Properties

Label 3300.2.c.b.1849.2
Level $3300$
Weight $2$
Character 3300.1849
Analytic conductor $26.351$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 3300 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3300.c (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(26.3506326670\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 660)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1849.2
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 3300.1849
Dual form 3300.2.c.b.1849.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{3} +4.00000i q^{7} -1.00000 q^{9} +O(q^{10})\) \(q+1.00000i q^{3} +4.00000i q^{7} -1.00000 q^{9} -1.00000 q^{11} -4.00000i q^{13} +6.00000i q^{17} -2.00000 q^{19} -4.00000 q^{21} -1.00000i q^{27} -4.00000 q^{31} -1.00000i q^{33} +10.0000i q^{37} +4.00000 q^{39} -4.00000i q^{43} -12.0000i q^{47} -9.00000 q^{49} -6.00000 q^{51} +6.00000i q^{53} -2.00000i q^{57} -12.0000 q^{59} -10.0000 q^{61} -4.00000i q^{63} +4.00000i q^{67} +8.00000i q^{73} -4.00000i q^{77} +10.0000 q^{79} +1.00000 q^{81} -6.00000i q^{83} +6.00000 q^{89} +16.0000 q^{91} -4.00000i q^{93} +10.0000i q^{97} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{9} - 2 q^{11} - 4 q^{19} - 8 q^{21} - 8 q^{31} + 8 q^{39} - 18 q^{49} - 12 q^{51} - 24 q^{59} - 20 q^{61} + 20 q^{79} + 2 q^{81} + 12 q^{89} + 32 q^{91} + 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3300\mathbb{Z}\right)^\times\).

\(n\) \(1201\) \(1651\) \(2201\) \(2377\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(-1\)

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
\(3\) 1.00000i 0.577350i
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 4.00000i 1.51186i 0.654654 + 0.755929i \(0.272814\pi\)
−0.654654 + 0.755929i \(0.727186\pi\)
\(8\) 0 0
\(9\) −1.00000 −0.333333
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) − 4.00000i − 1.10940i −0.832050 0.554700i \(-0.812833\pi\)
0.832050 0.554700i \(-0.187167\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 6.00000i 1.45521i 0.685994 + 0.727607i \(0.259367\pi\)
−0.685994 + 0.727607i \(0.740633\pi\)
\(18\) 0 0
\(19\) −2.00000 −0.458831 −0.229416 0.973329i \(-0.573682\pi\)
−0.229416 + 0.973329i \(0.573682\pi\)
\(20\) 0 0
\(21\) −4.00000 −0.872872
\(22\) 0 0
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) − 1.00000i − 0.192450i
\(28\) 0 0
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 0 0
\(33\) − 1.00000i − 0.174078i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 10.0000i 1.64399i 0.569495 + 0.821995i \(0.307139\pi\)
−0.569495 + 0.821995i \(0.692861\pi\)
\(38\) 0 0
\(39\) 4.00000 0.640513
\(40\) 0 0
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) − 4.00000i − 0.609994i −0.952353 0.304997i \(-0.901344\pi\)
0.952353 0.304997i \(-0.0986555\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) − 12.0000i − 1.75038i −0.483779 0.875190i \(-0.660736\pi\)
0.483779 0.875190i \(-0.339264\pi\)
\(48\) 0 0
\(49\) −9.00000 −1.28571
\(50\) 0 0
\(51\) −6.00000 −0.840168
\(52\) 0 0
\(53\) 6.00000i 0.824163i 0.911147 + 0.412082i \(0.135198\pi\)
−0.911147 + 0.412082i \(0.864802\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) − 2.00000i − 0.264906i
\(58\) 0 0
\(59\) −12.0000 −1.56227 −0.781133 0.624364i \(-0.785358\pi\)
−0.781133 + 0.624364i \(0.785358\pi\)
\(60\) 0 0
\(61\) −10.0000 −1.28037 −0.640184 0.768221i \(-0.721142\pi\)
−0.640184 + 0.768221i \(0.721142\pi\)
\(62\) 0 0
\(63\) − 4.00000i − 0.503953i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 4.00000i 0.488678i 0.969690 + 0.244339i \(0.0785709\pi\)
−0.969690 + 0.244339i \(0.921429\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 8.00000i 0.936329i 0.883641 + 0.468165i \(0.155085\pi\)
−0.883641 + 0.468165i \(0.844915\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) − 4.00000i − 0.455842i
\(78\) 0 0
