Properties

Label 1520.2.d.b.609.2
Level $1520$
Weight $2$
Character 1520.609
Analytic conductor $12.137$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 609.2
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 1520.609
Dual form 1520.2.d.b.609.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 + 2.00000i) q^{5} +2.00000i q^{7} +3.00000 q^{9} +O(q^{10})\) \(q+(-1.00000 + 2.00000i) q^{5} +2.00000i q^{7} +3.00000 q^{9} +4.00000 q^{11} -2.00000i q^{13} -4.00000i q^{17} +1.00000 q^{19} +6.00000i q^{23} +(-3.00000 - 4.00000i) q^{25} +6.00000 q^{29} +4.00000 q^{31} +(-4.00000 - 2.00000i) q^{35} +10.0000i q^{37} -10.0000 q^{41} -2.00000i q^{43} +(-3.00000 + 6.00000i) q^{45} -6.00000i q^{47} +3.00000 q^{49} +10.0000i q^{53} +(-4.00000 + 8.00000i) q^{55} +2.00000 q^{61} +6.00000i q^{63} +(4.00000 + 2.00000i) q^{65} +8.00000i q^{67} -4.00000 q^{71} +4.00000i q^{73} +8.00000i q^{77} +4.00000 q^{79} +9.00000 q^{81} +18.0000i q^{83} +(8.00000 + 4.00000i) q^{85} +2.00000 q^{89} +4.00000 q^{91} +(-1.00000 + 2.00000i) q^{95} -6.00000i q^{97} +12.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{5} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{5} + 6 q^{9} + 8 q^{11} + 2 q^{19} - 6 q^{25} + 12 q^{29} + 8 q^{31} - 8 q^{35} - 20 q^{41} - 6 q^{45} + 6 q^{49} - 8 q^{55} + 4 q^{61} + 8 q^{65} - 8 q^{71} + 8 q^{79} + 18 q^{81} + 16 q^{85} + 4 q^{89} + 8 q^{91} - 2 q^{95} + 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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
\(3\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(4\) 0 0
\(5\) −1.00000 + 2.00000i −0.447214 + 0.894427i
\(6\) 0 0
\(7\) 2.00000i 0.755929i 0.925820 + 0.377964i \(0.123376\pi\)
−0.925820 + 0.377964i \(0.876624\pi\)
\(8\) 0 0
\(9\) 3.00000 1.00000
\(10\) 0 0
\(11\) 4.00000 1.20605 0.603023 0.797724i \(-0.293963\pi\)
0.603023 + 0.797724i \(0.293963\pi\)
\(12\) 0 0
\(13\) 2.00000i 0.554700i −0.960769 0.277350i \(-0.910544\pi\)
0.960769 0.277350i \(-0.0894562\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 4.00000i 0.970143i −0.874475 0.485071i \(-0.838794\pi\)
0.874475 0.485071i \(-0.161206\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 6.00000i 1.25109i 0.780189 + 0.625543i \(0.215123\pi\)
−0.780189 + 0.625543i \(0.784877\pi\)
\(24\) 0 0
\(25\) −3.00000 4.00000i −0.600000 0.800000i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −4.00000 2.00000i −0.676123 0.338062i
\(36\) 0 0
\(37\) 10.0000i 1.64399i 0.569495 + 0.821995i \(0.307139\pi\)
−0.569495 + 0.821995i \(0.692861\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −10.0000 −1.56174 −0.780869 0.624695i \(-0.785223\pi\)
−0.780869 + 0.624695i \(0.785223\pi\)
\(42\) 0 0
\(43\) 2.00000i 0.304997i −0.988304 0.152499i \(-0.951268\pi\)
0.988304 0.152499i \(-0.0487319\pi\)
\(44\) 0 0
\(45\) −3.00000 + 6.00000i −0.447214 + 0.894427i
\(46\) 0 0
\(47\) 6.00000i 0.875190i −0.899172 0.437595i \(-0.855830\pi\)
0.899172 0.437595i \(-0.144170\pi\)
\(48\) 0 0
\(49\) 3.00000 0.428571
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 10.0000i 1.37361i 0.726844 + 0.686803i \(0.240986\pi\)
−0.726844 + 0.686803i \(0.759014\pi\)
\(54\) 0 0
\(55\) −4.00000 + 8.00000i −0.539360 + 1.07872i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) 2.00000 0.256074 0.128037 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) 0 0
