\(472\) 0 0
\(473\) 8.74531i 0.402110i
\(474\) 0 0
\(475\) −1.14134 4.86799i −0.0523681 0.223359i
\(476\) 0 0
\(477\) 9.29200i 0.425451i
\(478\) 0 0
\(479\) −10.1214 −0.462457 −0.231228 0.972900i \(-0.574274\pi\)
−0.231228 + 0.972900i \(0.574274\pi\)
\(480\) 0 0
\(481\) −0.462642 −0.0210946
\(482\) 0 0
\(483\) 4.26995i 0.194290i
\(484\) 0 0
\(485\) −25.5233 20.2313i −1.15895 0.918657i
\(486\) 0 0
\(487\) 20.3854i 0.923750i 0.886945 + 0.461875i \(0.152823\pi\)
−0.886945 + 0.461875i \(0.847177\pi\)
\(488\) 0 0
\(489\) 19.1820 0.867442
\(490\) 0 0
\(491\) 7.78734 0.351438 0.175719 0.984440i \(-0.443775\pi\)
0.175719 + 0.984440i \(0.443775\pi\)
\(492\) 0 0
\(493\) 15.3120i 0.689617i
\(494\) 0 0
\(495\) −5.55602 + 7.00933i −0.249724 + 0.315046i
\(496\) 0 0
\(497\) 5.70329i 0.255828i
\(498\) 0 0
\(499\) 4.31537 0.193182 0.0965912 0.995324i \(-0.469206\pi\)
0.0965912 + 0.995324i \(0.469206\pi\)
\(500\) 0 0
\(501\) −20.1727 −0.901250
\(502\) 0 0
\(503\) 18.5526i 0.827221i −0.910454 0.413610i \(-0.864268\pi\)
0.910454 0.413610i \(-0.135732\pi\)
\(504\) 0 0
\(505\) −23.0807 + 29.1180i −1.02708 + 1.29573i
\(506\) 0 0
\(507\) 17.6960i 0.785908i
\(508\) 0 0
\(509\) 7.73599 0.342892 0.171446 0.985194i \(-0.445156\pi\)
0.171446 + 0.985194i \(0.445156\pi\)
\(510\) 0 0
\(511\) 2.35400 0.104135
\(512\) 0 0
\(513\) 5.64600i 0.249277i
\(514\) 0 0
\(515\) −15.8773 12.5853i −0.699638 0.554575i
\(516\) 0 0
\(517\) 36.0373i 1.58492i
\(518\) 0 0
\(519\) −23.5747 −1.03481
\(520\) 0 0
\(521\) 15.2080 0.666273 0.333136 0.942879i \(-0.391893\pi\)
0.333136 + 0.942879i \(0.391893\pi\)
\(522\) 0 0
\(523\) 18.2113i 0.796327i 0.917315 + 0.398163i \(0.130352\pi\)
−0.917315 + 0.398163i \(0.869648\pi\)
\(524\) 0 0
\(525\) −0.990671 4.22538i −0.0432364 0.184411i
\(526\) 0 0
\(527\) 16.6753i 0.726388i
\(528\) 0 0
\(529\) −1.19995 −0.0521715
\(530\) 0 0
\(531\) −6.44398 −0.279645
\(532\) 0 0
\(533\) 0.598038i 0.0259039i
\(534\) 0 0
\(535\) 0.157683 + 0.124989i 0.00681724 + 0.00540375i
\(536\) 0 0
\(537\) 24.1800i 1.04344i
\(538\) 0 0
\(539\) −23.1120 −0.995506
\(540\) 0 0
\(541\) 16.5140 0.709992 0.354996 0.934868i \(-0.384482\pi\)
0.354996 + 0.934868i \(0.384482\pi\)
\(542\) 0 0
\(543\) 8.42533i 0.361565i
\(544\) 0 0
\(545\) 18.8830 23.8223i 0.808860 1.02044i
\(546\) 0 0
\(547\) 16.2827i 0.696197i 0.937458 + 0.348098i \(0.113172\pi\)
−0.937458 + 0.348098i \(0.886828\pi\)
\(548\) 0 0
\(549\) −7.41336 −0.316395
\(550\) 0 0
\(551\) −7.15066 −0.304629
\(552\) 0 0
\(553\) 2.66127i 0.113169i
\(554\) 0 0
\(555\) −6.19863 + 7.82003i −0.263117 + 0.331942i
\(556\) 0 0
\(557\) 37.4533i 1.58695i −0.608604 0.793474i \(-0.708270\pi\)
0.608604 0.793474i \(-0.291730\pi\)