\(79\) 10.0000 1.12509 0.562544 0.826767i \(-0.309823\pi\)
0.562544 + 0.826767i \(0.309823\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) − 6.00000i − 0.658586i −0.944228 0.329293i \(-0.893190\pi\)
0.944228 0.329293i \(-0.106810\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) 0 0
\(91\) 16.0000 1.67726
\(92\) 0 0
\(93\) − 4.00000i − 0.414781i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 10.0000i 1.01535i 0.861550 + 0.507673i \(0.169494\pi\)
−0.861550 + 0.507673i \(0.830506\pi\)
\(98\) 0 0
\(99\) 1.00000 0.100504
\(100\) 0 0
\(101\) −12.0000 −1.19404 −0.597022 0.802225i \(-0.703650\pi\)
−0.597022 + 0.802225i \(0.703650\pi\)
\(102\) 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
\(107\) − 18.0000i − 1.74013i −0.492941 0.870063i \(-0.664078\pi\)
0.492941 0.870063i \(-0.335922\pi\)
\(108\) 0 0
\(109\) −14.0000 −1.34096 −0.670478 0.741929i \(-0.733911\pi\)
−0.670478 + 0.741929i \(0.733911\pi\)
\(110\) 0 0
\(111\) −10.0000 −0.949158
\(112\) 0 0
\(113\) − 6.00000i − 0.564433i −0.959351 0.282216i \(-0.908930\pi\)
0.959351 0.282216i \(-0.0910696\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 4.00000i 0.369800i
\(118\) 0 0
\(119\) −24.0000 −2.20008
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) − 8.00000i − 0.709885i −0.934888 0.354943i \(-0.884500\pi\)
0.934888 0.354943i \(-0.115500\pi\)
\(128\) 0 0
\(129\) 4.00000 0.352180
\(130\) 0 0
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) − 8.00000i − 0.693688i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) − 6.00000i − 0.512615i −0.966595 0.256307i \(-0.917494\pi\)
0.966595 0.256307i \(-0.0825059\pi\)
\(138\) 0 0
\(139\) −14.0000 −1.18746 −0.593732 0.804663i \(-0.702346\pi\)
−0.593732 + 0.804663i \(0.702346\pi\)
\(140\) 0 0
\(141\) 12.0000 1.01058
\(142\) 0 0
\(143\) 4.00000i 0.334497i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) − 9.00000i − 0.742307i
\(148\) 0 0
\(149\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(150\) 0 0
\(151\) 14.0000 1.13930 0.569652 0.821886i \(-0.307078\pi\)
0.569652 + 0.821886i \(0.307078\pi\)
\(152\) 0 0
\(153\) − 6.00000i − 0.485071i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 22.0000i 1.75579i 0.478852 + 0.877896i \(0.341053\pi\)
−0.478852 + 0.877896i \(0.658947\pi\)
\(158\) 0 0
\(159\) −6.00000 −0.475831
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 20.0000i 1.56652i 0.621694 + 0.783260i \(0.286445\pi\)
−0.621694 + 0.783260i \(0.713555\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) − 18.0000i − 1.39288i −0.717614 0.696441i \(-0.754766\pi\)
0.717614 0.696441i \(-0.245234\pi\)
\(168\) 0 0
\(169\) −3.00000 −0.230769
\(170\) 0 0
\(171\) 2.00000 0.152944
\(172\) 0 0
\(173\) − 18.0000i − 1.36851i −0.729241 0.684257i \(-0.760127\pi\)
0.729241 0.684257i \(-0.239873\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) − 12.0000i − 0.901975i
\(178\) 0 0
\(179\) −12.0000 −0.896922 −0.448461 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 0 0
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 0 0
\(183\) − 10.0000i − 0.739221i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) − 6.00000i − 0.438763i
\(188\) 0 0
\(189\) 4.00000 0.290957
\(190\) 0 0
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 0 0
\(193\) − 4.00000i − 0.287926i −0.989583 0.143963i \(-0.954015\pi\)
0.989583 0.143963i \(-0.0459847\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 18.0000i 1.28245i 0.767354 + 0.641223i \(0.221573\pi\)
−0.767354 + 0.641223i \(0.778427\pi\)
\(198\) 0 0
\(199\) 16.0000 1.13421 0.567105 0.823646i \(-0.308063\pi\)
0.567105 + 0.823646i \(0.308063\pi\)
\(200\) 0 0
\(201\) −4.00000 −0.282138
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 2.00000 0.138343
\(210\) 0 0
\(211\) −22.0000 −1.51454 −0.757271 0.653101i \(-0.773468\pi\)
−0.757271 + 0.653101i \(0.773468\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) − 16.0000i − 1.08615i