\(63\) 6.00000i 0.755929i
\(64\) 0 0
\(65\) 4.00000 + 2.00000i 0.496139 + 0.248069i
\(66\) 0 0
\(67\) 8.00000i 0.977356i 0.872464 + 0.488678i \(0.162521\pi\)
−0.872464 + 0.488678i \(0.837479\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −4.00000 −0.474713 −0.237356 0.971423i \(-0.576281\pi\)
−0.237356 + 0.971423i \(0.576281\pi\)
\(72\) 0 0
\(73\) 4.00000i 0.468165i 0.972217 + 0.234082i \(0.0752085\pi\)
−0.972217 + 0.234082i \(0.924791\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 8.00000i 0.911685i
\(78\) 0 0
\(79\) 4.00000 0.450035 0.225018 0.974355i \(-0.427756\pi\)
0.225018 + 0.974355i \(0.427756\pi\)
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) 18.0000i 1.97576i 0.155230 + 0.987878i \(0.450388\pi\)
−0.155230 + 0.987878i \(0.549612\pi\)
\(84\) 0 0
\(85\) 8.00000 + 4.00000i 0.867722 + 0.433861i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 2.00000 0.212000 0.106000 0.994366i \(-0.466196\pi\)
0.106000 + 0.994366i \(0.466196\pi\)
\(90\) 0 0
\(91\) 4.00000 0.419314
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −1.00000 + 2.00000i −0.102598 + 0.205196i
\(96\) 0 0
\(97\) 6.00000i 0.609208i −0.952479 0.304604i \(-0.901476\pi\)
0.952479 0.304604i \(-0.0985241\pi\)
\(98\) 0 0
\(99\) 12.0000 1.20605
\(100\) 0 0
\(101\) −6.00000 −0.597022 −0.298511 0.954406i \(-0.596490\pi\)
−0.298511 + 0.954406i \(0.596490\pi\)
\(102\) 0 0
\(103\) 16.0000i 1.57653i −0.615338 0.788263i \(-0.710980\pi\)
0.615338 0.788263i \(-0.289020\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 4.00000i 0.386695i −0.981130 0.193347i \(-0.938066\pi\)
0.981130 0.193347i \(-0.0619344\pi\)
\(108\) 0 0
\(109\) −6.00000 −0.574696 −0.287348 0.957826i \(-0.592774\pi\)
−0.287348 + 0.957826i \(0.592774\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 6.00000i 0.564433i 0.959351 + 0.282216i \(0.0910696\pi\)
−0.959351 + 0.282216i \(0.908930\pi\)
\(114\) 0 0
\(115\) −12.0000 6.00000i −1.11901 0.559503i
\(116\) 0 0
\(117\) 6.00000i 0.554700i
\(118\) 0 0
\(119\) 8.00000 0.733359
\(120\) 0 0
\(121\) 5.00000 0.454545
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 11.0000 2.00000i 0.983870 0.178885i
\(126\) 0 0
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 12.0000 1.04844 0.524222 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) 0 0
\(133\) 2.00000i 0.173422i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 12.0000i 1.02523i −0.858619 0.512615i \(-0.828677\pi\)
0.858619 0.512615i \(-0.171323\pi\)
\(138\) 0 0
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 8.00000i 0.668994i
\(144\) 0 0
\(145\) −6.00000 + 12.0000i −0.498273 + 0.996546i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 10.0000 0.819232 0.409616 0.912258i \(-0.365663\pi\)
0.409616 + 0.912258i \(0.365663\pi\)
\(150\) 0 0
\(151\) −24.0000 −1.95309 −0.976546 0.215308i \(-0.930924\pi\)
−0.976546 + 0.215308i \(0.930924\pi\)
\(152\) 0 0
\(153\) 12.0000i 0.970143i
\(154\) 0 0
\(155\) −4.00000 + 8.00000i −0.321288 + 0.642575i
\(156\) 0 0
\(157\) 8.00000i 0.638470i 0.947676 + 0.319235i \(0.103426\pi\)
−0.947676 + 0.319235i \(0.896574\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −12.0000 −0.945732
\(162\) 0 0
\(163\) 10.0000i 0.783260i −0.920123 0.391630i \(-0.871911\pi\)