\(558\) 0 0
\(559\) −0.352681 −0.0149168
\(560\) 0 0
\(561\) 10.2313 0.431967
\(562\) 0 0
\(563\) 29.1307i 1.22771i 0.789418 + 0.613856i \(0.210382\pi\)
−0.789418 + 0.613856i \(0.789618\pi\)
\(564\) 0 0
\(565\) 20.1927 + 16.0059i 0.849513 + 0.673375i
\(566\) 0 0
\(567\) 2.72072i 0.114259i
\(568\) 0 0
\(569\) −14.8480 −0.622461 −0.311231 0.950334i \(-0.600741\pi\)
−0.311231 + 0.950334i \(0.600741\pi\)
\(570\) 0 0
\(571\) −41.9087 −1.75382 −0.876912 0.480651i \(-0.840401\pi\)
−0.876912 + 0.480651i \(0.840401\pi\)
\(572\) 0 0
\(573\) 19.9546i 0.833615i
\(574\) 0 0
\(575\) −23.9473 + 5.61462i −0.998673 + 0.234146i
\(576\) 0 0
\(577\) 16.4427i 0.684517i −0.939606 0.342259i \(-0.888808\pi\)
0.939606 0.342259i \(-0.111192\pi\)
\(578\) 0 0
\(579\) 27.2920 1.13422
\(580\) 0 0
\(581\) −5.73599 −0.237969
\(582\) 0 0
\(583\) 28.5327i 1.18170i
\(584\) 0 0
\(585\) −0.282672 0.224063i −0.0116871 0.00926387i
\(586\) 0 0
\(587\) 42.5327i 1.75551i −0.479109 0.877755i \(-0.659040\pi\)
0.479109 0.877755i \(-0.340960\pi\)
\(588\) 0 0
\(589\) 7.78734 0.320872
\(590\) 0 0
\(591\) 13.5633 0.557919
\(592\) 0 0
\(593\) 3.92273i 0.161087i 0.996751 + 0.0805437i \(0.0256656\pi\)
−0.996751 + 0.0805437i \(0.974334\pi\)
\(594\) 0 0
\(595\) 1.89367 2.38900i 0.0776328 0.0979396i
\(596\) 0 0
\(597\) 13.2907i 0.543951i
\(598\) 0 0
\(599\) −10.7594 −0.439615 −0.219808 0.975543i \(-0.570543\pi\)
−0.219808 + 0.975543i \(0.570543\pi\)
\(600\) 0 0
\(601\) 25.2220 1.02883 0.514413 0.857542i \(-0.328010\pi\)
0.514413 + 0.857542i \(0.328010\pi\)
\(602\) 0 0
\(603\) 9.55602i 0.389151i
\(604\) 0 0
\(605\) 1.78164 2.24767i 0.0724338 0.0913807i
\(606\) 0 0
\(607\) 39.2920i 1.59481i 0.603442 + 0.797407i \(0.293795\pi\)
−0.603442 + 0.797407i \(0.706205\pi\)
\(608\) 0 0
\(609\) −6.20672 −0.251509
\(610\) 0 0
\(611\) −1.45331 −0.0587947
\(612\) 0 0
\(613\) 9.80599i 0.396060i 0.980196 + 0.198030i \(0.0634544\pi\)
−0.980196 + 0.198030i \(0.936546\pi\)
\(614\) 0 0
\(615\) 10.1086 + 8.01272i 0.407620 + 0.323104i
\(616\) 0 0
\(617\) 35.0093i 1.40942i 0.709494 + 0.704711i \(0.248923\pi\)
−0.709494 + 0.704711i \(0.751077\pi\)
\(618\) 0 0
\(619\) 13.4206 0.539420 0.269710 0.962942i \(-0.413072\pi\)
0.269710 + 0.962942i \(0.413072\pi\)
\(620\) 0 0
\(621\) −27.7746 −1.11456
\(622\) 0 0
\(623\) 4.31537i 0.172891i
\(624\) 0 0
\(625\) −22.3947 + 11.1120i −0.895788 + 0.444481i
\(626\) 0 0
\(627\) 4.77801i 0.190815i
\(628\) 0 0
\(629\) −7.00933 −0.279480
\(630\) 0 0
\(631\) −40.5254 −1.61329 −0.806645 0.591036i \(-0.798719\pi\)
−0.806645 + 0.591036i \(0.798719\pi\)
\(632\) 0 0
\(633\) 28.3000i 1.12482i
\(634\) 0 0
\(635\) −5.76868 4.57260i −0.228923 0.181458i