\(218\) 0 0
\(219\) −8.00000 −0.540590
\(220\) 0 0
\(221\) 24.0000 1.61441
\(222\) 0 0
\(223\) 8.00000i 0.535720i 0.963458 + 0.267860i \(0.0863164\pi\)
−0.963458 + 0.267860i \(0.913684\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 18.0000i 1.19470i 0.801980 + 0.597351i \(0.203780\pi\)
−0.801980 + 0.597351i \(0.796220\pi\)
\(228\) 0 0
\(229\) −26.0000 −1.71813 −0.859064 0.511868i \(-0.828954\pi\)
−0.859064 + 0.511868i \(0.828954\pi\)
\(230\) 0 0
\(231\) 4.00000 0.263181
\(232\) 0 0
\(233\) − 6.00000i − 0.393073i −0.980497 0.196537i \(-0.937031\pi\)
0.980497 0.196537i \(-0.0629694\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 10.0000i 0.649570i
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) −22.0000 −1.41714 −0.708572 0.705638i \(-0.750660\pi\)
−0.708572 + 0.705638i \(0.750660\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 8.00000i 0.509028i
\(248\) 0 0
\(249\) 6.00000 0.380235
\(250\) 0 0
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 18.0000i 1.12281i 0.827541 + 0.561405i \(0.189739\pi\)
−0.827541 + 0.561405i \(0.810261\pi\)
\(258\) 0 0
\(259\) −40.0000 −2.48548
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) − 18.0000i − 1.10993i −0.831875 0.554964i \(-0.812732\pi\)
0.831875 0.554964i \(-0.187268\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 6.00000i 0.367194i
\(268\) 0 0
\(269\) −6.00000 −0.365826 −0.182913 0.983129i \(-0.558553\pi\)
−0.182913 + 0.983129i \(0.558553\pi\)
\(270\) 0 0
\(271\) 2.00000 0.121491 0.0607457 0.998153i \(-0.480652\pi\)
0.0607457 + 0.998153i \(0.480652\pi\)
\(272\) 0 0
\(273\) 16.0000i 0.968364i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 28.0000i 1.68236i 0.540758 + 0.841178i \(0.318138\pi\)
−0.540758 + 0.841178i \(0.681862\pi\)
\(278\) 0 0
\(279\) 4.00000 0.239474
\(280\) 0 0
\(281\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(282\) 0 0
\(283\) − 4.00000i − 0.237775i −0.992908 0.118888i \(-0.962067\pi\)
0.992908 0.118888i \(-0.0379328\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −19.0000 −1.11765
\(290\) 0 0
\(291\) −10.0000 −0.586210
\(292\) 0 0
\(293\) 30.0000i 1.75262i 0.481749 + 0.876309i \(0.340002\pi\)
−0.481749 + 0.876309i \(0.659998\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 1.00000i 0.0580259i
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 16.0000 0.922225
\(302\) 0 0
\(303\) − 12.0000i − 0.689382i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 16.0000i 0.913168i 0.889680 + 0.456584i \(0.150927\pi\)
−0.889680 + 0.456584i \(0.849073\pi\)
\(308\) 0 0
\(309\) 16.0000 0.910208
\(310\) 0 0
\(311\) −24.0000 −1.36092 −0.680458 0.732787i \(-0.738219\pi\)
−0.680458 + 0.732787i \(0.738219\pi\)
\(312\) 0 0
\(313\) − 22.0000i − 1.24351i −0.783210 0.621757i \(-0.786419\pi\)
0.783210 0.621757i \(-0.213581\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) − 6.00000i − 0.336994i −0.985702 0.168497i \(-0.946109\pi\)
0.985702 0.168497i \(-0.0538913\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 18.0000 1.00466
\(322\) 0 0
\(323\) − 12.0000i − 0.667698i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) − 14.0000i − 0.774202i
\(328\) 0 0
\(329\) 48.0000 2.64633
\(330\) 0 0
\(331\) −28.0000 −1.53902 −0.769510 0.638635i \(-0.779499\pi\)
−0.769510 + 0.638635i \(0.779499\pi\)
\(332\) 0 0
\(333\) − 10.0000i − 0.547997i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) − 8.00000i − 0.435788i −0.975972 0.217894i \(-0.930081\pi\)
0.975972 0.217894i \(-0.0699187\pi\)
\(338\) 0 0
\(339\) 6.00000 0.325875
\(340\) 0 0
\(341\) 4.00000 0.216612
\(342\) 0 0
\(343\) − 8.00000i − 0.431959i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 6.00000i 0.322097i 0.986947 + 0.161048i \(0.0514875\pi\)
−0.986947 + 0.161048i \(0.948512\pi\)
\(348\) 0 0
\(349\) −14.0000 −0.749403 −0.374701 0.927146i \(-0.622255\pi\)