0.920123 0.391630i \(-0.128089\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 12.0000i 0.928588i 0.885681 + 0.464294i \(0.153692\pi\)
−0.885681 + 0.464294i \(0.846308\pi\)
\(168\) 0 0
\(169\) 9.00000 0.692308
\(170\) 0 0
\(171\) 3.00000 0.229416
\(172\) 0 0
\(173\) 6.00000i 0.456172i −0.973641 0.228086i \(-0.926753\pi\)
0.973641 0.228086i \(-0.0732467\pi\)
\(174\) 0 0
\(175\) 8.00000 6.00000i 0.604743 0.453557i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) 0 0
\(181\) −18.0000 −1.33793 −0.668965 0.743294i \(-0.733262\pi\)
−0.668965 + 0.743294i \(0.733262\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −20.0000 10.0000i −1.47043 0.735215i
\(186\) 0 0
\(187\) 16.0000i 1.17004i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 24.0000 1.73658 0.868290 0.496058i \(-0.165220\pi\)
0.868290 + 0.496058i \(0.165220\pi\)
\(192\) 0 0
\(193\) 26.0000i 1.87152i −0.352636 0.935760i \(-0.614715\pi\)
0.352636 0.935760i \(-0.385285\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 12.0000i 0.854965i 0.904024 + 0.427482i \(0.140599\pi\)
−0.904024 + 0.427482i \(0.859401\pi\)
\(198\) 0 0
\(199\) 16.0000 1.13421 0.567105 0.823646i \(-0.308063\pi\)
0.567105 + 0.823646i \(0.308063\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 12.0000i 0.842235i
\(204\) 0 0
\(205\) 10.0000 20.0000i 0.698430 1.39686i
\(206\) 0 0
\(207\) 18.0000i 1.25109i
\(208\) 0 0
\(209\) 4.00000 0.276686
\(210\) 0 0
\(211\) −20.0000 −1.37686 −0.688428 0.725304i \(-0.741699\pi\)
−0.688428 + 0.725304i \(0.741699\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 4.00000 + 2.00000i 0.272798 + 0.136399i
\(216\) 0 0
\(217\) 8.00000i 0.543075i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −8.00000 −0.538138
\(222\) 0 0
\(223\) 16.0000i 1.07144i −0.844396 0.535720i \(-0.820040\pi\)
0.844396 0.535720i \(-0.179960\pi\)
\(224\) 0 0
\(225\) −9.00000 12.0000i −0.600000 0.800000i
\(226\) 0 0
\(227\) 20.0000i 1.32745i 0.747978 + 0.663723i \(0.231025\pi\)
−0.747978 + 0.663723i \(0.768975\pi\)
\(228\) 0 0
\(229\) 10.0000 0.660819 0.330409 0.943838i \(-0.392813\pi\)
0.330409 + 0.943838i \(0.392813\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 16.0000i 1.04819i 0.851658 + 0.524097i \(0.175597\pi\)
−0.851658 + 0.524097i \(0.824403\pi\)
\(234\) 0 0
\(235\) 12.0000 + 6.00000i 0.782794 + 0.391397i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −16.0000 −1.03495 −0.517477 0.855697i \(-0.673129\pi\)
−0.517477 + 0.855697i \(0.673129\pi\)
\(240\) 0 0
\(241\) −2.00000 −0.128831 −0.0644157 0.997923i \(-0.520518\pi\)
−0.0644157 + 0.997923i \(0.520518\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −3.00000 + 6.00000i −0.191663 + 0.383326i
\(246\) 0 0
\(247\) 2.00000i 0.127257i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −4.00000 −0.252478 −0.126239 0.992000i \(-0.540291\pi\)
−0.126239 + 0.992000i \(0.540291\pi\)
\(252\) 0 0
\(253\) 24.0000i 1.50887i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 6.00000i 0.374270i 0.982334 + 0.187135i \(0.0599201\pi\)
−0.982334 + 0.187135i \(0.940080\pi\)
\(258\) 0 0
\(259\) −20.0000 −1.24274
\(260\) 0 0
\(261\) 18.0000 1.11417
\(262\) 0 0
\(263\) 6.00000i 0.369976i 0.982741 + 0.184988i \(0.0592246\pi\)
−0.982741 + 0.184988i \(0.940775\pi\)
\(264\) 0 0