\(636\) 0 0
\(637\) 0.932062i 0.0369296i
\(638\) 0 0
\(639\) 10.2241 0.404458
\(640\) 0 0
\(641\) −26.0700 −1.02970 −0.514852 0.857279i \(-0.672153\pi\)
−0.514852 + 0.857279i \(0.672153\pi\)
\(642\) 0 0
\(643\) 30.1400i 1.18861i −0.804241 0.594303i \(-0.797428\pi\)
0.804241 0.594303i \(-0.202572\pi\)
\(644\) 0 0
\(645\) −4.72534 + 5.96137i −0.186060 + 0.234729i
\(646\) 0 0
\(647\) 20.1086i 0.790552i −0.918562 0.395276i \(-0.870649\pi\)
0.918562 0.395276i \(-0.129351\pi\)
\(648\) 0 0
\(649\) 19.7873 0.776721
\(650\) 0 0
\(651\) 6.75935 0.264920
\(652\) 0 0
\(653\) 28.0373i 1.09718i −0.836090 0.548592i \(-0.815164\pi\)
0.836090 0.548592i \(-0.184836\pi\)
\(654\) 0 0
\(655\) −25.0280 + 31.5747i −0.977924 + 1.23372i
\(656\) 0 0
\(657\) 4.21992i 0.164635i
\(658\) 0 0
\(659\) 4.90069 0.190904 0.0954518 0.995434i \(-0.469570\pi\)
0.0954518 + 0.995434i \(0.469570\pi\)
\(660\) 0 0
\(661\) −8.03863 −0.312667 −0.156333 0.987704i \(-0.549967\pi\)
−0.156333 + 0.987704i \(0.549967\pi\)
\(662\) 0 0
\(663\) 0.412609i 0.0160244i
\(664\) 0 0
\(665\) 1.11566 + 0.884340i 0.0432635 + 0.0342932i
\(666\) 0 0
\(667\) 35.1766i 1.36204i
\(668\) 0 0
\(669\) 14.6240 0.565395
\(670\) 0 0
\(671\) 22.7640 0.878793
\(672\) 0 0
\(673\) 4.82936i 0.186158i −0.995659 0.0930791i \(-0.970329\pi\)
0.995659 0.0930791i \(-0.0296709\pi\)
\(674\) 0 0
\(675\) −27.4847 + 6.44398i −1.05789 + 0.248029i
\(676\) 0 0
\(677\) 12.8094i 0.492305i −0.969231 0.246152i \(-0.920834\pi\)
0.969231 0.246152i \(-0.0791663\pi\)
\(678\) 0 0
\(679\) 9.27334 0.355878
\(680\) 0 0
\(681\) 17.1133 0.655785
\(682\) 0 0
\(683\) 37.1307i 1.42077i −0.703815 0.710383i \(-0.748522\pi\)
0.703815 0.710383i \(-0.251478\pi\)
\(684\) 0 0
\(685\) 25.2757 + 20.0350i 0.965733 + 0.765498i
\(686\) 0 0
\(687\) 34.7267i 1.32490i
\(688\) 0 0
\(689\) 1.15066 0.0438368
\(690\) 0 0
\(691\) 18.1986 0.692308 0.346154 0.938178i \(-0.387487\pi\)
0.346154 + 0.938178i \(0.387487\pi\)
\(692\) 0 0
\(693\) 2.54669i 0.0967406i
\(694\) 0 0
\(695\) 21.4906 27.1120i 0.815186 1.02842i
\(696\) 0 0
\(697\) 9.06068i 0.343198i
\(698\) 0 0
\(699\) −4.24272 −0.160474
\(700\) 0 0
\(701\) −26.2827 −0.992683 −0.496341 0.868127i \(-0.665324\pi\)
−0.496341 + 0.868127i \(0.665324\pi\)
\(702\) 0 0
\(703\) 3.27334i 0.123456i
\(704\) 0 0
\(705\) −19.4720 + 24.5653i −0.733357 + 0.925184i
\(706\) 0 0
\(707\) 10.5794i 0.397879i
\(708\) 0 0
\(709\) 14.9253 0.560531 0.280265 0.959923i \(-0.409578\pi\)
0.280265 + 0.959923i \(0.409578\pi\)
\(710\) 0 0
\(711\) −4.77075 −0.178917
\(712\) 0 0
\(713\) 38.3086i 1.43467i
\(714\) 0 0
\(715\) 0.867993 + 0.688023i 0.0324611 + 0.0257306i
\(716\) 0 0
\(717\) 2.10402i 0.0785761i
\(718\) 0 0