−0.374701 + 0.927146i \(0.622255\pi\)
\(350\) 0 0
\(351\) −4.00000 −0.213504
\(352\) 0 0
\(353\) − 30.0000i − 1.59674i −0.602168 0.798369i \(-0.705696\pi\)
0.602168 0.798369i \(-0.294304\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) − 24.0000i − 1.27021i
\(358\) 0 0
\(359\) 36.0000 1.90001 0.950004 0.312239i \(-0.101079\pi\)
0.950004 + 0.312239i \(0.101079\pi\)
\(360\) 0 0
\(361\) −15.0000 −0.789474
\(362\) 0 0
\(363\) 1.00000i 0.0524864i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 16.0000i 0.835193i 0.908633 + 0.417597i \(0.137127\pi\)
−0.908633 + 0.417597i \(0.862873\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −24.0000 −1.24602
\(372\) 0 0
\(373\) − 4.00000i − 0.207112i −0.994624 0.103556i \(-0.966978\pi\)
0.994624 0.103556i \(-0.0330221\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −8.00000 −0.410932 −0.205466 0.978664i \(-0.565871\pi\)
−0.205466 + 0.978664i \(0.565871\pi\)
\(380\) 0 0
\(381\) 8.00000 0.409852
\(382\) 0 0
\(383\) − 12.0000i − 0.613171i −0.951843 0.306586i \(-0.900813\pi\)
0.951843 0.306586i \(-0.0991866\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 4.00000i 0.203331i
\(388\) 0 0
\(389\) −18.0000 −0.912636 −0.456318 0.889817i \(-0.650832\pi\)
−0.456318 + 0.889817i \(0.650832\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) − 26.0000i − 1.30490i −0.757831 0.652451i \(-0.773741\pi\)
0.757831 0.652451i \(-0.226259\pi\)
\(398\) 0 0
\(399\) 8.00000 0.400501
\(400\) 0 0
\(401\) 30.0000 1.49813 0.749064 0.662497i \(-0.230503\pi\)
0.749064 + 0.662497i \(0.230503\pi\)
\(402\) 0 0
\(403\) 16.0000i 0.797017i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) − 10.0000i − 0.495682i
\(408\) 0 0
\(409\) 10.0000 0.494468 0.247234 0.968956i \(-0.420478\pi\)
0.247234 + 0.968956i \(0.420478\pi\)
\(410\) 0 0
\(411\) 6.00000 0.295958
\(412\) 0 0
\(413\) − 48.0000i − 2.36193i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) − 14.0000i − 0.685583i
\(418\) 0 0
\(419\) 36.0000 1.75872 0.879358 0.476162i \(-0.157972\pi\)
0.879358 + 0.476162i \(0.157972\pi\)
\(420\) 0 0
\(421\) 26.0000 1.26716 0.633581 0.773676i \(-0.281584\pi\)
0.633581 + 0.773676i \(0.281584\pi\)
\(422\) 0 0
\(423\) 12.0000i 0.583460i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) − 40.0000i − 1.93574i
\(428\) 0 0
\(429\) −4.00000 −0.193122
\(430\) 0 0
\(431\) −36.0000 −1.73406 −0.867029 0.498257i \(-0.833974\pi\)
−0.867029 + 0.498257i \(0.833974\pi\)
\(432\) 0 0
\(433\) 38.0000i 1.82616i 0.407777 + 0.913082i \(0.366304\pi\)
−0.407777 + 0.913082i \(0.633696\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 10.0000 0.477274 0.238637 0.971109i \(-0.423299\pi\)
0.238637 + 0.971109i \(0.423299\pi\)
\(440\) 0 0
\(441\) 9.00000 0.428571
\(442\) 0 0
\(443\) 24.0000i 1.14027i 0.821549 + 0.570137i \(0.193110\pi\)
−0.821549 + 0.570137i \(0.806890\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 30.0000 1.41579 0.707894 0.706319i \(-0.249646\pi\)
0.707894 + 0.706319i \(0.249646\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 14.0000i 0.657777i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 28.0000i 1.30978i 0.755722 + 0.654892i \(0.227286\pi\)
−0.755722 + 0.654892i \(0.772714\pi\)
\(458\) 0 0
\(459\) 6.00000 0.280056
\(460\) 0 0
\(461\) −24.0000 −1.11779 −0.558896 0.829238i \(-0.688775\pi\)
−0.558896 + 0.829238i \(0.688775\pi\)
\(462\) 0 0
\(463\) 32.0000i 1.48717i 0.668644 + 0.743583i \(0.266875\pi\)
−0.668644 + 0.743583i \(0.733125\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) − 12.0000i − 0.555294i −0.960683 0.277647i \(-0.910445\pi\)
0.960683 0.277647i \(-0.0895545\pi\)
\(468\) 0 0
\(469\) −16.0000 −0.738811
\(470\) 0 0
\(471\) −22.0000 −1.01371
\(472\) 0 0
\(473\) 4.00000i 0.183920i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) − 6.00000i − 0.274721i
\(478\) 0 0