\(265\) −20.0000 10.0000i −1.22859 0.614295i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 18.0000 1.09748 0.548740 0.835993i \(-0.315108\pi\)
0.548740 + 0.835993i \(0.315108\pi\)
\(270\) 0 0
\(271\) −24.0000 −1.45790 −0.728948 0.684569i \(-0.759990\pi\)
−0.728948 + 0.684569i \(0.759990\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −12.0000 16.0000i −0.723627 0.964836i
\(276\) 0 0
\(277\) 8.00000i 0.480673i −0.970690 0.240337i \(-0.922742\pi\)
0.970690 0.240337i \(-0.0772579\pi\)
\(278\) 0 0
\(279\) 12.0000 0.718421
\(280\) 0 0
\(281\) −26.0000 −1.55103 −0.775515 0.631329i \(-0.782510\pi\)
−0.775515 + 0.631329i \(0.782510\pi\)
\(282\) 0 0
\(283\) 14.0000i 0.832214i −0.909316 0.416107i \(-0.863394\pi\)
0.909316 0.416107i \(-0.136606\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 20.0000i 1.18056i
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 14.0000i 0.817889i −0.912559 0.408944i \(-0.865897\pi\)
0.912559 0.408944i \(-0.134103\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 12.0000 0.693978
\(300\) 0 0
\(301\) 4.00000 0.230556
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −2.00000 + 4.00000i −0.114520 + 0.229039i
\(306\) 0 0
\(307\) 20.0000i 1.14146i −0.821138 0.570730i \(-0.806660\pi\)
0.821138 0.570730i \(-0.193340\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −24.0000 −1.36092 −0.680458 0.732787i \(-0.738219\pi\)
−0.680458 + 0.732787i \(0.738219\pi\)
\(312\) 0 0
\(313\) 24.0000i 1.35656i −0.734803 0.678280i \(-0.762726\pi\)
0.734803 0.678280i \(-0.237274\pi\)
\(314\) 0 0
\(315\) −12.0000 6.00000i −0.676123 0.338062i
\(316\) 0 0
\(317\) 22.0000i 1.23564i −0.786318 0.617822i \(-0.788015\pi\)
0.786318 0.617822i \(-0.211985\pi\)
\(318\) 0 0
\(319\) 24.0000 1.34374
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 4.00000i 0.222566i
\(324\) 0 0
\(325\) −8.00000 + 6.00000i −0.443760 + 0.332820i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 12.0000 0.661581
\(330\) 0 0
\(331\) 4.00000 0.219860 0.109930 0.993939i \(-0.464937\pi\)
0.109930 + 0.993939i \(0.464937\pi\)
\(332\) 0 0
\(333\) 30.0000i 1.64399i
\(334\) 0 0
\(335\) −16.0000 8.00000i −0.874173 0.437087i
\(336\) 0 0
\(337\) 22.0000i 1.19842i −0.800593 0.599208i \(-0.795482\pi\)
0.800593 0.599208i \(-0.204518\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 16.0000 0.866449
\(342\) 0 0
\(343\) 20.0000i 1.07990i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 6.00000i 0.322097i −0.986947 0.161048i \(-0.948512\pi\)
0.986947 0.161048i \(-0.0514875\pi\)
\(348\) 0 0
\(349\) −2.00000 −0.107058 −0.0535288 0.998566i \(-0.517047\pi\)
−0.0535288 + 0.998566i \(0.517047\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 4.00000i 0.212899i 0.994318 + 0.106449i \(0.0339482\pi\)
−0.994318 + 0.106449i \(0.966052\pi\)
\(354\) 0 0
\(355\) 4.00000 8.00000i 0.212298 0.424596i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −8.00000 −0.422224 −0.211112 0.977462i \(-0.567708\pi\)
−0.211112 + 0.977462i \(0.567708\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −8.00000 4.00000i −0.418739 0.209370i
\(366\) 0 0
\(367\) 22.0000i 1.14839i −0.818718 0.574195i \(-0.805315\pi\)
0.818718 0.574195i \(-0.194685\pi\)
\(368\) 0 0
\(369\) −30.0000 −1.56174
\(370\) 0 0
\(371\) −20.0000 −1.03835
\(372\) 0 0