\(719\) 32.3327 1.20581 0.602903 0.797814i \(-0.294011\pi\)
0.602903 + 0.797814i \(0.294011\pi\)
\(720\) 0 0
\(721\) 5.76868 0.214837
\(722\) 0 0
\(723\) 14.0187i 0.521359i
\(724\) 0 0
\(725\) 8.16131 + 34.8094i 0.303104 + 1.29279i
\(726\) 0 0
\(727\) 42.0246i 1.55861i −0.626647 0.779303i \(-0.715573\pi\)
0.626647 0.779303i \(-0.284427\pi\)
\(728\) 0 0
\(729\) −27.9694 −1.03590
\(730\) 0 0
\(731\) −5.34335 −0.197631
\(732\) 0 0
\(733\) 26.5840i 0.981903i 0.871187 + 0.490951i \(0.163351\pi\)
−0.871187 + 0.490951i \(0.836649\pi\)
\(734\) 0 0
\(735\) −15.7546 12.4881i −0.581119 0.460630i
\(736\) 0 0
\(737\) 29.3434i 1.08088i
\(738\) 0 0
\(739\) 8.14728 0.299702 0.149851 0.988709i \(-0.452121\pi\)
0.149851 + 0.988709i \(0.452121\pi\)
\(740\) 0 0
\(741\) −0.192688 −0.00707855
\(742\) 0 0
\(743\) 35.8247i 1.31428i −0.753769 0.657139i \(-0.771766\pi\)
0.753769 0.657139i \(-0.228234\pi\)
\(744\) 0 0
\(745\) 23.8760 30.1214i 0.874749 1.10356i
\(746\) 0 0
\(747\) 10.2827i 0.376223i
\(748\) 0 0
\(749\) −0.0572907 −0.00209336
\(750\) 0 0
\(751\) 14.8994 0.543686 0.271843 0.962342i \(-0.412367\pi\)
0.271843 + 0.962342i \(0.412367\pi\)
\(752\) 0 0
\(753\) 3.42740i 0.124901i
\(754\) 0 0
\(755\) −4.57260 + 5.76868i −0.166414 + 0.209944i
\(756\) 0 0
\(757\) 47.7920i 1.73703i 0.495664 + 0.868514i \(0.334925\pi\)
−0.495664 + 0.868514i \(0.665075\pi\)
\(758\) 0 0
\(759\) 23.5047 0.853165
\(760\) 0 0
\(761\) −38.9053 −1.41032 −0.705158 0.709050i \(-0.749124\pi\)
−0.705158 + 0.709050i \(0.749124\pi\)
\(762\) 0 0
\(763\) 8.65533i 0.313344i
\(764\) 0 0
\(765\) −4.28267 3.39470i −0.154840 0.122736i
\(766\) 0 0
\(767\) 0.797984i 0.0288135i
\(768\) 0 0
\(769\) −8.74663 −0.315412 −0.157706 0.987486i \(-0.550410\pi\)
−0.157706 + 0.987486i \(0.550410\pi\)
\(770\) 0 0
\(771\) 33.8060 1.21749
\(772\) 0 0
\(773\) 23.4707i 0.844181i −0.906554 0.422090i \(-0.861297\pi\)
0.906554 0.422090i \(-0.138703\pi\)
\(774\) 0 0
\(775\) −8.88797 37.9087i −0.319265 1.36172i
\(776\) 0 0
\(777\) 2.84124i 0.101929i
\(778\) 0 0
\(779\) −4.23132 −0.151603
\(780\) 0 0
\(781\) −31.3947 −1.12339
\(782\) 0 0
\(783\) 40.3727i 1.44280i
\(784\) 0 0
\(785\) −26.6167 21.0980i −0.949991 0.753020i
\(786\) 0 0
\(787\) 1.26063i 0.0449364i 0.999748 + 0.0224682i \(0.00715246\pi\)
−0.999748 + 0.0224682i \(0.992848\pi\)
\(788\) 0 0
\(789\) 30.7640 1.09523
\(790\) 0 0
\(791\) −7.33657 −0.260859
\(792\) 0 0
\(793\) 0.918026i 0.0326000i
\(794\) 0 0
\(795\) 15.4170 19.4497i 0.546784 0.689809i
\(796\) 0 0
\(797\) 38.6481i 1.36898i 0.729020 + 0.684492i \(0.239976\pi\)
−0.729020 + 0.684492i \(0.760024\pi\)
\(798\) 0 0
\(799\) −22.0187 −0.778964
\(800\) 0 0
\(801\) 7.73599 0.273338
\(802\) 0 0