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) 40.0000 1.82384
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 16.0000i 0.725029i 0.931978 + 0.362515i \(0.118082\pi\)
−0.931978 + 0.362515i \(0.881918\pi\)
\(488\) 0 0
\(489\) −20.0000 −0.904431
\(490\) 0 0
\(491\) 24.0000 1.08310 0.541552 0.840667i \(-0.317837\pi\)
0.541552 + 0.840667i \(0.317837\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 4.00000 0.179065 0.0895323 0.995984i \(-0.471463\pi\)
0.0895323 + 0.995984i \(0.471463\pi\)
\(500\) 0 0
\(501\) 18.0000 0.804181
\(502\) 0 0
\(503\) 42.0000i 1.87269i 0.351085 + 0.936344i \(0.385813\pi\)
−0.351085 + 0.936344i \(0.614187\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) − 3.00000i − 0.133235i
\(508\) 0 0
\(509\) 42.0000 1.86162 0.930809 0.365507i \(-0.119104\pi\)
0.930809 + 0.365507i \(0.119104\pi\)
\(510\) 0 0
\(511\) −32.0000 −1.41560
\(512\) 0 0
\(513\) 2.00000i 0.0883022i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 12.0000i 0.527759i
\(518\) 0 0
\(519\) 18.0000 0.790112
\(520\) 0 0
\(521\) 6.00000 0.262865 0.131432 0.991325i \(-0.458042\pi\)
0.131432 + 0.991325i \(0.458042\pi\)
\(522\) 0 0
\(523\) − 16.0000i − 0.699631i −0.936819 0.349816i \(-0.886244\pi\)
0.936819 0.349816i \(-0.113756\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) − 24.0000i − 1.04546i
\(528\) 0 0
\(529\) 23.0000 1.00000
\(530\) 0 0
\(531\) 12.0000 0.520756
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) − 12.0000i − 0.517838i
\(538\) 0 0
\(539\) 9.00000 0.387657
\(540\) 0 0
\(541\) 14.0000 0.601907 0.300954 0.953639i \(-0.402695\pi\)
0.300954 + 0.953639i \(0.402695\pi\)
\(542\) 0 0
\(543\) 2.00000i 0.0858282i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) − 8.00000i − 0.342055i −0.985266 0.171028i \(-0.945291\pi\)
0.985266 0.171028i \(-0.0547087\pi\)
\(548\) 0 0
\(549\) 10.0000 0.426790
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 40.0000i 1.70097i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 6.00000i 0.254228i 0.991888 + 0.127114i \(0.0405714\pi\)
−0.991888 + 0.127114i \(0.959429\pi\)
\(558\) 0 0
\(559\) −16.0000 −0.676728
\(560\) 0 0
\(561\) 6.00000 0.253320
\(562\) 0 0
\(563\) 18.0000i 0.758610i 0.925272 + 0.379305i \(0.123837\pi\)
−0.925272 + 0.379305i \(0.876163\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 4.00000i 0.167984i
\(568\) 0 0
\(569\) −24.0000 −1.00613 −0.503066 0.864248i \(-0.667795\pi\)
−0.503066 + 0.864248i \(0.667795\pi\)
\(570\) 0 0
\(571\) 2.00000 0.0836974 0.0418487 0.999124i \(-0.486675\pi\)
0.0418487 + 0.999124i \(0.486675\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 34.0000i 1.41544i 0.706494 + 0.707719i \(0.250276\pi\)
−0.706494 + 0.707719i \(0.749724\pi\)
\(578\) 0 0
\(579\) 4.00000 0.166234
\(580\) 0 0
\(581\) 24.0000 0.995688
\(582\) 0 0
\(583\) − 6.00000i − 0.248495i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) − 36.0000i − 1.48588i −0.669359 0.742940i \(-0.733431\pi\)
0.669359 0.742940i \(-0.266569\pi\)
\(588\) 0 0
\(589\) 8.00000 0.329634
\(590\) 0 0
\(591\) −18.0000 −0.740421
\(592\) 0 0
\(593\) 6.00000i 0.246390i 0.992382 + 0.123195i \(0.0393141\pi\)
−0.992382 + 0.123195i \(0.960686\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 16.0000i 0.654836i
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) −10.0000 −0.407909 −0.203954 0.978980i \(-0.565379\pi\)
−0.203954 + 0.978980i \(0.565379\pi\)
\(602\) 0 0
\(603\) − 4.00000i − 0.162893i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 40.0000i 1.62355i 0.583970 + 0.811775i \(0.301498\pi\)
−0.583970 + 0.811775i \(0.698502\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −48.0000 −1.94187
\(612\) 0 0
\(613\) 44.0000i 1.77714i 0.458738 + 0.888572i \(0.348302\pi\)
−0.458738 + 0.888572i \(0.651698\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 6.00000i 0.241551i 0.992680 + 0.120775i \(0.0385381\pi\)