\(373\) 6.00000i 0.310668i −0.987862 0.155334i \(-0.950355\pi\)
0.987862 0.155334i \(-0.0496454\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 12.0000i 0.618031i
\(378\) 0 0
\(379\) 28.0000 1.43826 0.719132 0.694874i \(-0.244540\pi\)
0.719132 + 0.694874i \(0.244540\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 12.0000i 0.613171i −0.951843 0.306586i \(-0.900813\pi\)
0.951843 0.306586i \(-0.0991866\pi\)
\(384\) 0 0
\(385\) −16.0000 8.00000i −0.815436 0.407718i
\(386\) 0 0
\(387\) 6.00000i 0.304997i
\(388\) 0 0
\(389\) 30.0000 1.52106 0.760530 0.649303i \(-0.224939\pi\)
0.760530 + 0.649303i \(0.224939\pi\)
\(390\) 0 0
\(391\) 24.0000 1.21373
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −4.00000 + 8.00000i −0.201262 + 0.402524i
\(396\) 0 0
\(397\) 8.00000i 0.401508i 0.979642 + 0.200754i \(0.0643393\pi\)
−0.979642 + 0.200754i \(0.935661\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 18.0000 0.898877 0.449439 0.893311i \(-0.351624\pi\)
0.449439 + 0.893311i \(0.351624\pi\)
\(402\) 0 0
\(403\) 8.00000i 0.398508i
\(404\) 0 0
\(405\) −9.00000 + 18.0000i −0.447214 + 0.894427i
\(406\) 0 0
\(407\) 40.0000i 1.98273i
\(408\) 0 0
\(409\) 14.0000 0.692255 0.346128 0.938187i \(-0.387496\pi\)
0.346128 + 0.938187i \(0.387496\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −36.0000 18.0000i −1.76717 0.883585i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 36.0000 1.75872 0.879358 0.476162i \(-0.157972\pi\)
0.879358 + 0.476162i \(0.157972\pi\)
\(420\) 0 0
\(421\) −30.0000 −1.46211 −0.731055 0.682318i \(-0.760972\pi\)
−0.731055 + 0.682318i \(0.760972\pi\)
\(422\) 0 0
\(423\) 18.0000i 0.875190i
\(424\) 0 0
\(425\) −16.0000 + 12.0000i −0.776114 + 0.582086i
\(426\) 0 0
\(427\) 4.00000i 0.193574i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) 34.0000i 1.63394i −0.576683 0.816968i \(-0.695653\pi\)
0.576683 0.816968i \(-0.304347\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 6.00000i 0.287019i
\(438\) 0 0
\(439\) 20.0000 0.954548 0.477274 0.878755i \(-0.341625\pi\)
0.477274 + 0.878755i \(0.341625\pi\)
\(440\) 0 0
\(441\) 9.00000 0.428571
\(442\) 0 0
\(443\) 2.00000i 0.0950229i 0.998871 + 0.0475114i \(0.0151291\pi\)
−0.998871 + 0.0475114i \(0.984871\pi\)
\(444\) 0 0
\(445\) −2.00000 + 4.00000i −0.0948091 + 0.189618i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −10.0000 −0.471929 −0.235965 0.971762i \(-0.575825\pi\)
−0.235965 + 0.971762i \(0.575825\pi\)
\(450\) 0 0
\(451\) −40.0000 −1.88353
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −4.00000 + 8.00000i −0.187523 + 0.375046i
\(456\) 0 0
\(457\) 8.00000i 0.374224i 0.982339 + 0.187112i \(0.0599128\pi\)
−0.982339 + 0.187112i \(0.940087\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 14.0000 0.652045 0.326023 0.945362i \(-0.394291\pi\)
0.326023 + 0.945362i \(0.394291\pi\)
\(462\) 0 0
\(463\) 2.00000i 0.0929479i −0.998920 0.0464739i \(-0.985202\pi\)
0.998920 0.0464739i \(-0.0147984\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 38.0000i 1.75843i −0.476425 0.879215i \(-0.658068\pi\)
0.476425 0.879215i \(-0.341932\pi\)
\(468\) 0 0
\(469\) −16.0000 −0.738811
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 8.00000i 0.367840i
\(474\) 0 0
\(475\) −3.00000 4.00000i −0.137649 0.183533i
\(476\) 0 0
\(477\) 30.0000i 1.37361i