−0.992680 + 0.120775i \(0.961462\pi\)
\(618\) 0 0
\(619\) 4.00000 0.160774 0.0803868 0.996764i \(-0.474384\pi\)
0.0803868 + 0.996764i \(0.474384\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 24.0000i 0.961540i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 2.00000i 0.0798723i
\(628\) 0 0
\(629\) −60.0000 −2.39236
\(630\) 0 0
\(631\) 8.00000 0.318475 0.159237 0.987240i \(-0.449096\pi\)
0.159237 + 0.987240i \(0.449096\pi\)
\(632\) 0 0
\(633\) − 22.0000i − 0.874421i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 36.0000i 1.42637i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −30.0000 −1.18493 −0.592464 0.805597i \(-0.701845\pi\)
−0.592464 + 0.805597i \(0.701845\pi\)
\(642\) 0 0
\(643\) − 4.00000i − 0.157745i −0.996885 0.0788723i \(-0.974868\pi\)
0.996885 0.0788723i \(-0.0251319\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 36.0000i 1.41531i 0.706560 + 0.707653i \(0.250246\pi\)
−0.706560 + 0.707653i \(0.749754\pi\)
\(648\) 0 0
\(649\) 12.0000 0.471041
\(650\) 0 0
\(651\) 16.0000 0.627089
\(652\) 0 0
\(653\) 18.0000i 0.704394i 0.935926 + 0.352197i \(0.114565\pi\)
−0.935926 + 0.352197i \(0.885435\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) − 8.00000i − 0.312110i
\(658\) 0 0
\(659\) −36.0000 −1.40236 −0.701180 0.712984i \(-0.747343\pi\)
−0.701180 + 0.712984i \(0.747343\pi\)
\(660\) 0 0
\(661\) 38.0000 1.47803 0.739014 0.673690i \(-0.235292\pi\)
0.739014 + 0.673690i \(0.235292\pi\)
\(662\) 0 0
\(663\) 24.0000i 0.932083i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −8.00000 −0.309298
\(670\) 0 0
\(671\) 10.0000 0.386046
\(672\) 0 0
\(673\) 44.0000i 1.69608i 0.529936 + 0.848038i \(0.322216\pi\)
−0.529936 + 0.848038i \(0.677784\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) − 42.0000i − 1.61419i −0.590421 0.807096i \(-0.701038\pi\)
0.590421 0.807096i \(-0.298962\pi\)
\(678\) 0 0
\(679\) −40.0000 −1.53506
\(680\) 0 0
\(681\) −18.0000 −0.689761
\(682\) 0 0
\(683\) 24.0000i 0.918334i 0.888350 + 0.459167i \(0.151852\pi\)
−0.888350 + 0.459167i \(0.848148\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) − 26.0000i − 0.991962i
\(688\) 0 0
\(689\) 24.0000 0.914327
\(690\) 0 0
\(691\) 32.0000 1.21734 0.608669 0.793424i \(-0.291704\pi\)
0.608669 + 0.793424i \(0.291704\pi\)
\(692\) 0 0
\(693\) 4.00000i 0.151947i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 6.00000 0.226941
\(700\) 0 0
\(701\) 12.0000 0.453234 0.226617 0.973984i \(-0.427233\pi\)
0.226617 + 0.973984i \(0.427233\pi\)
\(702\) 0 0
\(703\) − 20.0000i − 0.754314i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) − 48.0000i − 1.80523i
\(708\) 0 0
\(709\) 10.0000 0.375558 0.187779 0.982211i \(-0.439871\pi\)
0.187779 + 0.982211i \(0.439871\pi\)
\(710\) 0 0
\(711\) −10.0000 −0.375029
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 24.0000 0.895049 0.447524 0.894272i \(-0.352306\pi\)
0.447524 + 0.894272i \(0.352306\pi\)
\(720\) 0 0
\(721\) 64.0000 2.38348
\(722\) 0 0
\(723\) − 22.0000i − 0.818189i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) − 8.00000i − 0.296704i −0.988935 0.148352i \(-0.952603\pi\)
0.988935 0.148352i \(-0.0473968\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 24.0000 0.887672
\(732\) 0 0
\(733\) 32.0000i 1.18195i 0.806691 + 0.590973i \(0.201256\pi\)
−0.806691 + 0.590973i \(0.798744\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) − 4.00000i − 0.147342i
\(738\) 0 0
\(739\) 22.0000 0.809283 0.404642 0.914475i \(-0.367396\pi\)
0.404642 + 0.914475i \(0.367396\pi\)
\(740\) 0 0
\(741\) −8.00000 −0.293887
\(742\) 0 0
\(743\) − 6.00000i − 0.220119i −0.993925 0.110059i \(-0.964896\pi\)
0.993925 0.110059i \(-0.0351041\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 6.00000i 0.219529i
\(748\) 0 0
\(749\) 72.0000 2.63082
\(750\) 0 0
\(751\) 8.00000 0.291924 0.145962 0.989290i \(-0.453372\pi\)