\(478\) 0 0
\(479\) −24.0000 −1.09659 −0.548294 0.836286i \(-0.684723\pi\)
−0.548294 + 0.836286i \(0.684723\pi\)
\(480\) 0 0
\(481\) 20.0000 0.911922
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 12.0000 + 6.00000i 0.544892 + 0.272446i
\(486\) 0 0
\(487\) 20.0000i 0.906287i −0.891438 0.453143i \(-0.850303\pi\)
0.891438 0.453143i \(-0.149697\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 20.0000 0.902587 0.451294 0.892375i \(-0.350963\pi\)
0.451294 + 0.892375i \(0.350963\pi\)
\(492\) 0 0
\(493\) 24.0000i 1.08091i
\(494\) 0 0
\(495\) −12.0000 + 24.0000i −0.539360 + 1.07872i
\(496\) 0 0
\(497\) 8.00000i 0.358849i
\(498\) 0 0
\(499\) 4.00000 0.179065 0.0895323 0.995984i \(-0.471463\pi\)
0.0895323 + 0.995984i \(0.471463\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 10.0000i 0.445878i −0.974832 0.222939i \(-0.928435\pi\)
0.974832 0.222939i \(-0.0715651\pi\)
\(504\) 0 0
\(505\) 6.00000 12.0000i 0.266996 0.533993i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 6.00000 0.265945 0.132973 0.991120i \(-0.457548\pi\)
0.132973 + 0.991120i \(0.457548\pi\)
\(510\) 0 0
\(511\) −8.00000 −0.353899
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 32.0000 + 16.0000i 1.41009 + 0.705044i
\(516\) 0 0
\(517\) 24.0000i 1.05552i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 42.0000 1.84005 0.920027 0.391856i \(-0.128167\pi\)
0.920027 + 0.391856i \(0.128167\pi\)
\(522\) 0 0
\(523\) 44.0000i 1.92399i 0.273075 + 0.961993i \(0.411959\pi\)
−0.273075 + 0.961993i \(0.588041\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 16.0000i 0.696971i
\(528\) 0 0
\(529\) −13.0000 −0.565217
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 20.0000i 0.866296i
\(534\) 0 0
\(535\) 8.00000 + 4.00000i 0.345870 + 0.172935i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 12.0000 0.516877
\(540\) 0 0
\(541\) −22.0000 −0.945854 −0.472927 0.881102i \(-0.656803\pi\)
−0.472927 + 0.881102i \(0.656803\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 6.00000 12.0000i 0.257012 0.514024i
\(546\) 0 0
\(547\) 28.0000i 1.19719i 0.801050 + 0.598597i \(0.204275\pi\)
−0.801050 + 0.598597i \(0.795725\pi\)
\(548\) 0 0
\(549\) 6.00000 0.256074
\(550\) 0 0
\(551\) 6.00000 0.255609
\(552\) 0 0
\(553\) 8.00000i 0.340195i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 16.0000i 0.677942i 0.940797 + 0.338971i \(0.110079\pi\)
−0.940797 + 0.338971i \(0.889921\pi\)
\(558\) 0 0
\(559\) −4.00000 −0.169182
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 12.0000i 0.505740i −0.967500 0.252870i \(-0.918626\pi\)
0.967500 0.252870i \(-0.0813744\pi\)
\(564\) 0 0
\(565\) −12.0000 6.00000i −0.504844 0.252422i
\(566\) 0 0
\(567\) 18.0000i 0.755929i
\(568\) 0 0
\(569\) −42.0000 −1.76073 −0.880366 0.474295i \(-0.842703\pi\)
−0.880366 + 0.474295i \(0.842703\pi\)
\(570\) 0 0
\(571\) −4.00000 −0.167395 −0.0836974 0.996491i \(-0.526673\pi\)
−0.0836974 + 0.996491i \(0.526673\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 24.0000 18.0000i 1.00087 0.750652i
\(576\) 0 0
\(577\) 24.0000i 0.999133i −0.866276 0.499567i \(-0.833493\pi\)
0.866276 0.499567i \(-0.166507\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −36.0000 −1.49353
\(582\) 0 0
\(583\) 40.0000i 1.65663i
\(584\) 0 0
\(585\) 12.0000 + 6.00000i 0.496139 + 0.248069i
\(586\) 0 0
\(587\) 18.0000i 0.742940i 0.928445 + 0.371470i \(0.121146\pi\)
−0.928445 + 0.371470i \(0.878854\pi\)
\(588\) 0 0
\(589\) 4.00000 0.164817
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 8.00000i 0.328521i −0.986417 0.164260i \(-0.947476\pi\)
0.986417 0.164260i \(-0.0525237\pi\)
\(594\) 0 0
\(595\) −8.00000 + 16.0000i −0.327968 + 0.655936i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 12.0000 0.490307 0.245153 0.969484i \(-0.421162\pi\)
0.245153 + 0.969484i \(0.421162\pi\)
\(600\) 0 0
\(601\) 14.0000 0.571072 0.285536 0.958368i \(-0.407828\pi\)
0.285536 + 0.958368i \(0.407828\pi\)
\(602\) 0 0
\(603\) 24.0000i 0.977356i
\(604\) 0 0
\(605\) −5.00000 + 10.0000i −0.203279 + 0.406558i
\(606\) 0 0
\(607\) 44.0000i 1.78590i −0.450151 0.892952i \(-0.648630\pi\)
0.450151 0.892952i \(-0.351370\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −12.0000 −0.485468
\(612\) 0 0
\(613\) 24.0000i 0.969351i −0.874694 0.484675i \(-0.838938\pi\)
0.874694 0.484675i \(-0.161062\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 12.0000i 0.483102i −0.970388 0.241551i \(-0.922344\pi\)
0.970388 0.241551i \(-0.0776561\pi\)
\(618\) 0 0
\(619\) −20.0000 −0.803868 −0.401934 0.915669i \(-0.631662\pi\)
−0.401934 + 0.915669i \(0.631662\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 4.00000i 0.160257i
\(624\) 0 0
\(625\) −7.00000 + 24.0000i −0.280000 + 0.960000i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 40.0000 1.59490
\(630\) 0 0
\(631\) 8.00000 0.318475 0.159237 0.987240i \(-0.449096\pi\)
0.159237 + 0.987240i \(0.449096\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 6.00000i 0.237729i
\(638\) 0 0
\(639\) −12.0000 −0.474713
\(640\) 0 0
\(641\) 6.00000 0.236986 0.118493 0.992955i \(-0.462194\pi\)
0.118493 + 0.992955i \(0.462194\pi\)
\(642\) 0 0
\(643\) 38.0000i 1.49857i −0.662246 0.749287i \(-0.730396\pi\)
0.662246 0.749287i \(-0.269604\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 30.0000i 1.17942i 0.807614 + 0.589711i \(0.200758\pi\)
−0.807614 + 0.589711i \(0.799242\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 16.0000i 0.626128i 0.949732 + 0.313064i \(0.101356\pi\)
−0.949732 + 0.313064i \(0.898644\pi\)
\(654\) 0 0
\(655\) −12.0000 + 24.0000i −0.468879 + 0.937758i
\(656\) 0 0
\(657\) 12.0000i 0.468165i
\(658\) 0 0
\(659\) −16.0000 −0.623272 −0.311636 0.950202i \(-0.600877\pi\)
−0.311636 + 0.950202i \(0.600877\pi\)
\(660\) 0 0
\(661\) −30.0000 −1.16686 −0.583432 0.812162i \(-0.698291\pi\)
−0.583432 + 0.812162i \(0.698291\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −4.00000 2.00000i −0.155113 0.0775567i
\(666\) 0 0
\(667\) 36.0000i 1.39393i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 8.00000 0.308837
\(672\) 0 0
\(673\) 34.0000i 1.31060i 0.755367 + 0.655302i \(0.227459\pi\)
−0.755367 + 0.655302i \(0.772541\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 18.0000i 0.691796i −0.938272 0.345898i \(-0.887574\pi\)
0.938272 0.345898i \(-0.112426\pi\)
\(678\) 0 0
\(679\) 12.0000 0.460518
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 12.0000i 0.459167i −0.973289 0.229584i \(-0.926264\pi\)
0.973289 0.229584i \(-0.0737364\pi\)
\(684\) 0 0
\(685\) 24.0000 + 12.0000i 0.916993 + 0.458496i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 20.0000 0.761939