0.145962 + 0.989290i \(0.453372\pi\)
\(752\) 0 0
\(753\) 12.0000i 0.437304i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 22.0000i 0.799604i 0.916602 + 0.399802i \(0.130921\pi\)
−0.916602 + 0.399802i \(0.869079\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −24.0000 −0.869999 −0.435000 0.900431i \(-0.643252\pi\)
−0.435000 + 0.900431i \(0.643252\pi\)
\(762\) 0 0
\(763\) − 56.0000i − 2.02734i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 48.0000i 1.73318i
\(768\) 0 0
\(769\) −14.0000 −0.504853 −0.252426 0.967616i \(-0.581229\pi\)
−0.252426 + 0.967616i \(0.581229\pi\)
\(770\) 0 0
\(771\) −18.0000 −0.648254
\(772\) 0 0
\(773\) − 6.00000i − 0.215805i −0.994161 0.107903i \(-0.965587\pi\)
0.994161 0.107903i \(-0.0344134\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) − 40.0000i − 1.43499i
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) − 20.0000i − 0.712923i −0.934310 0.356462i \(-0.883983\pi\)
0.934310 0.356462i \(-0.116017\pi\)
\(788\) 0 0
\(789\) 18.0000 0.640817
\(790\) 0 0
\(791\) 24.0000 0.853342
\(792\) 0 0
\(793\) 40.0000i 1.42044i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 18.0000i 0.637593i 0.947823 + 0.318796i \(0.103279\pi\)
−0.947823 + 0.318796i \(0.896721\pi\)
\(798\) 0 0
\(799\) 72.0000 2.54718
\(800\) 0 0
\(801\) −6.00000 −0.212000
\(802\) 0 0
\(803\) − 8.00000i − 0.282314i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) − 6.00000i − 0.211210i
\(808\) 0 0
\(809\) −36.0000 −1.26569 −0.632846 0.774277i \(-0.718114\pi\)
−0.632846 + 0.774277i \(0.718114\pi\)
\(810\) 0 0
\(811\) −10.0000 −0.351147 −0.175574 0.984466i \(-0.556178\pi\)
−0.175574 + 0.984466i \(0.556178\pi\)
\(812\) 0 0
\(813\) 2.00000i 0.0701431i
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 8.00000i 0.279885i
\(818\) 0 0
\(819\) −16.0000 −0.559085
\(820\) 0 0
\(821\) 24.0000 0.837606 0.418803 0.908077i \(-0.362450\pi\)
0.418803 + 0.908077i \(0.362450\pi\)
\(822\) 0 0
\(823\) 32.0000i 1.11545i 0.830026 + 0.557725i \(0.188326\pi\)
−0.830026 + 0.557725i \(0.811674\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) − 18.0000i − 0.625921i −0.949766 0.312961i \(-0.898679\pi\)
0.949766 0.312961i \(-0.101321\pi\)
\(828\) 0 0
\(829\) 34.0000 1.18087 0.590434 0.807086i \(-0.298956\pi\)
0.590434 + 0.807086i \(0.298956\pi\)
\(830\) 0 0
\(831\) −28.0000 −0.971309
\(832\) 0 0
\(833\) − 54.0000i − 1.87099i
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 4.00000i 0.138260i
\(838\) 0 0
\(839\) 24.0000 0.828572 0.414286 0.910147i \(-0.364031\pi\)
0.414286 + 0.910147i \(0.364031\pi\)
\(840\) 0 0
\(841\) −29.0000 −1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 4.00000i 0.137442i
\(848\) 0 0
\(849\) 4.00000 0.137280
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) − 28.0000i − 0.958702i −0.877623 0.479351i \(-0.840872\pi\)
0.877623 0.479351i \(-0.159128\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 6.00000i 0.204956i 0.994735 + 0.102478i \(0.0326771\pi\)
−0.994735 + 0.102478i \(0.967323\pi\)
\(858\) 0 0
\(859\) −20.0000 −0.682391 −0.341196 0.939992i \(-0.610832\pi\)
−0.341196 + 0.939992i \(0.610832\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 36.0000i 1.22545i 0.790295 + 0.612727i \(0.209928\pi\)
−0.790295 + 0.612727i \(0.790072\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) − 19.0000i − 0.645274i
\(868\) 0 0
\(869\) −10.0000 −0.339227
\(870\) 0 0
\(871\) 16.0000 0.542139
\(872\) 0 0
\(873\) − 10.0000i − 0.338449i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 4.00000i 0.135070i 0.997717 + 0.0675352i \(0.0215135\pi\)
−0.997717 + 0.0675352i \(0.978487\pi\)
\(878\) 0 0
\(879\) −30.0000 −1.01187
\(880\) 0 0
\(881\) 30.0000 1.01073 0.505363 0.862907i \(-0.331359\pi\)
0.505363 + 0.862907i \(0.331359\pi\)
\(882\) 0 0
\(883\) 20.0000i 0.673054i 0.941674 + 0.336527i \(0.109252\pi\)
−0.941674 + 0.336527i \(0.890748\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) − 6.00000i − 0.201460i −0.994914 0.100730i \(-0.967882\pi\)
0.994914 0.100730i \(-0.0321179\pi\)
\(888\) 0 0
\(889\) 32.0000 1.07325
\(890\) 0 0
\(891\) −1.00000 −0.0335013
\(892\) 0 0
\(893\) 24.0000i 0.803129i
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) −36.0000 −1.19933
\(902\) 0 0
\(903\) 16.0000i 0.532447i
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 28.0000i 0.929725i 0.885383 + 0.464862i \(0.153896\pi\)
−0.885383 + 0.464862i \(0.846104\pi\)
\(908\) 0 0
\(909\) 12.0000 0.398015
\(910\) 0 0
\(911\) 24.0000 0.795155 0.397578 0.917568i \(-0.369851\pi\)
0.397578 + 0.917568i \(0.369851\pi\)
\(912\) 0 0
\(913\) 6.00000i 0.198571i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −38.0000 −1.25350 −0.626752 0.779219i \(-0.715616\pi\)
−0.626752 + 0.779219i \(0.715616\pi\)
\(920\) 0 0
\(921\) −16.0000 −0.527218
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 16.0000i 0.525509i
\(928\) 0 0
\(929\) −6.00000 −0.196854 −0.0984268 0.995144i \(-0.531381\pi\)
−0.0984268 + 0.995144i \(0.531381\pi\)
\(930\) 0 0
\(931\) 18.0000 0.589926
\(932\) 0 0
\(933\) − 24.0000i − 0.785725i
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) − 8.00000i − 0.261349i −0.991425 0.130674i \(-0.958286\pi\)
0.991425 0.130674i \(-0.0417142\pi\)
\(938\) 0 0
\(939\) 22.0000 0.717943
\(940\) 0 0
\(941\) 12.0000 0.391189 0.195594 0.980685i \(-0.437336\pi\)
0.195594 + 0.980685i \(0.437336\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 48.0000i 1.55979i 0.625910 + 0.779895i \(0.284728\pi\)
−0.625910 + 0.779895i \(0.715272\pi\)
\(948\) 0 0
\(949\) 32.0000 1.03876
\(950\) 0 0
\(951\) 6.00000 0.194563
\(952\) 0 0
\(953\) 30.0000i 0.971795i 0.874016 + 0.485898i \(0.161507\pi\)
−0.874016 + 0.485898i \(0.838493\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 24.0000 0.775000
\(960\) 0 0
\(961\) −15.0000 −0.483871
\(962\) 0 0
\(963\) 18.0000i 0.580042i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) − 8.00000i − 0.257263i −0.991692 0.128631i \(-0.958942\pi\)
0.991692 0.128631i \(-0.0410584\pi\)
\(968\) 0 0
\(969\) 12.0000 0.385496
\(970\) 0 0
\(971\) −36.0000 −1.15529 −0.577647 0.816286i \(-0.696029\pi\)
−0.577647 + 0.816286i \(0.696029\pi\)
\(972\) 0 0
\(973\) − 56.0000i − 1.79528i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) − 30.0000i − 0.959785i −0.877327 0.479893i \(-0.840676\pi\)
0.877327 0.479893i \(-0.159324\pi\)
\(978\) 0 0
\(979\) −6.00000 −0.191761
\(980\) 0 0
\(981\) 14.0000 0.446986
\(982\) 0 0
\(983\) − 36.0000i − 1.14822i −0.818778 0.574111i \(-0.805348\pi\)
0.818778 0.574111i \(-0.194652\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 48.0000i 1.52786i
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 44.0000 1.39771 0.698853 0.715265i \(-0.253694\pi\)
0.698853 + 0.715265i \(0.253694\pi\)
\(992\) 0 0
\(993\) − 28.0000i − 0.888553i
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) − 44.0000i − 1.39349i −0.717317 0.696747i \(-0.754630\pi\)
0.717317 0.696747i \(-0.245370\pi\)
\(998\) 0 0
\(999\) 10.0000 0.316386
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 3300.2.c.b.1849.2 2
3.2 odd 2 9900.2.c.j.5149.2 2
5.2 odd 4 660.2.a.c.1.1 1
5.3 odd 4 3300.2.a.h.1.1 1
5.4 even 2 inner 3300.2.c.b.1849.1 2
15.2 even 4 1980.2.a.c.1.1 1
15.8 even 4 9900.2.a.bc.1.1 1
15.14 odd 2 9900.2.c.j.5149.1 2
20.7 even 4 2640.2.a.f.1.1 1
55.32 even 4 7260.2.a.p.1.1 1
60.47 odd 4 7920.2.a.bl.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
660.2.a.c.1.1 1 5.2 odd 4
1980.2.a.c.1.1 1 15.2 even 4
2640.2.a.f.1.1 1 20.7 even 4
3300.2.a.h.1.1 1 5.3 odd 4
3300.2.c.b.1849.1 2 5.4 even 2 inner
3300.2.c.b.1849.2 2 1.1 even 1 trivial
7260.2.a.p.1.1 1 55.32 even 4
7920.2.a.bl.1.1 1 60.47 odd 4
9900.2.a.bc.1.1 1 15.8 even 4
9900.2.c.j.5149.1 2 15.14 odd 2
9900.2.c.j.5149.2 2 3.2 odd 2