\(690\) 0 0
\(691\) 12.0000 0.456502 0.228251 0.973602i \(-0.426699\pi\)
0.228251 + 0.973602i \(0.426699\pi\)
\(692\) 0 0
\(693\) 24.0000i 0.911685i
\(694\) 0 0
\(695\) 4.00000 8.00000i 0.151729 0.303457i
\(696\) 0 0
\(697\) 40.0000i 1.51511i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −30.0000 −1.13308 −0.566542 0.824033i \(-0.691719\pi\)
−0.566542 + 0.824033i \(0.691719\pi\)
\(702\) 0 0
\(703\) 10.0000i 0.377157i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 12.0000i 0.451306i
\(708\) 0 0
\(709\) 38.0000 1.42712 0.713560 0.700594i \(-0.247082\pi\)
0.713560 + 0.700594i \(0.247082\pi\)
\(710\) 0 0
\(711\) 12.0000 0.450035
\(712\) 0 0
\(713\) 24.0000i 0.898807i
\(714\) 0 0
\(715\) 16.0000 + 8.00000i 0.598366 + 0.299183i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) 32.0000 1.19174
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −18.0000 24.0000i −0.668503 0.891338i
\(726\) 0 0
\(727\) 2.00000i 0.0741759i 0.999312 + 0.0370879i \(0.0118082\pi\)
−0.999312 + 0.0370879i \(0.988192\pi\)
\(728\) 0 0
\(729\) 27.0000 1.00000
\(730\) 0 0
\(731\) −8.00000 −0.295891
\(732\) 0 0
\(733\) 12.0000i 0.443230i −0.975134 0.221615i \(-0.928867\pi\)
0.975134 0.221615i \(-0.0711328\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 32.0000i 1.17874i
\(738\) 0 0
\(739\) 4.00000 0.147142 0.0735712 0.997290i \(-0.476560\pi\)
0.0735712 + 0.997290i \(0.476560\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 4.00000i 0.146746i 0.997305 + 0.0733729i \(0.0233763\pi\)
−0.997305 + 0.0733729i \(0.976624\pi\)
\(744\) 0 0
\(745\) −10.0000 + 20.0000i −0.366372 + 0.732743i
\(746\) 0 0
\(747\) 54.0000i 1.97576i
\(748\) 0 0
\(749\) 8.00000 0.292314
\(750\) 0 0
\(751\) 40.0000 1.45962 0.729810 0.683650i \(-0.239608\pi\)
0.729810 + 0.683650i \(0.239608\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 24.0000 48.0000i 0.873449 1.74690i
\(756\) 0 0
\(757\) 4.00000i 0.145382i 0.997354 + 0.0726912i \(0.0231588\pi\)
−0.997354 + 0.0726912i \(0.976841\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 6.00000 0.217500 0.108750 0.994069i \(-0.465315\pi\)
0.108750 + 0.994069i \(0.465315\pi\)
\(762\) 0 0
\(763\) 12.0000i 0.434429i
\(764\) 0 0
\(765\) 24.0000 + 12.0000i 0.867722 + 0.433861i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −26.0000 −0.937584 −0.468792 0.883309i \(-0.655311\pi\)
−0.468792 + 0.883309i \(0.655311\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 46.0000i 1.65451i 0.561830 + 0.827253i \(0.310097\pi\)
−0.561830 + 0.827253i \(0.689903\pi\)
\(774\) 0 0
\(775\) −12.0000 16.0000i −0.431053 0.574737i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −10.0000 −0.358287
\(780\) 0 0
\(781\) −16.0000 −0.572525
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −16.0000 8.00000i −0.571064 0.285532i
\(786\) 0 0
\(787\) 44.0000i 1.56843i −0.620489 0.784215i \(-0.713066\pi\)
0.620489 0.784215i \(-0.286934\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −12.0000 −0.426671
\(792\) 0 0
\(793\) 4.00000i 0.142044i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 6.00000i 0.212531i 0.994338 + 0.106265i \(0.0338893\pi\)
−0.994338 + 0.106265i \(0.966111\pi\)
\(798\) 0 0
\(799\) −24.0000 −0.849059
\(800\) 0 0
\(801\) 6.00000 0.212000
\(802\) 0 0
\(803\) 16.0000i 0.564628i
\(804\) 0